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Determination of muscle, ligament and articular forces at the knee during a simulate skating thrust Halliwell, Albert A. 1977

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DETERMINATION OF MUSCLE, LIGAMENT AND ARTICULAR FORCES AT THE KNEE DURING A SIMULATED SKATING  THRUST  by ALBERT A . HALLIWELL B.Eng.,  Clarkson College  M.Eng.,  McGill  B.P.E.,  University  of  University, of  Technology,  I963  I967  B r i t i s h Columbia,  197^  A THESIS SUBMITTED IN PARTIAL 'FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF PHYSICAL EDUCATION in THE FACULTY OF GRADUATE STUDIES (School  of  P h y s i c a l E d u c a t i o n arid  We a c c e p t t h i s to  the  thesis  required  THE UNIVERSITY  as  Recreation)  conforming  standard  OF BRITISH COLUMBIA  September,  1977  A l b e r t Alexander H a l l i w e l l ,  1977  In p r e s e n t i n g t h i s t h e s i s  in p a r t i a l  an advanced degree at the U n i v e r s i t y the L i b r a r y I further  s h a l l make i t f r e e l y  f u l f i l m e n t o f the requirements of B r i t i s h C o l u m b i a , I agree  a v a i l a b l e for  agree t h a t p e r m i s s i o n f o r e x t e n s i v e  r e f e r e n c e and copying of t h i s  of  It  i s understood that copying or  thesis  Department of P h y s i c a l The U n i v e r s i t y  Education  and  of B r i t i s h Columbia  2075 Wesbrook Place Vancouver, Canada V6T 1W5  Date September 22nd. 1Q77  Recreation  or  publication  t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d without my  w r i t ten pe rm i ss i on .  that  study.  f o r s c h o l a r l y purposes may be g r a n t e d by the Head of my Department by h i s r e p r e s e n t a t i v e s .  for  ABSTRACT A number o f forces  acting  at  the  m o t i o n as r e l a t e d research  has  mation of the  knee  the  the  design  allow  the  f o r normal w a l k i n g . past research  joint  calculation forces  evaluate  for  joint  devices.  the  ligament  at  the  knee  A skilled  ice  h o c k e y p l a y e r was  This  or  esti-  operating  The c u r r e n t  to  the  n o r m a l human l o c o -  of p r o s t h e t i c  sequence o f . t h e m u s c l e ,  acting  determined  m u s c u l a r and l i g a m e n t o u s  upon the  and t e m p o r a l forces  to  have  h i p and knee f o r  been extended to  joint  expanded  investigators  at  study magnitude  and a r t i c u l a r  a simulated  skating  thrust.  ence p l a n e s force the  platform.  force  gonal  while  plate  forces  orthogonal  inertial,  the  lower  ligament derived  The c i n e output  from the of  allow  forces  synchronized  on t h e  determined  of  knee  forces The  were d e t e r m i n e d  from  of  joint  with  orthoThe  acting  of on  muscle, equations  equilibrium.  e q u i l i b r i u m were i n d e t e r m i n a t e  r e d u c e d by m a k i n g a s s u m p t i o n s  the  joint.  thrust.  conditions  refer-  f r o m a knowledge  and r e a c t i o n  skating  i n two  from a l a b o r a t o r y  calculation  imposed  gravitational  l i m b d u r i n g the  thrust  f i l m d a t a was  s y s t e m was  and j o i n t  equations  to  and moments  force  the  making a s k a t i n g  filmed  The  and had t o  from e l e c t r o m y o g r a p h i c  be  records  to a l l o w s o l u t i o n .  Forces were c a l c u l a t e d f o r a s i m p l i f i e d  muscle and ligament system  which i n c l u d e d the hamstrings,  quadriceps and gastrocnemius  muscle groups,  the c o l l a t e r a l  ligaments and the c r u c i a t e ligaments o f the knee j o i n t . a d d i t i o n , the a r t i c u l a r  joint force,  of p r e s s u r e o f the j o i n t f o r c e were  In  j o i n t torque and centre determined.  R e s u l t s o f the i n v e s t i g a t i o n r e v e a l e d that the magnitude o f the muscle, ligament and j o i n t f o r c e s developed  ina  s k a t i n g t h r u s t were c o n s i d e r a b l y g r e a t e r than r e s p e c t i v e f o r c e s e x e r t e d d u r i n g l e v e l walking while the temporal sequence o f the s k a t i n g f o r c e s was comparable to walking upstairs.  The quadriceps muscle group exerted the g r e a t e s t  c o n t r a c t i l e f o r c e while the gastrocnemius groups developed much s m a l l e r f o r c e s . f o r c e s were developed  and hamstrings  The l a r g e s t  ligament  i n the c o l l a t e r a l ligaments and the  p o s t e r i o r c r u c i a t e ligament to m a i n t a i n s t a b i l i t y o f the joint.  The knee j o i n t i s s u b j e c t to the combined e f f e c t s of  a j o i n t f o r c e s i x times body weight superimposed  and a l a r g e j o i n t  torque  upon each other d u r i n g the s k a t i n g t h r u s t and  t h i s f a c t i s considered important when d i s c u s s i n g the cause of m e n i s c i knee i n j u r i e s .  iv  TABLE OF CONTENTS  CHAPTER I. II. III.  Page  INTRODUCTION  1  REVIEW OF LITERATURE  7  METHODS AND PROCEDURES Anatomy o f t h e Knee J o i n t Concepts o f A n a l y s i s Anthropometry T e s t i n g Procedures Analysis  IV.  RESULTS AND DISCUSSION Results Discussion  V.  SUMMARY AND CONCLUSIONS  ,  19 19 27 35 39 ^9 73 73 89 106  REFERENCES  110  APPENDICES  117  V  L I S T OF TABLES TABLE  Page  1.  Anthropometric  Data  37  2.  Anthropometric  Data  7k  3.  Maximum M u s c l e , for  k. 5.  the  Ligament  Simulated  Skating  and. J o i n t Thrust  The Maximum M u s c l e and L i g a m e n t of Various A c t i v i t i e s . . . . ; Maximum J o i n t F o r c e s Various A c t i v i t i e s  Forces  and T o r q u e s  i . . . .  90  Forces 102 of lO^J-  vi  LIST OF "FIGURES FIGURE 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 4.01  Page R i g h t Knee J o i n t - Bone S t r u c t u r e Superior Surface - T i b i a Ligaments o f Knee J o i n t Ligaments o f Knee J o i n t P a t e l l a r Ligament M u s c l e s C o n t r o l l i n g Knee J o i n t T i b i a l R e f e r e n c e Axes T i b i a l Condyles R e f e r e n c e Axes - Femur, T i b i a E r r o r i n Assumed -Centre o f R o t a t i o n o f Femur i n 9 0 ° F l e x i o n P e l v i c Reference Axes S i m p l i f i e d Muscle and Ligament System A c t i n g a t Knee J o i n t Angle o f P a t e l l a r Ligament R e l a t i v e to Angle o f Knee F l e x i o n L o c a t i o n o f R e f e r e n c e Markers E x p e r i m e n t a l Set-Up F o r c e Record o f F o r c e P l a t e E x p r e s s e d as S i x Measured V a r i a b l e s E x p e r i m e n t a l Set-Up Showing T e s t S u b j e c t on F o r c e P l a t f o r m A n a l y s i s o f Data E x t e r n a l F o r c e System a t Knee E x p r e s s e d i n Terms o f T i b i a l R e f e r e n c e Axes o f R i g h t Knee F o r c e s A c t i n g on Lower Limb I n c l u d i n g R e a c t i o n F o r c e s , G r a v i t y F o r c e s and A c c e l e r a t i o n Forces M u s c l e F o r c e i n Quadriceps t o Balance Moment + Mxk " Muscle F o r c e i n Hamstrings t o Balance Moment - Mxk , M u s c l e F o r c e i n Gastrocnemius t o Balance Moment - Mxk F o r c e i n P o s t e r i o r C r u c i a t e and A n t e r i o r C r u c i a t e Ligaments. . . . C o l l a t e r a l Ligament F o r c e s Compressive J o i n t F o r c e , Rz F o r c e P l a t e Output i n Form o f O s c i l l o s c o p e Trace - T r i a l No. 4  '.  20 22 22 24 24 26 28 28 3° 31 32 35 38 41 43 44 47 50 52 53 58 58 62 64 67 69 76  vii 4.02 4.03 4.04 4.05 4.06 4.07 4.08 4.09 4.10  E l e c t r o m y o g r a m - S k a t i n g T h r u s t on I c e I l l u s t r a t e d Sequence o f S k a t i n g T h r u s t Limb L i n e a r A c c e l e r a t i o n s Limb A n g u l a r A c c e l e r a t i o n s R e s o l v e d F o r c e Components a t Knee T r i a l No. 4 . . M u s c l e and L i g a m e n t F o r c e s . f o r T r i a l No. M u s c l e and L i g a m e n t F o r c e s J o i n t F o r c e s A c t i n g a t Knee C e n t r e o f P r e s s u r e on C o n d y l e s o f Knee  77 78 80 81  4  83 85 86 88 99  viii  NOTATIONS Reference Xg,  Axes  Y g , Zg  Grid reference plate,  Xs,  Y s , Zs  point  Reference tibial  Xf,  Yf,  Zf  Xp,  Y p , Zp  femoral  axes o f  tibia, point  axes o f  condyles,  Reference  o r i g i n at  of  force  femur, point  point  o r i g i n at  centre  of  o r i g i n at  centre  of  k.  fc.  axes o f p e l v i s ,  head,  centre  p.  condyles,  Reference femoral  axes,  o r i g i n at  centre  of  fh.  Co-ordinates The reference  co-ordinates axes,  of  a point,  f o r example,  the  p,  relative  grid reference  to  a set  axes,  of  are  e x p r e s s e d as X g p , Y g p , and Z g p . Points a  Ankle  joint  centre.  k  Knee j o i n t  fc  Centre of  femoral  fh  Centre of  f e m o r a l head o f h i p  centre  at  centre  of  superior surface  condyles.  M u s c l e and L i g a m e n t A t t a c h m e n t s h  Insertion  of  hamstrings,  g  Insertion  of  gastrocnemius.  joint.  of  tibia,  ix q  Insertion  1  Lateral  m  Medial  a  Anterior  p  Posterior  ph  Origin of hamstrings.  fg  Origin of  fl  Lateral  fm  Medial  fa  Anterior  fp  Posterior  Force Fxi,  of p a t e l l a r  collateral collateral cruciate cruciate  attachment  to to  tibia.  attachment  to  tibia.  attachment  femoris).  fibula.  attachment  collateral  to  tibia.  to  femur.  !•'.-..  collateral cruciate cruciate  attachment attachment  to  femur.  attachment  to  femur.  attachment  to  femur.  Actions Fyi, Fzi  Components o f  Myi, Mzi  R y , Rz  force  Y,and Z reference  acting  i n directions  axes  axes  Components o f  of  respectively.  Components o f moment a c t i n g reference  Rx,  (quadriceps  gastrocnemius.  X, Mxi,  ligament  i n X , Y and Z  respectively. joint  force  a c t i n g at  the  knee  joint. Pa,  P p , Pm  and PI  Force actions cruciate, lateral  Pq, Pg  Ph and  medial c o l l a t e r a l  ligaments  Force actions strings  i n anterior cruciate,  and l a t e r a l  col-  respectively.  i n quadriceps  and g a s t r o c n e m i u s  respectively.  posterior  femoris,  muscle  ham-  groups  X  Fxm, Fym, Fz.m  Components  o f f o r c e a c t i n g i n muscle groups  i n the Xs, Ys and Zs d i r e c t i o n s r e s p e c t i v e l y . Fxcr, and  Fycr  Components  Fzcr  of f o r c e a c t i n g i n the c r u c i a t e  ligaments i n the Xs, Ys and Zs d i r e c t i o n s respectively.  Fxcol, Fycol  Components  and  ligaments i n the Xs, Ys and Zs d i r e c t i o n s  Fzcol  of f o r c e a c t i n g i n the c o l l a t e r a l  respectively. Symbols  ,  ]  g  A c c e l e r a t i o n of g r a v i t y ,  bw  Body weight o f subject,  wi  Weight o f body segment i .  Ii  Moment o f i n e r t i a o f segment i about a x i s to the l o n g a x i s of the segment and p a s s i n g centre  perpendicular through the  o f mass o f the segment.  t  Thigh segment.  s  Shank  f  Foot segment.  Ri  Radius o f segment or j o i n t i .  Li  Length o f body segment i .  ri  Radius o f g y r a t i o n o f segment i about the a x i s perpen-  segment.  d i c u l a r to the l o n g a x i s o f the segment and p a s s i n g through the centre  of mass of the segment.  LFO  L e f t foot o f f during  skating  thrust.  PO  Push o f f o f r i g h t f o o t i n s k a t i n g  thrust.  ^  xi  ACKNOWLEDGEMENTS  The guidance To  author i s  indebted  and a s s i s t a n c e  to  several  i n completing  t h e s e i n d i v i d u a l s I would l i k e  to  people  this  for  their  investigation.  e x p r e s s my  sincere  appreciation. Dr.  Ted Rhodes,  inspirational study  and m o n e t a r y  and made h i m s e l f  consultation. Dr.  my c o m m i t t e e  To t h e  Merv O l s o n ,  extend  the  available  thanks.  advice  A f u r t h e r thanks Grant Cumberbirch, Terry Schultz collection development The of  In p a r t i c u l a r ,  at  testing  investigator  E c o l o g y at U . B . C .  is  expressed  committee,  Dr. M i l l e r  to  the  I who  their  technical  techniques.  test  p a r t i c i p a t i o n i n the help  subject, study,  to  i n the  data  advice  and  equipment. is the  also  indebted  Institute  i n making a v a i l a b l e  the  to  author g r a t e f u l l y  to  the  of Animal film  assistance Resource  reduction  appreciates  D r . .James M o r r i s o n who p r o v i d e d a c o p y o f h i s thesis.  helpful  t h e U n i v e r s i t y o f W a s h i n g t o n and  and to M r . Hsu f o r h i s  Finally,  research  of  r e g a r d i n g cinematography  for his  M r . Frank Maurer of  ment.  the  f o r many h o u r s  and B r u c e G o l d s m i d f o r  of  towards  o t h e r members o f my t h e s i s  testing  gave i n v a l u a b l e  assistance  D r . Bob H i n d m a r c h and D r . D o r i s M i l l e r ,  a special  supervised  chairman, provided both  equip-  the  doctoral  aid  of  xii The author i s f u r t h e r indebted to E l i z a b e t h Orne f o r the t y p i n g of t h i s  manuscript.  CHAPTER  I  INTRODUCTION  The  s t u d y o f human l o c o m o t i o n o v e r t h e  decades has Dillman  "been a p p r o a c h e d f r o m two  (1970)  and o t h e r s  of  techniques.  D i l l m a n was  a c t i o n of and  lower l i m b d u r i n g the  A second  Paul  joints  i n under-  studied  the  concerned with  r e c o v e r y phase  and a c c e l e r a t i o n of  the  time-  the  of  running  data which  t e m p o r a l sequence  group o f r e s e a r c h e r s  point  (1964)  of  the  of view.  persons  fitted  were more  to  cated  force  hip  of  interested  joints.  ankle,  knee  strike  to  toe  off.  joints  at  These  the  force-time  s u c h as  the  aid of  joint  d u r i n g the  of  artificial sophisti-  accurately record  These  (1968)  b i o m e d i c a l problems  With the  calculated  and h i p  Morrison  developed  devices  measuring devices that  these researchers  from h e e l  forces  study the  with prosthetic  and r e p l a c e m e n t  the  (1950),  lower limbs d u r i n g walking.  limbs  forces,  Bresler  determined the  a n a l y s e s were i n i t i a t e d  at  directions.  e x a m i n i n g human l o c o m o t i o n f r o m a b i o m e c h a n i c a l and "bio-  engineering and  specifically  an i n d e p t h a n a l y s i s  running.  performance  several  lower limbs u t i l i z i n g cinematographic  determined limb v e l o c i t y  allowed  in  the  the  separate  who were i n t e r e s t e d  standing accomplished a t h l e t i c displacement  past  forces  walking  studies indicated  reaction acting cycle that  - 2 the  joint  level  forces  imposed a t  w a l k i n g were  weight.  Morrison  m o t i o n to forces  developed  e q u a l to (1970)  include  the at  knee  of  joint  and t h e  of  at  the  quite  the  of  the  knee  joint  joint,  skating thrust. this  manoeuvre  anatomy o f  affecting hockey.  the  walking,  of  the  Chao  lateral  moment o f  study of  forces  and  the  These  energetic  the is  of  i n judgements of  (I968)  respective therefore  the  push  work o f  to  examine  forces  forces of  c o n c e r n i n g the  Because  is  at  t h e knee  considered  forces  of  are  normal  finding  movement,  acting  the  im-  it  a fact  athletic  and c o u l d a s s i s t  t h e knee  the  skating thrust.  are i m p o r t a n t i n terms joint  extend  developed  a specific  A knowledge  to  skating thrust  compared to  stability  in-  study,  the  and l i g a m e n t  during a simulated  t h e knee  or t h e r a p i s t  twisting  of Morrison  The i n v e s t i g a t i o n  and d e s c r i p t i v e  ligament  In a recent  muscle  and l i g a m e n t  significant  locomotion.  and  for level  s t u d y was d e s i g n e d  the p o w e r f u l nature  that  s t u d y o f human l o c o -  plate.  Chao u t i l i z i n g t h e m e t h o d o l o g y  posed  body-  were r e c o r d e d f o r a s i m u l a t e d  The p r e s e n t  magnitude  f o u r times the  v e r t i c a l reaction force,  action with a force  the  the  normal  a hockey p l a y e r wearing s k a t e s .  reaction forces off  to  climbing.  posterior reaction forces pushing foot  three  and h i p d u r i n g  c a l c u l a t i o n o f muscle  the  measured t h e  knee  extended  c l i n e d w a l k i n g and s t a i r (1973)  the  the  during  functional  the  practitioner  specific  d u r i n g the  forces  game o f  ice  Significance  of  To d a t e , magnitude o f  the  lower limb  movement.  above f o r c e s (Morrison, plane, has  the  extended  forces  Also,  of  t h e m e t h o d o l o g y so  the  force plate  anterior-posterior plane.  athletic  that  skills  it  is  s u c h as  the  single  more g e n e r a l and s k a t i n g w h i c h have  investigation is forces  to  imposed a t  determine  t h e knee  the  joint  hockey p l a y e r .  Terms  The f o l l o w i n g l i s t to  forces  movement.  and l i g a m e n t o u s  of  reaction  The c u r r e n t s t u d y  d u r i n g a s i m u l a t e d s k a t i n g t h r u s t by an i c e  Definition  ath-  Problem  The p u r p o s e o f articular  d e v e l o p e d d u r i n g an e x e r t e d  the methodology o f d e t e r m i n i n g the  more t h a n one p l a n e o f  of  including muscle,liga-  was d e v e l o p e d f o r l o c o m o t i o n i n a  c a n be a p p l i e d t o  Statement  joint forces  from a knowledge  I968)  i.e.,  Study  no d a t a has b e e n p u b l i s h e d r e g a r d i n g t h e  ment and a r t i c u l a r letic  3 -  of d e f i n i t i o n of  allow i n t e r p r e t a t i o n of  the  somewhat  terms i s  essential  technical text  of  the  report. Articular at  the  articular  represent the  forces  the  femur o f  -  the  surfaces  forces the  compressive  and s h e a r f o r c e s  of a j o i n t .  i m p o s e d on t h e  acting  F o r the knee,  condyles  of  the  they tibia  and  joint.  Ligamentous f o r c e s  - the  tensile  forces  a c t i n g i n the  liga-  merits t h a t in  the  support a j o i n t .  collateral  and c r u c i a t e  Time-space  co-ordinates  a point  that  of  knee  F o r the  displacement  shank and t h e  of  l o c a t i o n of  with that  the  or  as  defined  centre  o f mass o f  of  joint  the  -  the  by t h e  the  centres  e q u a l and o p p o s i t e  body o r s u r f a c e  body o r s u r f a c e .  exerted  on t h e  skate  In t h i s  blade  r e c o r d e d by t h e  force platform.  Inertial  -  forces  acceleration principles  of  the  the  study r e p r e s e n t  of  the  centre  mass o f  Inertial  the  planar forces  o f mass t i m e s  x,  y and  foot of  repand  the'.hip,  axes.  exerted  point the  force  of  contact  reaction  plate  on a  forces  surface  by t h e  and  linear  d e t e r m i n e d by N e w t o n i a n The i n e r t i a l the  linear  forces  acceleration  o r shank and t h e  respective  segment.  torques  - the  moment d e t e r m i n e d f r o m t h e  angular a c c e l e r a t i o n  pective  foot  the  developed  product of  the  forces  study  acceleration.  the  o f mass o f  at  by t h e  a body segment as  of  z  a body segment  and a n k l e .  body by a r e s i s t i n g  the  act  lower l i m b these c o - o r d i n a t e s  displacement  Reaction forces  are  - the  these f o r c e s  ligaments.  segment w i t h t i m e  z co-ordinates. resent  For the knee,  moment o f  of  i n e r t i a of  the the  foot  product  and shank and t h e  segment a b o u t t h e  x,  of  resy and  Skating thrust the  weight  -  shift  s k a t i n g has t h r e e to  the  glide  A skating thrust represents to  d r i v e the  5 -  skater  leg  the  components: and t h e  extension  the  glide of  thrust,  on t h a t  the  thrust  leg. leg  forward.  Limitations The knee for  a simulated  plate  contact  teristics  of  joint  forces  skating thrust.  does not the  the  skate  blade  actual  s k a t i n g environment.  forces  represent  forces  as r e c o r d e d i n t h e  resistance  those  at  the  into of  coverings. the  of  s k a t i n g t h r u s t be  the  force  contact  the  of  calculated the  force  the joint  reaction platform  the  required f r i c t i o n a l  surface  the  force  the  skating thrust of  were  To d e v e l o p of  specially  executed  The n a t u r e o f the  ice  platform  prepared rubber  This procedure introduced f u r t h e r  a skating thrust  cular  to  c o r r e s p o n d i n g to  l a b o r a t o r y estimate of  The r e s u l t s  b l a d e to  l a b o r a t o r y by t h e  s k a t e r was r e q u i r e d t o wear blade  study  same f r i c t i o n a l c h a r a c -  Therefore,  forces  technique. force  The s k a t e  exhibit  normal  measurement  c a l c u l a t e d i n the  the  on  skate  error forces  ice.  study  one  actual reaction  the  are l i m i t e d to  the  parti-  s k i l l e d hockey p l a y e r .  experimental  executed  set-up required  from a s t a r t i n g  that  stationary  position. Delimitations  and A s s u m p t i o n s  The f o l l o w i n g  assumptions  were made f o r t h e  purpose  - 6 of  force (i)  analysis  of  the  knee  joint  R o t a t i o n at  the  knee  is  three  major muscle  hamstrings  (ii)  (Morrison,  c o n t r o l l e d by t h e  groups,  the  and g a s t r o c n e m i u s  quadriceps  groups.  each group are c o n s i d e r e d  of  a c t i o n and t h e • d i r e c t i o n  of  in  each group i s  be c o n s t a n t  creasing  force,  The l i n e  of to  assumed  a c t i o n of  to  a muscle  be c o i n c i d e n t  o r i g i n and  to  The  of  assumed  (iii)  forces  1968):  forces  femoris, muscles  have - c o n f l u e n t the  in  resultant with  lines  force in-  group or l i g a m e n t  w i t h the  line  joining  is its  insertion,  The a x i s  of r o t a t i o n of  constant  relative  to  the  the  femur i s  assumed  to  be  co-ordinate  axes o f  the  tibia. (iv)  The e f f e c t s the  knee  of  joint  friction is  p o s t e r i o r movement To a l l o w the  knee  joint  shown i n F i g u r e  analysis the  of  at  the  neglected of the  the  for  was  external  adopted.  the  surface  anterior-  joint.  s i m p l i f i e d muscle  3-12  articular  forces  imposed  and l i g a m e n t  system  on  of  -  7 -  CHAPTER  REVIEW  II  OF LITERATURE  Introduction The  joints  o f the  lower l i m b s p r o v i d e the  means f o r human l o c o m o t i o n i n a l l of  muscular actions  of  c o - o r d i n a t e d l o c o m o t i v e movements  joints. subject to  the  activities.  forces  increases  joints  and t h e  effect  and a c t i v i t i e s  of  these f o r c e s  on t h e  joints  Hughston,  and K l e i n  W h a t l e y and D o d e l i n  (1961)  s u c h as  Bender (1964)  f u n c t i o n o f t h e knee  (1963).  and S m i l l i e  several  (1970)  joint i n various a c t i v i t i e s  t h e most  and was i n i t i a l l y  who examined t h e  changes  The  while  of  loco-  (1969).  Studies  Walking i s  1939)  the  as p o i n t e d o u t by  m o t i o n has b e e n s t u d i e d and d e t a i l e d by M o r r i s o n  ivities  athletics of  o f knee i n j u r i e s h a s b e e n documented by  investigators  Locomotion  structures  The n a t u r e o f  joint  the  necessarily  supporting ligamentous  l o w e r l i m b and s p e c i f i c a l l y t h e knee  prevalence  aid  through the a r t i c u l a t i n g  t h a t must be e q u i l i b r a t e d . the  With the  human body c a n p e r f o r m a m u l t i t u d e  However t h e s e movements the  structural  i n the  leg  common o f human l o c o m o t i v e investigated  external  and t h e  forces  by E l f t m a n exerted,  (193&\  the  f u n c t i o n o f the muscles  act-  energy . in  - 8 walking.  Elftman  determined tions  of  employed an e x p e r i m e n t a l  ground r e a c t i o n  a force  plate  forces  from the  s u p p o r t e d by s t i f f  and F r a n k e l  (1950)  and moments  of walking using a force  force-time  measured the  of  by Cunningham and Brown ( 1 9 5 2 ) . together with cine  the  in  leg  space a l l o w e d  joint  forces  level  walking.  in  the  the  the  kinematics  to  of  the  o f n o r m a l men w h i l e  by r e s e a r c h e r s  vestigators,  ankle,  Murray,  displacement  The d e v e l o p m e n t tool  forces  based  the  knee  study  of  the  limbs i n  W i n t e r (197^)  electromyography  as  Basmajian (I962)  activity  using of  f u n c t i o n o f muscles  muscles  of  the  the  the has  allowed  in-  and m u s c l e (1952)  function of  (1959)  while  iour  of. t h e  q u a d r i c e p s muscle  techniques. leg  (I96I)  Todd  electromyograms.  Linge  (196^-)  the  and muscles  d u r i n g w e i g h t b e a r i n g and n o r m a l  electromyographic  the  role  a research has  analyzed  extremity  the  o f n o r m a l l o c o m o t i o n f r o m TV d a t a .  s u c h as  and W a l s h ( 1 9 5 9 )  posture  evaluate  D r o u g h t and K o r y lower  of  and h i p d u r i n g  Houtz  lower  and  position  to  J o s e p h and N i g h t i n g a l e  the  designed  forces  the  groups i n l o c o m o t i o n .  of  on  s t r a i n g a u g e s and  records of  the  locomotion.  walking patterns studied  at  Bresler  C i n e m a t o g r a p h y h a s p l a y e d an i m p o r t a n t  of  investigated  plate  deflec-  reaction  B r e s l e r and F r a n k e l  transmitted  study  springs.  The r e a c t i o n  film  that  calibrated  orthogonal  measuring p r o p e r t i e s  moments  technique  was  The p h a s i c  studied  examined t h e  by C l o s e  specific  behav-  group d u r i n g w a l k i n g from  A l t h o u g h e l e c t r o m y o g r a p h y has  been  and  - 9 accepted,  as  a means o f m e a s u r i n g m u s c l e  between the tension  as  action potentials studied  of  by L i p p o l d  activity  the  relation  a n e l e c t r o m y o g r a m and m u s c l e  (1952)  and o t h e r s  is  not  well  established.  Biomechanical  Analyses of J o i n t  The o r i g i n a l s t u d i e s  of  joint  hip  joint  as r e l a t e d  for  the  hip.  Direct determination of hip (1965,  the  forces  the  c o n d u c t e d by R y d e l l  to  Forces  1966)  t i e n t s with h i p - j o i n t protheses gauges. 4.33  The l a r g e s t  times  the  force  (1962)  and Cunningham and Brown ( 1 9 5 2 )  prosthetic Evenson joint  forces  the  Denham ( 1 9 5 9 )  value  removed.  of hip  joint  M c L e i s h and C h a r n l e y  forces  i n the  one-legged  The most  the  definitive  I966,  1967,  have b o t h  (1970)  1971).  pa-  strain was  level  walking Radcliffe  investigated instrumented  s u c h as W i l l i a m s and . determined limbs  Dynamometers were f o r the  with  used  standing  determined h i p  to posi-  joint  stance. analysis  of r e a c t i o n forces  j o i n t , d u r i n g w a l k i n g has been the  (1964,  of his  body w e i g h t .  on d i s s e c t e d  force  to  was  f e m o r a l head  and Inman ( 1 9 ^ 7 )  d i r e c t l y from t e s t s  tion.  hip  times  Other r e s e a r c h e r s  and l i g a m e n t s  estimate  two  b e l o w knee p r o s t h e s e s u s i n g  devices.  (1968),  muscles  of  force  instrumented with  reached values  biomechanics  joint  during running while  3-3  confined  endo-prostheses  who. f i t t e d  forces  the  of  a c t i n g on t h e  body w e i g h t of  design  were  Paul  recent  work o f  determined the  at  Paul  variation  the  -  w i t h time  of  the  magnitude  w a l k i n g from c i n e  film  ground r e a c t i o n f o r c e s plate. 3.39  to  of  records on t h e  foot  k.k6  t i m e s body w e i g h t . s t u d i e s to  forces  transmitted  of  knee  mum knee  joint  joint  hip  muscle  groups  phasic  r e l a t i o n of  plate,  to  acting  evaluate  the  the  across  d e t e r m i n e d was  joint  to  ligamentous  Recent  the  (1968,  Morrison  from  1970)  analysis  f e m o r a l and t i b i a l  forces  the  of  the  condyles  knee  magnitude of  of  of  3«03-  electro-  joint  including  in the  By a d o p t i n g  j o i n t Morrison expressed terms  from t h e  lateral  the  Morrison  and  during walking.  g r o u p and t h e  p r o v i d e d the  first  collateral  during  Analyses  The a d v e n t  computer t e c h n o l o g y  to  data.  acting  in force  ligament..  data published forces  the  able  experimental  maximum l i g a m e n t  tensile  a joint  and was  was ^ 0 5 l b  Biomechanical of  Maxi-  tensions developed  calculated  1^8 l b i n t h e  structures  value  i n mathematical  force  femoris  Morrison's studies respect  t h e knee  ligamentous  quadriceps  the  these forces  The g r e a t e s t m u s c l e the  ranging  cinematographic  estimate  a s i m p l i f i e d model o f of  forces  force  measured v a r i e d between 2 . 0 6 and ^ . 0  force  myographic r e c o r d s  mechanics  the  during various walking a c t i v i t i e s .  forces  integrated  during  segments and  an e n g i n e e r i n g  between t h e  force  measured w i t h a  joint  t i m e s body w e i g h t w i t h a n a v e r a g e also  joint  of l e g  f o u n d maximum h i p  Paul's  -  the  Paul  extended  the  10  acting  with in  the  activity.  led  to  new methods  of  evaluating (1968)  l o c o m o t i o n d a t a from f i l m .  determined  made a s p e c i f i c sprint to  cine  the  kinematics  kinematic  running.  reduce  11 -  These film  analysis  of  Trump and D a h e r ( 1 9 7 5 )  gait of  calculate  the  used  moments  acting  tion forces  at  the  from g a i t  of  analysis  ented at  the  the  polycentric  the  ankles,  develop  a series  knees,  c a r r y i n g but the tical  used  lower  to  tensile  statically  study  Seireg  data for  approximate forces.  and  knee  have  seven s o l i d  and knee the  been  several  and A r v i k a r  of  developed repres-  articulating  elbows and w r i s t s  to  body movements.  made l i m i t e d  of l i f t i n g the  (1973i  the  models  the  of  o r i g i n and  lines  of  action of  mathematical  and  devel-  actions  postures.  points  The  prac-  1975)  muscular  static  the  design  (1969)  links  body movements  the  reac-  joint.  Chaffin  simulate  predict  floor  forces  for different  Since  indeterminate  analysis  Thornton-  i n e r t i a to  problem of  shoulders,  model t o  extremeties  anatomical  of muscles cular  to  applications.  the  hips,  assumptions  oped a m a t h e m a t i c a l of  of  a c o m p u t e r i z e d model f o r  model was d e s i g n e d  computer  translational  The r e a c t i o n  o f human body d y n a m i c s .  body as  during  and t h e  A number o f m a t h e m a t i c a l m o d e l s for  recovery leg  of  the  h i p and knee  data.  prosthetic  (1970)  anthropometric data i n c l u d i n g  moment d a t a were t h e n a p p l i e d t o an e x t e r n a l  Dillman  lower l i m b segments.  l i m b segment w e i g h t and mass moments the  and Chang  while  the  s t u d i e s made use  d a t a to  angular accelerations  of  Beckett  They  insertion the  mus-  formulation  a l i n e a r p r o g r a m m i n g method b a s e d  is on  a selected,  m i n i m i z i n g c r i t e r i a was u s e d t o  muscle l o a d joint  load  In a subsequent  t h e i r p r e v i o u s work t o  the  body w e i g h t .  their  forces  were  7-1  were and a n k l e  and 5 - 2  joint  Mechanics of  used  Maximum  but joint  walking for hip,  s u c h as Chao and -Kwam ( 1 9 7 3 ) evaluate  during walking while a s i m i l a r method t o  the  Penrod,  estimate  have  applied D a r y and  tendon  comprehensive  and t h e  study of  function of  the  t h e movements  ligaments  force.  Tests  of  fresh  and p r e s e r v e d knee  of  the  controlling  t h e s e movements was made by B r a n t i g a n and V o s h e l l  the  muscle  results  body w e i g h t  to  t h e Knee J o i n t  The most joint  leg  (1969)  the  employed o p t i m i z a t i o n p r i n c i p l e s t o  (197^)  ground to  considered q u a s i - s t a t i c times  and  respectively.  Other r e s e a r c h e r s  moments i n t h e  and t h e  considerably larger.  cycle  knee  walking  v a r y l i n e a r l y from zero  with Morrison's  d u r i n g the  Singh  of muscular  S e i r e g and. A r ' v i k a r ' s c a l c u l a t e d  agreed c l o s e l y joint  analysis  was assumed t o  reaction forces  knee  analysis  for quasi-static  i n c l u d e d i n the  reaction force  forces  and a n k l e  Dynamic l i m b d a t a i n c l u d i n g i n e r t i a f o r c e s  moments were n o t foot  knee  the  s t u d y S e i r e g and A r v i k a r  the  s h a r i n g and j o i n t r e a c t i o n s  patterns.  determine  s h a r i n g and c o r r e s p o n d i n g h i p ,  reactions.  extended  12 -  (19^1).  f u n c t i o n and m o t i o n were made on a p p r o x i m a t e l y 100  ligaments.  joints  stripped of  I n d i v i d u a l ligaments  a l l parts  and c o m b i n a t i o n s  except of  ligaments  were c u t  and m o t i o n o f paratus  was  used  rotation of that  there  the  the is  maintaining  and t h e joint  to  function of  was  the  t i b i a on t h e  joint  the  observed.  measure  a close  13 -  A simple  degree o f  femur.  lateral  of  w h i c h c a n be  ligaments  vice  The r e s u l t s  interrelationship  stability  intact  the  ap-  m o t i o n and indicated  ligaments  summarized  in  as  follows: (1)  Lateral  motion i n extension i s  capsule, in  collateral  flexion  by the  ligaments  controlled  by  and c r u c i a t e  same s t r u c t u r e s  the  ligaments;  minus t h e  lateral  collateral. (2)  Rotary motion i n extension i s sule, in  collateral  flexion  ligaments  by t h e  controlled  and c r u c i a t e  same s t r u c t u r e s  by t h e  cap-  ligaments;  minus t h e  lateral  collateral. (3)  Forward g l i d i n g o f trolled  (4)  (5)  trolled  by t h e  Lateral  g l i d i n g of  trolled  by t h e  femoral  ligaments, the  posterior the  tibial  is  popliteal  femur i s  femur i s  inter-condyloid aid of  of  all  ligament  con-  eminence  and  the  ligaments.  by b o t h t h e  collateral  ligaments, the  con-  ligament.  t i b i a on t h e  with  con-  ligament.  cruciate  controlled  aspect  femur i s  t i b i a on t h e  both c r u c i a t e  posterior  oblique  cruciate  the  condyles  Hyperextension  t i b i a on t h e  anterior  Backward g l i d i n g o f  the (6)  by t h e  the  both  menisci,  a r t i c u l a r capsule,  and t h e  architecture  the  11+  -  of (7)  the  femoral  condyles.  Hyperflexion is  c o n t r o l l e d by b o t h c r u c i a t e  ments, both m e n i s c i , posterior  -  aspect  the  femoral attachment  o f the  capsule,  attachment' o f b o t h heads the  condyles  Recent  studies  ments  for different  Lange  (1970)  joint  t o measure  and t h e r e b y (1973)  o f the  o f the  femur and  have examined t h e  knee p o s i t i o n s .  a t t a c h e d gauges t o the  tensions  estimate  determined the  ligament  the  femoral  tibia. length of  ligaments  different  ligament length.  of  g a s t r o c n e m i u s and  Edwards,  the  at  the  liga-  the  liga-  Lafferty of  a  and  dissected  angles of  flexion  Wang, W a l k e r and W o l f  length patterns  for  12  speci-  mens f o r v a r i o u s a n g l e s o f f l e x i o n and d e g r e e s o f r o t a t i o n . The  joint  capsule,  ceps muscle i n the  the  together  testing.  f o u r major l i g a m e n t s  and t h e  w i t h p a t e l l a a t t a c h m e n t were  The l e n g t h o f  of  the p i n s  Results cent  h o l e s i n the  femur and t i b i a  located  the  respective  showed t h a t  the  collaterals  i n length  reciprocal posterior  i n f l e x i o n while  w i t h the cruciate  retained  t h e l i g a m e n t s was d e t e r m i n e d  f r o m r a d i o g r a p h i c measurement o f l o n g m e t a l p i n s through d r i l l  ligament  the  inserted  so t h a t  shortening during  The b i o m e c h a n i c s o f n o r m a l  the  ends  attachments.  s h o r t e n e d a b o u t 20 p e r cruciates  a c t i o n was  anterior cruciate lengthening  was examined by E n g i n and K o r d e  quadri-  and t h e  flexion.  and a b n o r m a l knee  (197*0 •  joints  The- i n v e s t i g a t i o n  was c o n c e r n e d w i t h an e x p e r i m e n t a l and t h e o r e t i c a l  study  of  the  c h a n g e s i n knee  15 -  j o i n t mechanics  i n degenerative  disease.  E x p e r i m e n t a l t e s t s were c o n d u c t e d  s t r a i n at  the  tibia  s t r a i n gauged c r o s s - s e c t i o n s  ments o f normal  the  joint  was g r e a t e r  joint  to  away l e a v i n g m a i n t a i n the  c o n f i g u r a t i o n the than the  medial  valgus  condyle  on t h e  axial  collateral  degree  load.  o f knee  condyle  ligaments  contact  found  force  d i s t r i b u t i o n with valgus  deformity  lower  limb.  Experimental The types of  the  the  the  knee.  leg  of  above  stability  leg  as  later  of  l o a d i n g on t h e Klein  the  knee  joint  (1962)  The d e v i c e  has  article,  been  depen-  similar and v a r u s  was a t t a c h e d  with cuffs  studied  (1964),  to  the  the': d e v i a t i o n  that  various several for  dial of  tes-  stability  t h i g h and  and a m a c h i n i s t ' s  stated  of by  ligament  adducted o r abducted the Klein  effect  an i n s t r u m e n t  collateral  p i v o t p o i n t measured  a tester  and t h e  designed  m e d i a l and l a t e r a l  a subject the  be  The  Testing  researchers. ting  force.  on m a g n i t u d e  v a r i a t i o n i n the of  a  and a  were f o u n d t o  (1972)  force  with  force  a b n o r m a l i t y and n o t  K e t t l e k a m p and Chao  For  contact  force  contact  lateral  Soft  remaining l i g a -  integrity.  contact  medial  d e f o r m i t y i n c r e a s i n g the  t e n s i o n s i n the  joint  the  a femur and  o n l y the  lateral  v a r u s d e f o r m i t y i n c r e a s i n g the  of  of  determine  s p e c i m e n f o r n o r m a l and a b n o r m a l c o n f i g u r a t i o n .  t i s s u e s were d i s s e c t e d  dent  to  joint  of  lower attached  the  lower  lower l e g .  In a  the  of  ability  the  test of  to  the  demonstrate  16 -  s t a b i l i t y or i n s t a b i l i t y of  j o i n t was d e p e n d e n t u p o n t h e Degradation of  been the  subject  the knees o f loading  to  the  experience  of recent  research.  a d u l t r a b b i t s to  Radin  suddenly a p p l i e d loads  and G e r a t h  (1975)  investigated  speed r u b b i n g o f the p a t e l l a constant  static  cartilage ature  of  isolated  subject of  1967)  rabbit  of  the  (O'Donoghue,  to  the  1950)  of high to  showed  skin  (1967,  a  that  temperthe  cartilage.  and t e n d o n s h a s b e e n al.  ef-  Seireg  inves-  197*+) who m e a s u r e d  s t r e n g t h i n r a t s and tensile  strength  A r e v i e w o f l i t e r a t u r e on the  i n man a l t h o u g h much l i t e r a t u r e has  published with respect injuries.  the  subjected  h a s n o t r e v e a l e d any s t u d i e s r e l a t i n g t o  the l i g a m e n t s  clinically  effects  o f the  who d e t e r m i n e d t h e  tendons.  to  i n surface roughness,  content  strength of ligaments  (1966,  the  The r e s u l t s  j u n c t i o n s t r e n g t h and l i g a m e n t o u s  by V i i d i k of  and a change  i n a n i m a l s by T i p t o n e t  impulse  investigated  j o i n t of r a t s  s t r u c t u r e and m i n e r a l  The  the  joint,  has  R a d i n ' s s t u d i e s and  i n vivo,  compressive l o a d .  tester.  subjected  or impact l o a d i n g .  damage i n c l u d e s an i n c r e a s e the  cellular  tigated  (1972)  the  (1973)  d a i l y i n t e r v a l s of  R a d i n and P a u l  ligaments  joint  induce c a r t i l a g e d e s t r u c t i o n s i m i l a r  those o f Simon, of  of  c a r t i l a g e i n t h e knee  o b s e r v e d d e g e n e r a t i o n i n human k n e e s .  fects  the  s u r g i c a l treatment  of  this  strength been ligament  Exercise  and t h e Knee J o i n t  Several of  exercise  Again,  studies.  that  studies  on t h e  these  (1967,  17 -  have "been made c o n c e r n i n g t h e  strength of ligaments  investigations  Adams ( 1 9 6 6 ) ,  1975)  the  al.  s t r e n g t h o f knee l i g a m e n t s  crease  ligament  o f dogs  i n strength of  rabbits  after  i n rats  animal  T i p t o n et 1973)  al.  all  found  increased  after  al.  (1970)  strength of  and V i i d i k  joint.  (1968)  made  the m e d i a l  f o u n d an i n -  a n t e r i o r c r u c i a t e ligament  in  training.  Although the ments i s  well  felt  effect  the  the  (1969,  T i p t o n et  same o b s e r v a t i o n c o n c e r n i n g t h e  collateral  (1967),  and Zuckerman and S t u l l  a t r a i n i n g program o f r u n n i n g . the  o f t h e knee  have b e e n c o n f i n e d t o  Rasch et  effects  value of  exercise  documented, K a r p o v i c h  i n strengthening  (1970)  o f deep knee bends o r deep  was d e t r i m e n t a l t o  the  ligaments  and K l e i n squat  o f the knee.  exercises  K l e i n and  conducted extensive  found t h a t  f o o t b a l l p l a y e r s and w e i g h t  lifters  deep  exercises  and c o m p e t i t i o n were  subject  to  stretching.  ligament  in their training  s u c h e x e r c i s e s and  and knee i n s t a b i l i t y due t o  Similarily,  squat  jumps i n t r a i n i n g ,  joint  instability,  ligaments.  of  (1971)  associates  squat  studies  liga-  who i n c l u d e d  abnormal  a s t u d y o f p a r a t r o o p e r s , who u s e d showed a h i g h i n c i d e n c e o f  especially  knee  i n t h e m e d i a l and l a t e r a l  - 18 Summary The r e v i e w ics' of  the  involved the  knee  to  joint  of l i t e r a t u r e  joint  make a t h o r o u g h a n a l y s i s structures  of of  The b i o m e c h a n i c a l a n a l y s e s  1966; M o r r i s o n , have t h e r e f o r e reduction of  1968,  the  ( B r a n t i g a n and V o s h e l l ,  and w i t h i n t h e  ficult.  revealed, that  1970;  necessarily  the the  to  biomechan-  1941)  forces joint  date  are  acting  very  (Paul,  S e i r e g and A r v i k a r ,  so at  dif-  1964,  1973.  1975)  i n v o l v e d procedures which r e q u i r e d  indeterminancy through assumptions  of  minimi-  z i n g p r o c e d u r e s and l i n e a r p r o g r a m m i n g . There i s strength testing the  the  the  a paucity_of research with regards  ligaments  methods  stability  ments of  of  also  of  the  of  cartilage  the  knee  of  structure  test  i n terms  joint  remains a ' l a c k and s t r a i n s of  the  of  of  the  athletics.  to  . Similar  state-  properties  have b e e n t h o r o u g h l y i n gait  patterns,  involvement  but  information d i r e c t l y related joints  evaluate  knee.  to  and m u s c l e  i m p o s e d on t h e  "body i n t h e  subjects.  of kinematics,  forces  1962)  f u n c t i o n and p h y s i c a l  Human l o c o m o t i o n a p p e a r s  devices,  i n man a l t h o u g h some  have b e e n d e v e l o p e d ( K l e i n ,  c a n be made a b o u t t h e  vestigated  knee  the  of  the  lower  more dynamic l o c o m o t i v e  prosthetic there  to  the  forces  extremities  activities  of  - 19 -  CHAPTER  III  METHODS AND PROCEDURES  Anatomy o f  the  Knee  Joint  Introduction- • The that  knee  allows  while  joint  flexion  restricting  axis.  is  a synovial  and e x t e n s i o n i n t h e  valgus  The p o s i t i o n  and s t r u c t u r e  joint  stability  and e q u i l i b r i u m o f  joint.  joint the  Bone  structure  surfaces  stability.  the  plane the  knee makes  long  it  an  the  knee i s  maintained  o f m u s c l e s and l i g a m e n t s capsule  and t h e  between the  menisci  by  the  crossing  the  deepened  femur and t i b i a a l s o  R e l a t e d knee  structures  The  are  the  arti-  aid  in  fibula  and  patella.  structure The  the  of  about  joint  i n b o t h w e i g h t b e a r i n g and l o c o m o t i o n .  The s y n o v i a l  culating  sagittal  and v a r u s r o t a t i o n  important  supporting  condylar hinge  leg  femur and t i b i a a r e  and t h e r e f o r e  function while only i n d i r e c t l y  end o f  the  the  are d i r e c t l y  non-weight  w e i g h t b e a r i n g bones associated with  knee  joint  the  femur has  has two  joint  b e a r i n g f i b u l a and p a t e l l a  i n v o l v e d w i t h knee f u n c t i o n .  The  of  three  (Figure  articulations.  c y l i n d r i c a l shaped  The  condyles  are  3-01)  lower which  FIG. 3.01  RIGHT K N E E  J O I NT - B O N E  STRUCTURE  t r a n s m i t the the  upper s u r f a c e  r e d to are  "body w e i g h t to  as  the  separated  The l a r g e  of  the  the  c i r c u l a r concave  tibia.  (Fig.  m e d i a l and l a t e r a l  3-02)  condyles  These  are  of  refer-  condylar a r t i c u l a t i o n s  and  by a n o n - a r t i c u l a t i n g i n t e r c o n d y l a r n o t c h .  sesamoid  p a t e l l a bone  c e p s t e n d o n and a r t i c u l a t e s femoral  21 -  condyles  to  is  embedded i n t h e  w i t h the  anterior  form the p a t e l l a r  quadri-  surface'of  articulation.  the  (Fig.  3.01) The f i b u l a , functioning  part of  s i t e s f o r muscle Ligamentous The  l a t e r a l bone  the  joint  stability  of  the  limit they  as  shown i n F i g . 3-0*1-  The c o l l a t e r a l  extension  cross  of  the  ligaments  j o i n t while  i n the  is  a  provides  the  i n the  plane.  and  middle  T h e i r main f u n c t i o n i s of  the  joint  r o t a t i o n about the  of  to  but  long  axis  joint. prevent  a b d u c t i o n and a d d u c -  a l l o w i n g a wide r a n g e o f  sagittal  a d h e r i n g to  cruciates  two  3-03)  each o t h e r  flexion  The m e d i a l c o l l a t e r a l  a s u p e r f i c i a l p a r t and a deep p a r t w i t h t h e ligament  not  c o n t r o l l e d by  (Fig.  dislocation  check h y p e r e x t e n s i o n ,  the  but r a t h e r  joint  collaterals.  and s i d e t o s i d e movement  t i o n of  is  attachments.  t h e knee  a n t e r i o r and p o s t e r i o r also  leg,  a n t e r i o r and p o s t e r i o r  m e d i a l and l a t e r a l  joint  o f the  Structure  The s t r o n g c r u c i a t e s the  itself  and l i g a m e n t  sets of ligaments; the  the  medial meniscus  deep f i b r e s  (Fig.  3• 0*4-).  and has of  The  -  FIG. 3.02  FIG. 3.03  SUPERIOR  22  -  SURFACE  -TIBIA  L I G A M E N T S O F K N E E JOINT  - 23 lateral  collateral  adherence slack  to  the  in flexion  ween t h e  joint  along with  The  l a t e r a l meniscus. but  taut  the  femur r e l a t i v e  attachment  (Fig.  popliteal  to  provides to  distance  The c o l l a t e r a l  the  the  bet-  ligaments  restrict  tibia.  is  an e x t e n s i o n  anterior  tibial  joint  of  the  stability  tuberosity  the main l i g a m e n t s  two m i n o r l i g a m e n t s are  the  are  of  the  3-05)  I n a d d i t i o n to  These  as  and i n t e r c o n d y l a r n o t c h  t e n d o n and i t  through i t s '  are  i n extension  increases.  cruciates  w i t h no  The c o l l a t e r a l s  strong p a t e l l a r ligament  quadriceps  tibia.  a s i n g u l a r c o r d - l i k e ligament  surfaces  the  r o t a t i o n of  is  the  whose f u n c t i o n i s  oblique p o p l i t e a l  ligament  situated  ligament  on t h e  of  the  knee,  not w e l l and t h e  posterior  there  defined.  arcuate  side  of  the  joint. Menisci  and A s s o c i a t e d The m e n i s c i  to  a i d the  Structures  deepen  a r t i c u l a t i o n of  surfaces.  The m e n i s c i ,  wedge l i k e  cross-section  thin  edges.  diameter, the  (Fig.  surface  margins of  the  as  it  but is  the  concave  condyles  femoral  which are  condyles  semi-lunar  of  the  shaped,  The l a t e r a l m e n i s c u s the  is  tibial  have  a  taper  to  smaller  in  p e r i p h e r y and more c i r c u l a r t h a n  covers wider.  two m e n i s c i  tibia  on t h e  w i t h i n t e r i o r "borders t h a t  3-03)  t h i c k e r about  medial meniscus  cular  the  are  a l a r g e r p o r t i o n of (Fig.  J.Ok)  continuous  the  arti-  The a n t e r i o r w i t h the  transverse  - 2^  ANTERIOR  CRUCIATE  -  TRANSVERSE  CORONARY  FIG, 3.04  LIGAMENTS  OF  LIGAMENT  LIGAMENT  KNEE  JOINT  TEN DON OF QUADRICEPS  PATELLA  PAT E L L A R LIGAMENT  TIBIAL  FIG, 3.05  PATELLAR  LIGAMENT  TUBERCLE  -  ligament the  while  periphery of  -  the m e n i s c i  t i b i a by a f i b r o u s p o r t i o n o f  known as  the  meniscus  is  cus  the  25  coronary ligament attached  accounting for  Muscle  (Fig.  articular J.Ok).  compared t o  to  capsule  The m e d i a l the  lateral  menis-  a difference .in mobility.  System The m u s c l e  knee  tightly  the  a r e connected,  joint  groups t h a t  c o n t r o l t h e movements  c a n be d i v i d e d i n t o  of  the  e x t e n s o r s and f l e x o r s .  (Fig.  3.06)  The m a i n e x t e n s o r s form t h e g r o u p and i n c l u d e r e c t u s medialis j o i n to  and v a s t u s form the  tendon i n s e r t p a t e l l a to  quadriceps tendon.  into  the  the  biceps  semitendinosus  (Fig.  j o i n t p o s t e r i o r l y to  of  the  3-06).  a t t a c h to  unite  this the  hamstring group.  semimembranosus  These m u s c l e s the  surfaces  of  cross the  and the  fibula  tibia.  of  fibres  of  pass over  form t h e  the  The two headed g a s t r o c n e m i u s part  vastus  3 - ° 6 ) which  (Fig.  others  femoris  ligament.  knee  femoris,  lateralis,  Some f i b r e s  p a t e l l a while  b l e n d w i t h the p a t e l l a r  These i n c l u d e  and t h e  vastus  intermedius muscles  The m a i n f l e x o r s  the  femoris,  strong quadriceps  the of  to  calcaneus  calf  the  a weak f l e x o r  gastrocnemius  form the bone  and i s  of  tendo the  muscle  and t h e  calcaneus  foot.  of  forms t h e  the knee.  deeper  soleus  which a t t a c h e s  greater The  muscle to  the  The s m a l l p l a n t a r i s m u s c l e ,  the  FIG. 3.06  MUSCLES  CONTROLLING  5.  GRACILIS  6.  GASTROCNEMIUS  SEMITE N D i . N O S U S  7.  GASTROCNEMIUS  SEMI M E M B R A N O S U S  8,  SARTORl US  1.  BICEPS  LONG  2.  BICEPS  SHORT  3. 4.  13.  HEAD HEAD  PLANTARIS  14.  KNEE  JOINT 9.  VASTUS  LATE RA LIS  MED.  HEAD  10.  VASTUS  INTERME DI U S  LAT.  HEAD  11.  VASTUS  MEDIALIS  12.  RECTUS  FEMORIS  POPLITEAL  FOSSA  s o l e u s and t h e the  foot  gastrocnemius  (Fig.  the  triangular gracilis  thin flat popliteus  assist  the p o p l i t e u s  are the main p l a n t a r f l e x o r s  of  3.06).  O t h e r weak f l e x o r s muscle,  27 -  of  t h e knee  g r a c i l i s muscle, muscle  (Fig.  the  3.06).  medial r o t a t i o n of  aids  are the  the  i n u n l o c k i n g the  long  sartorius  p l a n t a r i s and  the  The s a r t o r i u s and  tibia in flexion  joint  at  the  onset  while of  flexion.  Concepts of A n a l y s i s Reference  A x e s o f Knee  To a n a l y z e Morrison's  (1973)  the  forces  reference  a c t i n g at a x e s were  the  adopted.  Ys, Z s a x e s a r e r e f e r e n c e d w i t h r e s p e c t their  o r i g i n at  3.O7)  the  assumed  The h o r i z o n t a l Xs a x i s  lateral  axis  of  the  p o s t e r i o r Ys a x i s  tibial  of  the  tibia.  to  centre  coincides  condyle  coincides  condylar notch while axis  joint  knee  the of  joint, These X s ,  t i b i a and have  the knee.  w i t h the m e d i a l -  surfaces,  the  anterior-  w i t h the-mid-raxis , d f the  the  Zs a x i s  (Fig.  3.08)  (Fig.  represents  the  inter-  vertical  Axes o f Femur and P e l v i s I n o r d e r to ments are  to  the  calculate  the  femur and p e l v i s ,  muscle  two  and l i g a m e n t  attach-  additional reference  axes  required. Morrison's  (1973)  femoral reference  axes X f , Y f , Z f  -  FIG. 3.07  TIBIAL  28  -  REFERENCE I  t Y FIG.3.08  TIBIAL  AXES CONTACT AREA  s  CONDYLES  - 29 were  adopted  centre axis .of  of  the  the  line  (Fig.  3-09).  o f the  the  The X f a x i s  femoral condyles  t i b i a and t h e Y f a x i s  tibia.  The Z f a x i s  is  t i b i a but only i n 180° The i n t e r s e c t i o n  condyles oral  and t h e  reference  the  tibial  a r t i c u l a t i o n discussed  The r e f e r e n c e  axes  the  centre  of  the h i p bones,  and t h e  extension  Zp a x i s  t h r o u g h about  resistance F o r the  cylindrical  fixed the  dyles  line last roll  t h e Xs  Ys  axis  Zs a x i s  of  femoral  u  to  e  the  fem-  in  flexion  the  character  to  the  X p , Y p , Zp were acetabulum ( F i g .  line the  j o i n i n g the  Yp a x i s , l i e s  anterin  the  is perpendicular.  t h e Knee J o i n t .  g o v e r n e d by t h e  joint.  to  the  o f the  fixed d  o f the  superior spines plane  the  below.  parallel  The m a i n movements  in  3*1°)  is  Movements o f  the  not  The Xp a x i s  sagittal  to  o r i g i n of  axes o f the p e l v i s ,  chosen with o r i g i n at  the  (Fig.  line  the  This, o r i g i n i s  of  ior  parallel  centre  determines  to  3-11).  is  parallel  c o i n c i d e n t w i t h the  relative joint  the  axes.  and i s  with  extension.  of  Zs a x i s  coincides  shape o f the  o f the  knee  135 d e g r e e s .  of  the  joint  ligaments  greater part of  10 t o forward  on t h e  on t h e  tibial  articular  surfaces  and  the  range o f motion,  joint's  slide  on t h e  tibial  extension surface.  cross  are  that  concave  20 d e g r e e s o f  T h e s e movements  and m u s c l e s  femoral condyles  contact  j o i n t a r e f l e x i o n and  t i b i a with  condyles. the  the  a  However,  femoral con-  Similarily  the  FIG. 3.09  REFERENCE  A X E S - FEMUR TIBIA ;  - 31  90°  FLEXION  -  -  cc  i  FIG. 3.11  PELVIC  REFERENCE  AXES  first of  10 to  the  20 d e g r e e s o f  femoral condyles.  faces  is  assumed  tibia  (Fig.  to  33 -  flexion The l i n e  be c o i n c i d e n t  3-°8).  of  w i t h the the  the  joint  Xs a x i s o f  femoral  displacement  d u r i n g a r t i c u l a t i o n and i n t r o d u c e s  above  a backward r o l l i n g  contact  The r o l l i n g o f  c a u s e s an a n t e r i o r o r p o s t e r i o r line  involve  of  this  contact  an e r r o r i n  10 to  15 d e g r e e s o f knee  the  extension  the  the  "locking" of  femur.  T h i s movement  is  known as  and a s i m i l a r " u n l o c k i n g " a c t i o n o c c u r s flexion.  r o l l i n g phase  long axis is  Also  allowable Muscle  restricted as  the  knee,  actions.  the  the  onset  joint  of  coincide  the  joint  b u t up t o  25 d e g r e e s o f  ligaments  across  with  the  about  rotation  joint  the;jjoint  the can  begin  surfaces  to  is  flexion.  System complete  an a n a l y s i s  a s i m p l i f i e d muscle  (1970:3*0  model,  and t h e  r o t a t i o n of  b e t w e e n 30 and 50 d e g r e e s  and L i g a m e n t  Morrison  at  the  to  movement.  some l a t e r a l m o t i o n a t  I n o r d e r to the  joint  extension,  occur i n f l e x i o n slack.  of  are  tibia relative  The l o c k i n g and u n l o c k i n g a c t i o n s  In f u l l  cal  •  condyles  a c c o m p a n i e d by an o u t w a r d r o t a t i o n o f  at  the  assumption. The f i n a l  the  sur-  was  adopted.  The m u s c l e s  a r e assumed that  cross  the  and l i g a m e n t In t h i s  four, main ligaments  collaterals,  of  of  to the  the  have  forces system  simplified joint,  the  individual  imposed after  anatomicruciates force  j o i n t were d i v i d e d  into  - 3^ three  separate  groups  synchronously.  so  that  The c o m p l e t e  the muscles system  is  of  each group  defined  as  follows:  3.12)  (Fig.  (1)  Hamstrings; i n c l u d i n g biceps o s u s and  (2)  femoris,  semitendin-  semimembranosus.  Gastrocnemius; i n c l u d i n g l a t e r a l of  gastrocnemius  and m e d i a l  including rectus  femoris,  m e d i a l i s v a s t u s .intermedius"and.vastus  C r u d i a t e L i g a m e n t s ; a n t e r i o r and p o s t e r i o r .  (5)  Collateral  L i g a m e n t s ; m e d i a l and l a t e r a l .  The f o u r m u s c l e s  popliteus  are  study  tensor  to  the  group,  gracilis is  the  tensor  knee  latae,  be o f  and a r e t h e r e f o r e  fact,  popliteus  of  fascia  assumed  actual  vastus  lateralis.  (4)  above m o d e l ,  heads  and p l a n t a r i s .  (3) ' Q u a d r i c e p s f e m o r i s ;  this  act  not  gracilis,  insignificant  excluded  fascia latae  with the  for in  sartorius  the  and  importance  from the  for  analysis.  a c t s w i t h the  and s a r t o r i u s a i d t h e  associated  accounted  hamstrings  In  quadriceps  g r o u p and  "unlocking" a c t i o n of  the  knee. Anthropometry  Introduction I n o r d e r to the of  muscle their  calculate  the  g r o u p s and l i g a m e n t s  skeletal  The p r e s e n t  attachments analysis  lines at  of  force  t h e knee,,  the  action  of  co-ordinates  are r e q u i r e d .  utilizes  Morrison's  (1970)  anthro-  - 35 -  FIG. 3.12  SIMPLIFIED MUSCLE S Y S T E M A C T I N G AT  A N D LIGAMENT KNEE JOINT  1.  HAMSTRINGS  4.  GRUCIATE  2.  GASTROCNEMIUS  5.  COLLATERAL  3.  QUADRICEPS  FEMORIS  LIGAMENTS LIGAMENTS  p o m e t r i c measurements tachment  f o r the  to  test  36 -  determine  the  co-ordinates  of  at-  subject.  Measurements Morrison muscle  (1970)  and l i g a m e n t  attachment  These m e a s u r e m e n t s , the  tibial  (s)  determined the  pelvis  and f e m o r a l  represent  pelvic  (p)  of  r i g h t h i p bone  the  axis  for a dissected  w h i c h were made i n i n c h e s  a r e g i v e n i n T a b l e No. the  co-ordinates  (f)  1.  axes o f  the  measurements  (Fig.  at  relative  the  "},!!).  F o r the  semimembranosus  and s e m i t e n d i n o s u s  muscles.  line  mid-point  muscle  of  posterior  Since  the  line  group i s  surface  of  action of  continuous  flexion  (Fig.  q = 0.31  of  the  biceps  tendo the  the  w i t h the  l i g a m e n t , M o r r i s o n (1970) angle  for  spine  hamstrings  Also,  femur was  t h r o u g h the  the  between t h e  theta  a c t i o n passed  of  limb,  group  femoris, since  assumed calcaneus  femoral  quadriceps  line  of  developed  p a t e l l a r ligament  an  that  to  the  condyles. femoris  a c t i o n of a  so  •  the  a m e d i a l and l a t e r a l h e a d ,  common i n s e r t i o n on t h e  of  patellar  knee  g r o u p has  to  Morrison's  anterior superior  f o r the  its  relative  to  o r i g i n was assumed  equivalent  limb.  Muscle o r i g i n c o - o r d i n a t e s  with centre  muscle  male  amputated  a common m u s c l e  gastrocnemius  of  the  relationship  and t h e  angle  of  3-13)-  x 10"^  (phi)  + O.37 x 10~  2  - 8.4  x 10"  ( p h i ) + 15  3  (phi)  2  ..3.01  -  T A B L E NO.1  Xsq  37  -  ANTHROPOMETRIC  DATA  0.0  Xsl  1.65  Xffa  0.15  Ysq  -1.3  Ysl  1.0  Yffa  0.4  Zsq  -1.55  Zsl  -1.1  Zffa  0-2  Xsh  0.0  Xffl  1.6  Xsp  0.0  Ysh  1.0  Yffl  0.2  Ysp  0.65  Zsh  -105  Zffl  0.25  Zsp  Xph  -2.24  Xsm  -0.85  Xffp  -0.3  Yph  4.35  Ysm  0.3  Yffp  -03  Zph  -3.95  Zsm  2.35  Zffp  -0.2  Xsg  0.0  Xffm  -1.8  Xpfh  -1.1  Ysg  2.0  Yffm  0.1  Ypfh  2.0  Zsg  -16.0  Zffm  0.65  Zpfh  -2.4  Xsfg  0.0  Xsa  -0.15  XI  0.72  Ysfg  1.1  Ysa  -0.4  Zsfc  0.8  Zsfg  1.1  Zsa  KNEE  X 3.5  SCALING  Y 3.35  DIMENSIONS  -0.25  0.15 PELVIC  Z  X  16  8.7  SCALING  DIMENSIONS  Y 4.3.5  Z 5.0  -  38 -  PHI  FIG. 3.13  -  DEGREES  ANGLE OF LIGAMENT  PATELLAR RELATIVE  A N G L E O F KNEE  THETA  cj,  -  ANGLE  BETWEEN  PATELLAR AXIS PHI  -  ANGLE JOINT  OF  FLEXION  LINE  OF  L I G A M E N T AND TIBIA  TO  LONG  ( Z )  OF F L E X I O N  s  OF  KNEE  - 39 where, theta  q = angle the  phi  = angle  Scaling  between the l i n e  v e r t i c a l axis  of flexion  subject  were  factors.  subject  of Table  To d e t e r m i n e  t h e knee were  scaling  f o r the t e s t  subject  of Morrison's  are l i s t e d  i n Table  for  anthro-  o f the  sub-  test  compared t o t h e c o r r e s p o n d i n g measurements  section  test  attachment  No. 1 and a p p r o p r i a t e  s c a l i n g dimensions  a m p u t a t e d l i m b and s k e l e t o n  results  and l i g a m e n t  the s c a l i n g f a c t o r s  and p e l v i c  The s c a l i n g d i m e n s i o n s  the  o f muscle  o b t a i n e d by u s i n g M o r r i s o n ' s  p o m e t r i c measurements  the  joint  Factors  test  ject,  o f the t i b i a ( Z s ) .  o f t h e knee  The c o - o r d i n a t e s the  o f p a t e l l a r l i g a m e n t and  (1970)  from  study.  No. 2 o f t h e  along with a d d i t i o n a l anthropometric data f o r while  the s c a l i n g f a c t o r  calculations  are  given i n Appendix A.  Testing  Procedures  Introduction The t e s t  subject  f o r t h e s t u d y was an e x p e r i e n c e d and  accomplished i c e hockey p l a y e r . laboratories sity  plate  was c o n d u c t e d i n  o f t h e U n i v e r s i t y o f W a s h i n g t o n and t h e  of B r i t i s h  oscilloscope  The t e s t i n g  Columbia.  force  Synchronized f i l m  r e c o r d s were  Univer-  r e c o r d s and  obtained with the  force  apparatus at the U n i v e r s i t y of Washington f o r a simu-  .Isolated at  skating  the  muscle  stride.  U n i v e r s i t y of activity  of  E l e c t r o m y o g r a p h t e s t s were British  a simulated  t o r y w i t h an a c t u a l  on-ice  g r a p h d a t a was n e c e s s a r y indeterminate  equations  Cinematography  planes  subject  while  to of  Fig.  the  the  at  i n the  The  labora-  electromyoof  the  system.  f i l m e d i n the a simulated  of  the  sagittal  skating test  the  on t h e  the  joint  sides of knee  of  and  fron-  stride.  subject  c i r c u l a r reference  wore  markers,  lower  0.75  r i g h t l i m b and  reference\imarkers,  shown  in  centre  over  the  f e m o r a l head  of  a c e t a b u l u m a r t i c u l a t i o n on t h e  dyle  phasic  follows:  hip  frontal (2)  stride.  force  were p l a c e d  The l o c a t i o n s  at  stride  for a solution  l i m b movement,  i n diameter,  3 - 1 ^ were as (1)  allow the  was  swimming t r u n k s and w h i t e  pelvis.  skating  executing  To d e t e r m i n e  inches  skating  compare t h e  Procedures  The t e s t tal  C o l u m b i a to  completed  the  the  joint  lateral  and  hip  centre  femur and a t  over the the  lateral  corresponding  epiconfrontal  location (3)  at  the  ankle  joint  centre  on t h e  front  and l a t e r a l  sides (4)  at  the  centre  and l a t e r a l (5)  at  the  of g r a v i t y of  sides  centre  of  (see  the  shank on t h e  front  A p p e n d i x A)  gravity of  the  foot  and s k a t e  on  FIG. 3.14  LOCATION OF R E F E R E N C E  MARKERS  - k2 the  front  and l a t e r a l  sides  (see  A p p e n d i x A)  Two 16 mm m o t i o n p i c t u r e cameras d e t a i l e d B,  were  used  to  record  of  6^ f r a m e s p e r  the  second.  skating stride The f i l m  markers. allowed.' l o c a t i o n i n time of  the  joint  lower r i g h t  centres  and o f  Force  the  equipment.  analysis  use  of  co-ordinates  of g r a v i t y of  l o c a t i o n of  a movement d u r i n g any  of precise  and s o p h i s t i c a t e d  A KISTLER p i e z o - e l e c t r i c  determine  the  skating  reaction forces  stride.  stored  the  the  as  continuous  to  force  photograph these  record  as  the  at  the  co-ordinates (Fig.  obtained  three  the  the  output  traces  from t h e  of  plate  with a  six-  force  the  plate  plate  was  A then  digitization. output  components  moment a b o u t t h e  force  attachment  (Fxp,  Z-axis  is  The  expres-  F y p and  (Mzp) and  a p p l i c a t i o n (Ax, Ay) o f  the  the  3.16).  The s y n c h r o n i z a t i o n o f  the  force  plate  to  simulated  oscilloscopes.  for later  force  point of  measuring  d u r i n g the  on t h r e e  oscilloscope  orthogonal  plate, of  developed  traces  suitable  force  activity  ( A p p e n d i x B) was u t i l i z e d  The s i x - c h a n n e l  35 mm c a m e r a w i t h  force  X , Y, Z  reference  3-15-  f o r c e measuring system  Fzp)  the  centres  component  sed  of  speed  Measurements  involves  used  r e c o r d s and t h e  s e t - u p w i t h the  shown i n F i g .  A force  was  a filming  limb.  The e x p e r i m e n t a l cameras i s  the  at  i n Appendix  oscilloscope  - 4  FIG. 3.15  3  -  EXPERIMENTAL  SET-UP  - 44  FIG.3,16  FORCE PLATE  -  RECORD OF FORCE E X P R E S S E D AS SIX  MEASURED F  x p  ,  F p, F Y  z p  -  ORTHOGONAL OF  M A  x  Z P  — , Ay -  MOMENT POINT OF  VARIABLES  FORCE  ABOUT  FORCE , F  p  VERTICAL  APPLICATION  COMPONENTS  OF  AXIS FORCE , Fp  - 45 traces  with  t h e 16 mm f i l m  r e c o r d , was a c h i e v e d  source  as shown i n F i g . J.15.  The f l a s h  in  the f i e l d  o f the  16 mm cameras  to  a control  switch  and t h e e x t e r n a l  oscilloscope. cope  trace  C l o s i n g the switch  plate  source  a  trigger  initiated  in  source the  series  o f the  oscillos-  simultaneously  output with  flash  was p l a c e d  and was c o n n e c t e d  and i l l u m i n a t e d t h e f l a s h  s y n c h r o n i z i n g the f o r c e  with  the f i l m  thereby record.  Electromyography To compare t h e m u s c l e stride  to an a c t u a l  skating  activity thrust,  of a simulated  electromyograph  were conducted^ b o t h i n t h e l a b o r a t o r y and on i c e . independent  electromyograph t e s t s  exercise physiology  were c o n d u c t e d  skating tests  Therefore, at the  l a b o r a t o r y o f the U n i v e r s i t y o f  British  C o l u m b i a and o n i c e a t t h e T h u n d e r b i r d W i n t e r S p o r t s Surface  e l e c t r o d e s were a t t a c h e d  rectus  femoris,  record  the e l e c t r i c a l  hamstrings two-channel the  biceps  over  the b e l l y  femoris  and g a s t r o c n e m i u s  activity  o f the q u a d r i c e p s  and g a s t r o c n e m i u s  muscle  o f the  muscles  to  femoris,  groups r e s p e c t i v e l y .  S a n b o r n R e c o r d e r ( A p p e n d i x B) was u s e d  electrical  Centre.  to  A  monitor  signals.  The e l e c t r o m y o g r a p h r e c o r d s were s y n c h r o n i z e d w i t h 16 mm f i l m the  r e c o r d s by means  camera t r i g g e r e d  order.  Since  of a flash  simultaneously  the muscle  source  i n the f i e l d  with the Sanborn Rec-  g r o u p s were c o n n e c t e d  channel r e c o r d e r i n p a i r s ,  before  of  each t e s t  the  to the twooutput  signal the  o f one m u s c l e  output  signal  Simulated Skating The n o r m a l  the  o f the other monitored muscle  skating stride  group.  has t h r e e  extension  (2)  the weight  shift  (3)  the g l i d e  movements  by t h e p u s h i n g l e g ,  to the g l i d e  l e g and  on t h e s u p p o r t i n g g l i d e study i s  leg.  c o n c e r n e d w i t h an a n a l y s i s  a c t i n g a t t h e knee  of a simulated  distinct  follows:  the t h r u s t  phase  from  Thrust  (1)  forces  -  g r o u p was c h e c k e d f o r i n t e r f e r e n c e  w h i c h c a n be d e s c r i b e d as  The p r e s e n t  46  skating  d u r i n g the t h r u s t stride  executed  of  extension  i n a laboratory  environment. The t e s t stationary centre  shifting  performed the s k a t i n g t h r u s t  p o s i t i o n with the r i g h t  of a force  direction.  foot  subject  plate  t h e body w e i g h t  The s u b j e c t  o f the f o r c e  skates.  plate.  foot  The t e s t  foot  to the  the s k a t e r  on t h e f o r c e  l a b o r a t o r y u s i n g a hockey a hockey p l a y e r ' s  performed the s k a t i n g t h r u s t stick  stride.  to d u p l i c a t e  left to  plate,  g u a r d s were p l a c e d o n - b o t h o f t h e subject  right  to l a n d on the  To a l l o w  the r e q u i r e d t h r u s t i n g f o r c e  rubber skate blade  i n i t i a t e d movement by  from t h e r e a r l e f t  and t h e n d r i v i n g o f f t h e r i g h t  develop  of  skate blade p l a c e d at the  and p o i n t i n g i n t h e p o s i t i v e Y -  ( F i g . 3«1?)«  foot 'in front  from a  subject's i n the  t h e arm a c t i o n  - kl -  FIG.3.17  EXPERIMENTAL SET-UP SHOWING TEST S U B J E C T ON FORCE P L A T F O R M  -  48  -  Data Reduction For l i m b were force  each t e s t obtained  plate  trial,  from t h e  o u t p u t was  photographs  of  the  the  developed  obtained  respective  the  Ecology  to  e a c h frame o f the  the  co-ordinates  16 mm f i l m of  an o r i g i n l o c a t e d measured.  was u s e d  of  the  at  the  scale  of  d i n g s were  the  film  held  at  iding  the  the  stride  the  digitize  of  was  a five  centre  the  r e a d i n g s were  the  of  film  into  the  plate speed  of Animal  the  film  Resource  data.  skating  foot  stride,  marker r e l a t i v e force  0.001  the  length  force  of  plate  were by  inch with respect  scale  to  rea-  measurements  determined  s u r v e y o r ' s range  plate.  plate  The a c t u a l  Vanguard  from pole  ( A p p e n d i x C)  r e c o r d s on 35 mm f i l m  V a n g u a r d M o t i o n A n a l y z e r by d i v -  the  16 mm f i l m .  calibration factors of  taken f o r  64 f r a m e s / s e c  to  represented  or f o r  the  corres-  The a c t u a l  t h e n d e t e r m i n e d by a p p l y i n g t h e  r e a d i n g s were  For  The X , Y and Z c o - o r d i n a t e  c o - o r d i n a t e measure  of  A  50 e q u a l h o r i z o n t a l i n c r e m e n t s  50 f r a m e s  and o s c i l l o s c o p e  vertical  force  the  35 mm  traces.  Vanguard p r o j e c t e d image.  of  traces  developed  adequately  nearest  d i g i t i z e d w i t h the  p o n d i n g to  plate  the  o b t a i n e d by m u l t i p l y i n g t h e  image  also  and  Institute  centre  The s y n c h r o n i z e d f o r c e were  16 mm f i l m  from t h e  by an a p p r o p r i a t e s c a l i n g f a c t o r , the  lower  d e s c r i b i n g the  16 mm f i l m .  r e a d i n g s were made t o the  the  each l i m b r e f e r e n c e  The s k a t i n g  50 f r a m e s  for  oscilloscope  Vanguard M o t i o n A n a l y z e r o f (I.A.R.E.)  co-ordinates  suitable  ( A p p e n d i x C)  force to  Vanguard image.  e a c h frame o f f i l m every  force  0.16  sec  time  The at  a  interval.  - 49 The to  the  e l e c t r o m y o g r a p h i c o u t p u t was  time  frames  i n t e r v a l used  o r 0.80  muscle groups muscle  sec)  of  the  relative  external  force  joint  analyzed.  activity  the  film  DIFRN,  reactions,  for  the  each  frames.  system a c t i n g at  plate  of  was w r i t t e n  and l i g a m e n t , f o r c e s  force  respect  s t r i d e (50  activity  Input data i n c l u d e d limb  co-ordinates,  measurements  skating  phasic  to  computer program,  c o r r e s p o n d i n g muscle film  the  the  The p e r i o d o f  g r o u p was d e f i n e d  calculate  describe  determine  involved.  A general  the  to  to  examined w i t h  the for  to  knee each  and frame  co-ordinates,' anthropometric  and e l e c t r o m y o g r a p h i n f o r m a t i o n .  Analysis Introduction The ermine the knee  is  muscle,  of  the  film  ligament  o u t l i n e d i n the  lowing text while  analysis  a more d e t a i l e d  and j o i n t  flow  summarizes t h e  and f o r c e  plate  forces  chart of F i g .  d a t a to  a c t i n g at  3.18.  description is  the  The  s t e p s i n v o l v e d i n the  det-  fol-  analysis  g i v e n i n the  Appendices.  L i m b and J o i n t C o - o r d i n a t e s The  co-ordinates  of  the  joints  l o w e r l i m b were d e t e r m i n e d from t h e ponding reference The  actual  the  reference  markers i n the  co-ordinates  and mass c e n t r e s  l o c a t i o n of  respective  joint  the  corres-  f r o n t a l and s a g i t t a l  were c o r r e c t e d f o r t h e  markers from the  the  of  planes.  distance centre  of or  - 50 FILM RECORD  FORCE PLATE RECORD  ORTHOGONAL CO-ORDS  REACTION FORCES  OF JOINTS & LIMBS  LIMB DISPLACEMENT  LIMB PARAMETERS  ON  SKATE  ANGULAR CO-ORDINATES  ANGULAR DISPLACEMENT ANTHROPOMETRIC MEASUREMENTS LINEAR ACC'N OF LIMBS  ANGULAR ACC'N OF  LIMBS  FORCE SYSTEM AT  ORTHOGONAL CO-ORD  KNEE  MUSCLES,LIGAMENTS  ELECTROMYOGRAM RESOLVED FORCES AT  RECORD  KNEE  LIGAMENT MUSCLE  F I G . 3.18  ANALYSIS  OF  AND FORCES  DATA  - 51 centre  o f mass and f o r t h e  d i x D) the  rotation of  The a n g u l a r c o - o r d i n a t e s  tibial  a x e s and t h e  axes o f  of the  the  the  limb.  axes o f  foot  were  (Appenthe  also  thigh, deter-  mined.  Limb A c c e l e r a t i o n The d i s p l a c e m e n t s the  l o w e r l i m b were  e a c h frame o f ferentiation used  to  of  the  analyzed.  the  accelerations  shank and f o o t from the  the  centres  o f mass  about the  from the  the  the  was  then  mass  displacement  c a l c u l a t e d f o r the  Similarily  for  A ninerpoint numerical d i f -  l i n e a r acceleration of  were  of  limb co-ordinates  d e v e l o p e d by L a n c z o s ( 1 9 5 7 )  shank and f o o t  and Z d i r e c t i o n s .  of  d e t e r m i n e d from the  technique  calculate  centres Linear  film  i n time  data.  respective  X, Y  angular accelerations  X , Y and Z a x e s were  corresponding angular co-ordinates  of  the  determined  and a n g u l a r  displacements. The n u m e r i c a l d i f f e r e n t i a t i o n t e c h n i q u e w h i c h b a s e d on t h e  theory of  finite  differences  is  is  described  in  Appendix H. External  F o r c e System at  The knee  joint  mation of Fig.  six  component e x t e r n a l  centre,  F i g . 3.19  the  The f o r c e s force  force  represents  a l l moments and f o r c e s  3'20. (a)  t h e Knee system the  a c t i n g on t h e  reactions  the  o r t h o g o n a l sum-  a c t i n g o n the. l i m b are':  plate  a c t i n g at  lower  limb,  - 52 -  Zs  FIG. 3.19 E X T E R N A L F O R C E S Y S T E M AT K N E E E X P R E S S E D IN T E R M S OF TIBIAL REFERENCE A X E S OF RIGHT KNEE  FIG.3.20  F O R C E S A C T I N G O N LOWER  LIMB  REACTION FORCES, GRAVITY  FORCES  ACCELERATION  FORCES  INCLUDING AND  (b)  the  g r a v i t a t i o n a l forces  (c)  the  inertial  The foot  54 -  a c c e l e r a t i o n o f the  (1955)  the foot  shank and f o o t  percentage  shank and f o o t (1889)  foot  represent forces  the weight a r e due t o  The mass o f  and C ^ .  t h e knee r e f e r e n c e  a free  and moments a c t i n g on t h e axes,  six  body and by  limb  equations  g  g  Fyk = Fyp + ~  • Ys + ^  o  o  |^(g  3.02a  • Yf. . .  3.02b  + Zf)  3.02c  o  - Ay) - F y p ( Z k )  • Ys(Zk  - Zs)  + Zs)(Yk  = - Fzp(Xk  - —  • Yf(Zk  - |£(g + Z f ) ( Y k  -  Zf)  - Yf)  - Ys)  + I s x • Osx + I f x - Myk  expressing  o  Fzk = Fzp - p ( g + Zs) - | ^ ( g  -  ( F i g . 3.20)  lower l i m b are d e r i v e d .  Fxk = Fxp + — • X s + — • X f  | £  the  ( A p p e n d i x A)  e q u i l i b r i u m c o n d i t i o n s of the  -  the  were c a l c u l a t e d f r o m Braune and F i s c h e r ' s  in  = Fzp(Yk  the  the  and t h e moments o f i n e r t i a o f  forces  Mxk  of  was d e t e r m i n e d f r o m D e m p s t e r ' s  c o n s i d e r i n g t h e l o w e r l i m b as  terms o f  and s h a n k .  and shank m a s s e s .  summing t h e  the  the  inertial  figures  coefficients By  of  g r a v i t a t i o n a l forces  and shank w h i l e  subject's  forces  and  Qfx  - Ax) + F x p ( Z k )  3.02d + ^  • Xf(Zk  -  Zf)  + ^  . Xs(Zk  - Zs)  + | ^ ( g + Zs)(Xk  55 -  + |^(g  + Zf)(Xk  - Xf)  - Xs)  3.02e  - I s y • 9 s y - I f y • Qfy Mzk = Mzp + F y p ( X k  - Ax) - F x p ( Y k  - ^ g  • Xf(Yk  - Yf)  - ^ g  • Xs(Yk  -  + — g  • Ys(Xk  - Xs)  + — g  • Yf(Xk  - Xf)  - Ifz  • Qfz - I s z  The c a l c u l a t e d (Mxk,  axes at  the  the  .to  the  3.02f  forces  joint  (Fxk,  the  the  centre,  system  tibial  associated at  the  F y k , F z k ) and moments  complete k,  knee p e r p e n d i c u l a r t o  To d e t e r m i n e force  knee  Ys)  • 9sz  Myk, Mzk) r e p r e s e n t  a c t i n g at  the  - Ay)  external  i n terms  the  muscle,  force  of  ligament  See  system  reference  plate  knee must he r e s o l v e d  axes X s , Y s , Z s .  force  surface.  and j o i n t with  forces,  respect  Appendix G.  M u s c l e and L i g a m e n t C o - o r d i n a t e s For ligament  the  test  attachment  subject, to  the  the  tibia,  t a i n e d by m u l t i p l y i n g M o r r i s o n ' s of A) to  T a b l e No.  1 by t h e  The c o - o r d i n a t e s the  tibial  co-ordinates  femur and p e l v i s anthropometric  appropriate scaling of  axes f o r  o f muscle  attachment  were  e a c h frame o f  ob-  measurements  factor.  determined  film  were  and  (Appendix relative  describing  the  skating thrust  and. were  corrected for rotations  limb.  These  calculations  Muscle  and L i g a m e n t F o r c e s In o r d e r to  the  lines  of  force  and l i g a m e n t s muscle were to  expressed  the  tibial  The l i n e  the  respective  the  angles of  the  angle of  allowed  from the  of the  of  the  muscle  lower  co-ordinates  line  of  of  forces,  groups  force  action  of action relative  for r o t a t i o n of  the  are -given i n Appendix F .  q u a d r i c e p s femoris muscle  the  where t h e  angle  group  calculated  p a t e l l a r ligament with  respect  tibia.  the  lines  of  determination of  action of the  the muscles  and  acting i n  these  forces  known e q u i l i b r i u m c o n d i t i o n s  The e x t e r n a l  the  and l i g a m e n t  iTh-e l i n e s  from e q u a t i o n 3 . 0 1  the  knee.  from the  attachment.  a c t i o n of  long axis  ligaments  the  action of calculated  A knowledge  tissues  muscle  a x e s and w i t h c o r r e c t i o n s  calculated  the  the  These c a l c u l a t i o n s  of  represents to  as  of  are d e s c r i b e d i n Appendix E .  determine  and l i g a m e n t  lower limb.  was  were  56 -  force- system  that  a c t i n g at  the  exist knee  at is  b a l a n c e d by (a)  the of  (b)  force the  the  structures  femur and t i b i a  forces  ment Since  a c t i n g between t h e  developed  structures the  (4)  is  of  (condyles)  the  surfaces  and  i n the muscle  groups  and l i g a -  knee.  number o f m u s c l e greater  articulating  than the  groups  (3)  number o f  and  ligament  available  equi-  - 57 ibrium equations, Therefore  anatomy o f  of  muscle  plete  the  essentially  knee  based  and t h e  (EMG r e c o r d )  external  force  i n terms  of  known f u n c -  determined phasic were made t o  system, the  indeterminate.  on t h e  F o l l o w i n g M o r r i s o n ' s (1970)  separately  action  is  assumptions  the  groups  solution.  action of ered  analysis  a number o f  tional the  the  Fig.  activity  o b t a i n a com-  procedure,  3<19»  was  p a r t i c u l a r muscle  each  consid-  or  ligament  involved.  F o r c e s i n Muscle. Groups The moment a c t i o n , plane the  of  the  muscle  tibial  hamstrings  (2)  gastrocnemius  (3)  quadriceps femoris  limb that  obtained of  the  lower  both quadriceps  force limb.  the  gastrocnemius  was  assumed  group,  group  flex  the  i n the  be  to  a force  knee  Fig. 4.02,  the  that during  To r e d u c e  the  effect  of •  g r o u p on e q u i l i b r i u m c o n d i t i o n s  at  knee-  small.  quadriceps  P q , was  The f o r c e  therefore  antagonistic  is  e x t e n - ..  show  g r o u p s were a c t i v e  the  the  and e q u i l i b r i u m  were i n a c t i v e .  situation  a c t i o n on  quadriceps group,  EMG r e c o r d s ,  hamstrings this  femoris  group  Mxk c o r r e s p o n d s  indeterminancy of  to  in  i.e.,  and g a s t r o c n e m i u s  period while  action  group  t e n d s to  by m u s c l e  anterior-posterior  e q u i l i b r a t e d by m u s c l e  plane,  (1)  lower  this  axes i s  groups i n t h a t  A positive  sors  Mxk, i n t h e  acting  determined  i n the  from F i g .  the  3.21  - 58  FIG.3.21 M U S C L E  -  F O R C E IN  QUADRICEPS  TO B A L A N C E M O M E N T + M x k  FIG.3.22 M U S C L E F O R C E IN TO  HAMSTRINGS  BALANCE MOMENT  - Mxk  - 59 and  equation 3 . 0 3 as,  equilibrium  Pq = M x k / ( C o s  3.03  9q • Y s q + s i n 9q • Z s q )  where, 9q = a n g l e long Xsq,  between l i n e axis  of  of  a c t i o n o f p a t e l l a r l i g a m e n t and  tibia.  Ysq = c o - o r d i n a t e s  of p a t e l l a r ligament  attachment  to  tibia. Since of  the  the  hamstrings are i n a c t i v e  gastrocnemius  force  and t h e  on t h e knee  is  antagonistic  action  discounted for  this  phase  Ph  = Pg = 0 The  the  3.04  h o r i z o n t a l component o f m u s c l e  v e r t i c a l component o f m u s c l e  force,  force,  Fzm, a r e  Fym, and then  Fym = Pq • s i n 9q  3.05a  Fzm = Pq - c o s 9q  3.05b  A negative oh  the  Mxk r e p r e s e n t s  lower l i m b which i s  an e x t e n s i o n  e q u i l i b r a t e d by m u s c l e  a c t i o n i n the h a m s t r i n g s group a n d / o r the group,  the  negative and  flexors  f o r the  f o r the  final  of  first  the  lower l i m b .  half  push-off  force  of of  the the  force  gastrocnemius  The moment,  skating thrust, thrust.  action  Mxk, was Fig.  EMG r e c o r d s  k.06 show  that  60  -  t h e h a m s t r i n g s were a c t i v e f o r t h e f i r s t p o r t i o n  t h r u s t w h i l e t h e g a s t r o c n e m i u s g r o u p was portion. istic  The  effect relative  g r o u p s , was Fig.  q u a d r i c e p s muscle  also  4.02.  forces  o f the  a c t i v e f o r the  g r o u p , w h i c h h a s an  to both the hamstring.and  final  antagon-  gastrocnemius  i n t e r m i t t e n t l y a c t i v e d u r i n g these periods,  In order to obtain a singular  s o l u t i o n f o r the  a c t i n g i n t h e h a m s t r i n g and g a s t r o c n e m i u s g r o u p s ,  antagonistic For  a c t i o n o f t h e q u a d r i c e p s - was i g n o r e d .  the f i r s t  phase o f the s k a t i n g  a c t i n g i n the h a m s t r i n g s group,  Ph, was  3.22  3.06.  and  the  equilibrium  equation  Ph = M x k / ( c o s 9 x h • Y s h + s i n Qxh  thrust,  the  force  determined from F i g .  3.06  • Zsh)  where, 9 x h = angle between l i n e o f a c t i o n o f the h a m s t r i n g s group  and l o n g a x i s o f t h e  tibia  Ysh, Zsh = c o - o r d i n a t e s o f h a m s t r i n g attachment Since the quadriceps a n t a g o n i s t i c cluded i n the c a l c u l a t i o n , the f o r c e represents a lower l i m i t  force  to the  tibia  i s not i n -  i n the hamstrings  group  v a l u e , where i n  P g = Pq = 0 and t h e h o r i z o n t a l  muscle  3.07 and v e r t i c a l  components o f muscle  force  are Fym  = -Ph  • sin 9xh  3.08a  Fzm  61 3.08b  = P h • c o s Qxh For  the  force  t h e f i n a l p u s h - o f f phase o f the a c t i n g i n the  thrust,  g a s t r o c n e m i u s g r o u p , P g , was d e t e r -  mined from F i g . 3-23 and e q u i l i b r i u m Pg  skating  e q u a t i o n 3 ' 0 9 so t h a t , 3.09  = M x k / ( c o s Qxg • Y s g + s i n 9 x g • Z s g )  where, 9xg  = angle between l i n e group and t h e l o n g  Xsg,  axis of the t i b i a  Z s g = c o - o r d i n a t e . s o f g a s t r o c n e m i u s mu,scle a t t a c h m e n t t o the  tibia.  Once a g a i n t h e muscle f o r c e Ph  o f a c t i o n o f the gastrocnemius  c a l c u l a t e d value o f gastrocnemius  i s l o w e r l i m i t and  = Pq = 0  3 - 10  and  thevertical  and h o r i z o n t a l m u s c l e components a r e  Fym  = -Pg • s i n 9xg  3-Ha  Fzm  = Pg • cos 9xg  3.11b  Forces i n Cruciate  Ligaments  Anterior-posterior the  joint  force  a c t i o n i n the  i s e q u i l i b r a t e d by t e n s i o n  i n the  m e n t s a s n o t e d b y B r a n t i g a n and V o s h e l l (1955)'  I t was f u r t h e r assumed t h a t  y-direction at  cruciate  liga-  (19^1) and S t e i n d l e r  a force  action  directed  FIG.3.23 M U S C L E F O R C E IN TO  BALANCE  GASTROCNEMIUS  M O M E N T - Mxk  forwards develops t e n s i o n o n l y i n the a n t e r i o r - c r u c i a t e a backwards f o r c e causes  t e n s i o n o n l y i n the  cruciate.  a f t e r M o r r i s o n (1970).  The  See  F i g . 3.24  equilibrium  e q u a t i o n f o r the  and  posterior  anterior-posterior  force actions i s Fyk  + Fym  = Pa  • c o s 9 x a + Pp  3.12  • c o s 9xp  where, Fyk Fym  =  y-component o f e x t e r n a l = y-component o f m u s c l e  force  system  force  Pa = f o r c e a c t i n g i n the a n t e r i o r c r u c i a t e Pp = f o r c e a c t i n g i n t h e p o s t e r i o r 9xa. = a n g l e b e t w e e n l i n e tibial 9xp  of a c t i o n of a n t e r i o r c r u c i a t e  of a c t i o n of p o s t e r i o r  from  and  cruciate  and  axis  For a forward d i r e c t e d developed  ligament  axis  = angle between l i n e tibial  cruciate  ligament  force action,  the f o r c e ,  i n t h e a n t e r i o r c r u c i a t e l i g a m e n t was  e q u a t i o n 3'12  by  Pa,  calculated  setting  Pp = 0  .3.13a  Pa = -(Fyk + Fym)/cos 9xa The  horizontal  and v e r t i c a l  3-13b components o f t h e a n t e r -  i o r cruciate ligament force r e l a t i v e  to the t i b i a l  axes are  -  (a) FORCE  IN  (Fyk+Fym)  64  -  ANTERIOR  CRUCIATE  IN FORWARD  Fzcr  FOR  DIRECTION  Ys  ( Fyk+ Fym)  (b) F O R C E  IN P O S T E R I O R  (Fyk+Fym) FIG. 3.24  C R U C I A T E FOR  IN B A C K W A R D  DIRECTION  F O R C E IN  POSTERIOR C R U C I A T E  ANTERIOR  CRUCIATE  LIGAMENTS  AND  - 65  -  Fycr = Pa • cos 9xa  3.l4a  Fzcr  3.l4b  = Pa • s i n 9xa For a backward d i r e c t e d  force,  Pp, d e v e l o p e d  calculated  from  force  a c t i o n a t t h e knee, t h e  i n the p o s t e r i o r  e q u a t i o n 3-12  cruciate ligament  was  by s e t t i n g  Pa = 0  3.15a  Pp  3-15b  = - ( F y k + F y m ) / c o s 9xp The  horizontal  and v e r t i c a l  components o f t h e p o s -  t e r i o r cruciate ligament force are F y c r = Pp • c o s 9xp  3.l6a  Fzcr  3-l6b  = Pp • s i n 9xp  F o r c e s i n C o l l a t e r a l L i g a m e n t s and J o i n t The medially  moment, Myk, t e n d s  i n the f r o n t a l plane.  the e q u i l i b r i u m actions  conditions  Force  t o bend t h e k n e e l a t e r a l l y and M o r r i s o n (1970)  a t t h e knee f o r these  interprets force  as f o l l o w s . When t h e r e i s a c o m p r e s s i v e  f e m o r a l and t i b i a l  force,  condyles, the force  Rz, between t h e  a c t i o n o f Myk  the centre o f pressure o f t h i s f o r c e m e d i a l l y  shifts  or l a t e r a l l y  d e p e n d i n g o n t h e d i r e c t i o n o f Myk. I f the s h i f t  o f weight  i s s u f f i c i e n t to reduce the  pressure a t the periphery o f the condyle  t o z e r o t h e n any  further increase collateral Morrison  66  -  i n Myk must he b a l a n c e d b y a t e n s i o n i n t h e  ligament at that  (1970) d e t e r m i n e d a l i m i t i n g  s h i f t of the centre at the periphery  ( F i g . 3.25)  side of the j o i n t .  of pressure  valve, X I , f o r the  that reduces the  of the condyle bearing  pressure  area to zero.  See  3.13-  Fig.  Essentially describe  there  a r e two e q u i l i b r i u m e q u a t i o n s  that  t h e f o r c e a c t i o n o f moment, Myk.  Rz = F z k + Fzm + F z c r + Pm  • c o s Gym  • c o s 9xm 3. 17  + P I • c o s 9 y l • c o s 9x1 0 = Myk - P I • c o s 9 y l • X s l + P I • s i n Q y l • Z s l + Pm  • c o s 9ym  • Xsm + Pm  • s i n 9ym  • Zsm 3.18  + Rz • Xo where, Fzk  = Z-component o f e x t e r n a l f o r c e  system  Fzm = Z-component o f m u s c l e f o r c e F z c r = Z-component o f c r u c i a t e l i g a m e n t Pm = f o r c e  acting i n medial  PI = f o r c e a c t i n g i n l a t e r a l  ligament ligament  Rz = c o m p r e s s i v e f o r c e b e t w e e n t i b i a l Xo = o f f s e t o f c e n t r e  force  of pressure  and f e m o r a l  from j o i n t  T h e s e two e q u a t i o n s a r e i n d e t e r m i n a n t c o n t a i n f o u r unknowns, R z , Xo, Pm and P I . tion  c a n be o b t a i n e d  by r e d u c i n g  condyles  centre i n that  they  However, a s o l u -  t h e number o f u n k n o w n s . t o  - 67  (a)  F O R C E IN L A T E R A L C O L L A T E R A L DUE TO  (b)  -  ADDUCTION  FORCE - Myk  F O R C E IN M E D I A L C O L L A T E R A L TO  FIG. 3.25  ABDUCTION  FORCE  COLLATERAL  DUE  + Myk  LIGAMENT  FORCES  two  by  considering  68  -  specific loading  conditions.  1:  Condition  Pressure  e x i s t s between the  condyles of the  joint  so  that Fzk Pm  + Fzm  + Fzcr  > 0  0  = PI =  t h e s e l o a d i n g c o n d i t i o n s , F i g . 3-26,  For  = Fzk  and  Xo  + Fzm  can  be  i s cal-  3-17  c u l a t e d d i r e c t l y from equation Rz  Rz  3.19  + Fzcr evaluated  by  s u b s t i t u t i o n f o r Rz  in  equation  3.18 Xo  = - M z k / ( F z k + Fzm  3.20  + Fzcr)  2:  Condition The  c a l c u l a t e d value  t i n g value  of XI  and  Myk  o f Xo  i s greater  than the  limi-  acts i n a p o s i t i v e d i r e c t i o n  medially. t h e s e l o a d i n g c o n d i t i o n s , F i g . 3-25>a s o l u t i o n i s  For obtained into  f o r Rz  and  e q u a t i o n s 3.17  P I = (Myk  +  [Fzk  - sin 9yl  P I by and  + Fzm  s u b s t i t u t i n g Pm  3.18  so  + FzcrJ  • Z s l - cos  9yl  = 0 and  Xo  =  XI  that, • XI) / • Xl)  (cos  9yl  • Xsl 3.21  - 69  FIG. 3.26  -  COMPRESSIVE  JOINT  FORCE Rz ;  Rz  = Fzk  + Fzm  + F z c r + PI  Therefore tensile  s u c h t h a t Xo >X1,  f o r Rz  +  [F.zm  + s i n 9ym = Fzk  and  a  the  centre  joint  con-  joint  centre.  i s greater  + Fzm  • Zsm-  Pm and  of the  by  3.18  so  Myk  • X l ) / ( c o s 9ym  cos  • XI)  9ym  Xo  =  that •  Xsm 3-23 3.24  • cos  9ym  • cos  f o r a negative  Myk  s u c h t h a t Xo >X1,  9xm  a c t s i n the m e d i a l ligament compressive f o r c e at the  a d i s t a n c e , X I , l a t e r a l l y from the  S h e a r F o r c e and  and  a solution  s u b s t i t u t i n g P I = 0 and  + Fzcr]  + F z c r + Pm  f o r c e , Pm,  of pressure  and  + Fzk  Therefore,  The  than XI  direction laterally.  3.17  XI i n t o equations = (Myk  o f Xo  t h e s e l o a d i n g c o n d i t i o n s , F i g . 3-25.  obtained  placed  3.22  9x1  a d i s t a n c e XI m e d i a l l y from the  c a l c u l a t e d value  For  tensile  • cos  o f the. c o m p r e s s i v e f o r c e b e t w e e n t h e  acts i n a negative  Rz  9yl  3-  The  Pm  • cos  f o r a p o s i t i v e Myk,  i s shifted  Condition  is  -  f o r c e , P I , a c t s i n the l a t e r a l ligament  of pressure dyles  70  and  a  the  centre  joint i s dis-  joint  centre.  Torque  shear f o r c e at the  d i r e c t i o n i s d e t e r m i n e d by  j o i n t i n the m e d i a l - l a t e r a l  summing t h e X component o f  e x t e r n a l f o r c e , t h e m u s c l e f o r c e and  the ligament  the  forces.  -  71  3-25  Rx = F x k + Fxm + F x c o l  where F x c o l i s t h e s u m m a t i o n o f t h e X c o m p o n e n t s o f Pm, t h e medial ligament  force.  F x c o l = P I • s i n 9 y l + Pm The mation  3-26  • s i n 9ym  t o r q u e a c t i n g o n t h e j o i n t i s e q u a l t o t h e sum-  o f t h e t w i s t i n g f o r c e s a c t i n g on t h e j o i n t .  Mz = Mzk + F x l c + Fylc  • Y s l + Fxmc • Ysm 3-27  • X s l + Fymc • Xsm  where, F x l c = x-component o f l a t e r a l l i g a m e n t  force  F y l c = y-component o f l a t e r a l l i g a m e n t  force  Fxmc = x - c o m p o n e n t m e d i a l l i g a m e n t  force  Fymc = y - c o m p o n e n t o f m e d i a l l i g a m e n t The  complete  s o l u t i o n f o r the muscle,  j o i n t f o r c e s a t t h e knee - compressive  Zo  - centre o f pressure o f compressive  Rx  l i g a m e n t and  includes,  Rz  f o r c e between j o i n t  the knee j o i n t  force  condyles force with respect to  centre  - shear f o r c e on j o i n t  Ph - f o r c e  a c t i n g i n h a m s t r i n g muscle group  Pg - f o r c e a c t i n g i n g a s t r o c n e m i u s  muscle  group  Pq - f o r c e a c t i n g i n q u a d r i c e p s m u s c l e g r o u p  -  72  -  Pa - f o r c e a c t i n g i n a n t e r i o r c r u c i a t e ligament Pp - f o r c e a c t i n g i n p o s t e r i o r c r u c i a t e ligament Pm  - f o r c e a c t i n g i n medial c o l l a t e r a l  PI - f o r c e a c t i n g i n l a t e r a l c o l l a t e r a l Mz  - torque on  joint  ligament ligament  -  73  -  CHAPTER I V RESULTS AND  DISCUSSION  Results F o r c e p l a t e o u t p u t and l i m b d i s p l a c e m e n t d a t a were collected  for a total  o f 15 t r i a l s .  From t h e s e d a t a t h e  l i n e a r and a n g u l a r a c c e l e r a t i o n s o f t h e l o w e r l i m b w e r e d e t ermined,  t h e e x t e r n a l f o r c e system  calculated  and f i n a l l y  were c a l c u l a t e d  a c t i n g a t t h e k n e e was  the muscle,ligament  f o r each  forces  trial.  These r e s u l t s a r e r e v i e w e d with reference to t r i a l  and j o i n t  i n the f o l l o w i n g  section  No. 4 w h i c h i s c o n s i d e r e d t o be r e p -  r e s e n t a t i v e o f t h e 15 t r i a l s made. Anthropometric  Measurements  The b o d y p a r a m e t e r s i n T a b l e No. 2.  f o r the t e s t subject are l i s t e d  The c a l c u l a t i o n s o f t h e s e  m e a s u r e s a r e shown i n A p p e n d i x In  A.  order to scale the b a s i c co-ordinates of muscle  and l i g a m e n t a t t a c h m e n t s  o f T a b l e No.  t h e t e s t s u b j e c t ' s k n e e and p e l v i c obtained.  anthropometric  1 to the t e s t subject,  s c a l i n g dimensions  were  T h e s e m e a s u r e m e n t s a r e g i v e n i n T a b l e No. 2 a l o n g  w i t h the a d d i t i o n a l anthropometric d a t a from the t e s t s u b j e c t . A l l m e a s u r e m e n t s a r e i n i n c h e s and r e p r e s e n t t h e  average  - 7^  TABLE NO.2  -  ANTHROPOMETRIC  DATA  Shank  Foot Lf  10.50  Ls  16.50  Rf  2.07  Rs  2.31  rfx  1.45  rsx  4.15  rfy  3.15  rsy  4.15  rfz  3.15  rsz  . 1.62  Ifx  0.15  I sx  3.92  Ify  0.71  Isy  3.92  Ifz  0.71  Isz  0.60  Wf  2.37  Ws  7.43  Ankle  Knee Rxk  1.90  Ryk  2.44  Knee Scaling X  Y  3.78  3.64  Ra  Dimensions Z 16.16  2.02  Pelvic X 8.2  -  75  -  value of at l e a s t f i v e independent measuring t r i a l s . k n e e and  p e l v i c d i m e n s i o n s were' u s e d t o c a l c u l a t e  s c a l i n g f a c t o r s f o r the listed  subject.  i n Appendix A with  Force Plate The  force plate  output i n the  r e p r e s e n t the  of a p p l i c a t i o n of the c o - o r d i n a t e s of the  measured w i t h  The  the  skating  t o r q u e and o b t a i n e d by  the  50  thrust.  applying  4.02  The  actual  the  the  thrust  values.  See  film  forces,  calibration factors  to  A p p e n d i x 'G.  Results shows r e p r e s e n t a t i v e  electromyograms  the  for  i n d i c a t e s the  the  skating  phasic  thrust.  a c t i v e throughout the  h a m s t r i n g s were a c t i v e f o r the and  was  o f a p p l i c a t i o n were  appropriate  q u a d r i c e p s m u s c l e g r o u p was the  the  resultant  v a l u e s of the  t h r e e m u s c l e g r o u p s i n s t r u m e n t e d and  cycle,  and  synchronized cine  a c t i v i t y of these muscle groups during The  plate  point  a m p l i t u d e of each t r a c e  frames of the  co-ordinates of point  Electromyograph  of the  of a p p l i c a t i o n of the  vertical  reaction  a x i s through the  force  4.  f o r a t r i a l No.  Vanguard M o t i o n A n a l y z e r at i n t e r v a l s  the measured t r a c e  Fig.  resultant  point  c o r r e s p o n d i n g to the of the  are  separate  three orthogonal plate  torque about a v e r t i c a l  F i g . 3.16.  form of s i x  i s shown i n F i g . 4 . 0 1  These t r a c e s  force,  scaling factors  Results  traces  the  the  calculations.  oscilloscope  forces,  The  The  entire  f i r s t portion  g a s t r o c n e m i u s g r o u p showed a c t i v i t y  of during  -  Fy  76  -  20C )N/( ii v.  3  Fx|)  10( DN/< jiv  Fzc )  5 0 ON/ciiv.  Mz D  2 N m/c Jiv.  Ax  Ay  l —f  2.5  0.2 sec FIG.4.01 F O R C E P L A T E OUTPUT IN FORM OF O S C I L L O S C O P E T R A C E - T R I A L NO.4  Hamstrings  Gastrocnemius  Quadriceps  Femoris -N3  TIME -  FIG.4.02  SECONDS  E L E C T R O M Y O G R A M - S K A T I N G THRUST  ON  ICE  FRAMES  d)  CO  L FO WEIGHT 0.  FIG. 4.03  SUPPORT  SHIFT 0.2 L  ILLUSTRATED  0.4  L_ SECONDS  PHASE 0.6  SEQUENCE OF SKATING  0-5  THRUST  the  l a t e r phase.  79  -  The e l e c t r o m y o g r a p h r e s u l t s f o r a  simulated  s k a t i n g t h r u s t i n t h e l a b o r a t o r y were c l o s e l y r e l a t e d t o onice  electromyograph r e s u l t s i n d i c a t i n g comparable muscle  activity. L i n e a r Limb  Accelerations  The l i n e a r a c c e l e r a t i o n s o f t h e shank and f o o t f o r t h e X, Y and Z d i r e c t i o n s a r e p l o t t e d i n F i g . 4 . 0 4 .  As  shown, t h e l i n e a r a c c e l e r a t i o n s o f t h e shank and f o o t a r e • small u n t i l push o f f . values  The d r a m a t i c p o s i t i v e i n c r e a s e  i n the  o f AXS, AYS and AZS a t p u s h o f f c o r r e s p o n d t o a n  a b r u p t i n w a r d , f o r w a r d and u p w a r d a c c e l e r a t i o n o f t h e s h a n k . The f o o t a c c e l e r a t e s u p w a r d and b a c k w a r d i n p l a n t a r a t p u s h o f f a s i n d i c a t e d by a p o s i t i v e AZF and a AYF.  flexion  negative  The i n w a r d a c c e l e r a t i o n o f t h e f o o t a t p u s h o f f a s  i n d i c a t e d by t h e p o s i t i v e i n c r e a s e  i n AXF i s a c c o m p a n i e d by  a n o u t w a r d r o t a t i o n o f t h e shank. A n g u l a r Limb The  Accelerations  a n g u l a r a c c e l e r a t i o n s o f t h e shank and f o o t  t h e X, Y and Z a x e s a r e p l o t t e d i n F i g . 4 . 0 5 . the  l i n e a r limb  accelerations,the  about  S i m i l a r to  angular accelerations are  minimal f o r the f i r s t p o r t i o n of the skating thrust but increase  r a p i d l y d u r i n g push o f f .  The l a r g e n e g a t i v e  o f AASZ and AAFZ a t p u s h o f f r e p r e s e n t  a sharp outward  r o t a t i o n o f t h e shank and f o o t a b o u t t h e v e r t i c a l while  the p o s i t i v e increase  values  axis  i n AASY and AAFY a t p u s h o f f  - 80 -  FIG.4.04  LIMB  LINEAR  ACCELERATIONS  -•81  0  0.1  .i  1  FIG.4.05  -  0.2  0.3  0.4  i  i  i  0.5  i T I M E , seconds  0.6  0.7  0.8  i  i  i  LIMB ANGULAR ACCELERATIONS  - 82. indicate axis  an i n w a r d r o t a t i o n o f  of progression.  flexion  at push o f f  AAFX w h i l e  the  The f o o t as  shank a l s o  positive  moments a c t i n g a t of  cated  the  on t h e  seconds  about  the  forward i n p l a n t a r  positive  value  increase  in  some f o r w a r d  rot-  o f AASX a t p u s h  off.  F o r c e S y s t e m a t Knee  skating stride  length  rotates  a p p e a r s t o have  The v a r i a t i o n s i n t h e one  shank and f o o t  shown by t h e  a t i o n as i n d i c a t e d by t h e  External  the  force  plate  right  foot.  i n terms o f the  knee  time base time  the  (LFO) u n t i l  i n the  skater's  the  final  The commencement o f  cident with a positive and a change  of  increase  sign of  system  forces  during  and  three  i n F i g . 4.06.  skating stride is  The  as  indi-  approximately  left  foot  lifted  0.4 off  push o f f . ( P 0 ) w i t h the  s u p p o r t phase  i n the  to p o s i t i v e .  extend  a.positive  the  the  is  coin-  v e r t i c a l f o r c e Fzk  t h e moment Mxk i n t h e  r e s s i o n from n e g a t i v e t h e knee w h i l e  three  of F i g . 4.03 the  force  are p l o t t e d  support phase  from t h e  external  plane  A negative  Mxk t e n d s  to  of  prog-  Mxk t e n d s flex  the  to  knee  joint. Moment Myk i s d u r i n g the valgus effect. limb, ting  i n i t i a l l y positive  support phase,  effect  on' t h e  knee  The t o r q u e o n t h e Mzk, i s  positive  a constant  a positive joint  about the  entire  counter-clockwise  negative  Myk r e p r e s e n t i n g  and a n e g a t i v e  joint  f o r the  and t h e n  Myk a v a r u s  long axis  s u p p o r t phase  t o r q u e on t h e  a  of  the  indica-  joint.  AT  KNEE  - TRIAL  NO.4  - 84 The remains  f o r c e Fzk, through the long a x i s o f the j o i n t ,  p o s i t i v e upward f o r t h e d u r a t i o n o f t h e s u p p o r t  phase b u t t h e shear f o r c e Fxk i s i n i t i a l l y  negative i n a  l a t e r a l d i r e c t i o n and t h e n becomes p o s i t i v e m e d i a l l y .  The  a n t e r i o r - p o s t e r i o r f o r c e , F y k , i s n e g a t i v e and t h e r e f o r e d i r ected p o s t e r i o r l y f o r the d u r a t i o n o f the skating Muscle  and L i g a m e n t Muscle  Forces  and l i g a m e n t f o r c e s c o r r e s p o n d i n g t o t h e e x -  t e r n a l f o r c e system Fig.  o f F i g . 4.06  and t h e e l e c t r o m y o g r a m s  4.02 a r e p l o t t e d i n F i g . 4.07  thrust.  thrust.  Muscle  f o r one c o m p l e t e  skating  and l i g a m e n t f o r c e s f o r t h e 15 t r i a l s  study are superimposed  i n F i g . 4.08  o f the  to i n d i c a t e the v a r i a t i o n  i n t h e r e s u l t s o b t a i n e d w h i l e maximum f o r c e s d e v e l o p e d each  o f t h e 15 t r i a l s  are g i v e n i n Table  Peak f o r c e s d e t e r m i n e d hamstrings  and g a s t r o c n e m i u s  118 p o u n d s r e s p e c t i v e l y .  of  during  No.'3-  i n the quadriceps femoris, m u s c l e g r o u p s w e r e 665,  As i n d i c a t e d i n F i g . 4 . 0 8 ,  273 and peak  q u a d r i c e p s f o r c e s o c c u r r e d d u r i n g t h e support phase as t h e s k a t e r extended  t h e s u p p o r t l e g :to d r i v e f o r w a r d w h e r e a s  maximum h a m s t r i n g s  f o r c e s were r e c o r d e d i m m e d i a t e l y  t h e commencement o f t h e s u p p o r t p h a s e . muscle,  The  before  gastrocnemius  a c t i v e o n l y a t push o f f , developed c o n s i d e r a b l y  s m a l l e r muscle  forces.  Maximum f o r c e s a c t i n g i n t h e l i g a m e n t s w e r e r e s p e c t ively  240 and 62 p o u n d s i n t h e p o s t e r i o r and a n t e r i o r c r u -  - 85  FIG.4.07  MUSCLE FOR  -  AND LIGAMENT  TRIAL  NO.4  FORCES  -  86 -  FIG. 4 . 0 8 . M U S C L E A N D L I G A M E N T  FORCES  -  8?  -  c i a t e s and 289 a n d 258 p o u n d s i n t h e m e d i a l and l a t e r a l laterals.  col-  The p o s t e r i o r c r u c i a t e l i g a m e n t was t e n s e f o r t h e  d u r a t i o n o f t h e s k a t i n g t h r u s t w i t h peak f o r c e s o c c u r r i n g a t the  onset o f t h e support phase w h i l e  were s l a c k u n t i l p u s h o f f .  the a n t e r i o r cruciates  The maximum m e d i a l  collateral  f o r c e s were r e c o r d e d a t p u s h o f f a s o p p o s e d t o p e a k collateral  forces which occurred  during  the i n i t i a l  lateral portion  o f t h e s u p p o r t p h a s e a s t h e s k a t e r moved f o r w a r d and l a t e r ally. I t i s i n t e r e s t i n g t o o b s e r v e t h a t peak  hamstrings  m u s c l e f o r c e s were c o i n c i d e n t s e q u e n t i a l l y w i t h maximum p o s terior  cruciate ligament forces  a n d maximum g a s t r o c n e m i u s  m u s c l e f o r c e s were c o i n c i d e n t w i t h maximum m e d i a l ligament forces.  On t h e o t h e r  collateral  hand, a t t h a t t i m e o f peak  quadriceps force, the c o l l a t e r a l  l i g a m e n t s were s l a c k , no  f o r c e was r e c o r d e d i n t h e a n t e r i o r c r u c i a t e l i g a m e n t and o n l y m i n i m a l f o r c e s were i n d i c a t e d i n t h e p o s t e r i o r c r u c i a t e ligament. Articular  Forces  The m a g n i t u d e o f t h e n o r m a l j o i n t the knee d u r i n g  the skating thrust i s plotted i n Fig.  The maximum v a l u e s  orded.  t h e peak v a l u e  o f Rz  i n t i m e w i t h t h e maximum q u a d r i c e p s f o r c e  The maximum v a l u e s  forces 4.2  t o 5-6  4.09.  o f Rz v a r i e d b e t w e e n 666 p o u n d s a n d 888  p o u n d s f o r t h e 15 t e s t t r i a l s w i t h coincident  f o r c e Rz a c t i n g a t  o f Rz d e v e l o p e d r e p r e s e n t  recjoint  t i m e s t h e 165 p o u n d body w e i g h t o f t h e  -.88  FIG.4.09  JOINT  -  FORCES  ACTING  AT K N E E  test  89 -  subject. The  v a r i a t i o n o f the m e d i a l - l a t e r a l  the a r t i c u l a r s u r f a c e s  shear f o r c e Rx on  o f the j o i n t i s shown i n Fig'. 4 . 0 9 .  The  shear f o r c e a c t s m e d i a l l y  the  skating  during  the support phase o f  t h r u s t but i s l a t e r a l a t push o f f .  medial and l a t e r a l  The maximum  shear f o r c e s recorded were 96 and 57  pounds r e s p e c t i v e l y . The  a n t e r i o r - p o s t e r i o r f o r c e , Ry, on the knee j o i n t  i s assumed to be e q u i l i b r a t e d "by the f o r c e s developed i n the c r u c i a t e ligaments, e i t h e r the p o s t e r i o r c r u c i a t e or the ante r i o r c r u c i a t e dependent upon the d i r e c t i o n o f the f o r c e , Ry. Fig.  3.24. The  maximum v a l u e s o f Mz,  about the l o n g a x i s o f the t i b i a ,  the torque on the j o i n t were developed d u r i n g the  support phase o f the s k a t i n g t h r u s t and were with peak quadriceps muscle f o r c e s .  coincident  A p l o t o f Mz i s g i v e n  i n F i g . 4 . 0 9 f o r T r i a l No. 4 with peak values o f torque f o r each t e s t t r i a l  g i v e n i n Table No. 3-  The maximum v a l u e s o f  torque on the j o i n t v a r i e d from 4 5 5 to 735 pound-inches and were d i r e c t e d m e d i a l l y  inward. Discussion  The tabulated  summary o f r e s u l t s as shown i n F i g . 4 . 0 8 and as i n Table No. 3 i n d i c a t e s t h a t although the c y c l i c  p a t t e r n o f muscle and ligament f o r c e s was q u i t e from t r i a l  to t r i a l ,  there was c o n s i d e r a b l e  consistent  variation i n  TABLE NO. 3 MAXIMUM MUSCLE LIGAMENT AND JOINT FORCES FOR THE SIMULATED SKATING THRUST  TR  Ph  Pq  Pg  Pp  Pa  Pm  Rz  PI  Rx  Mz  2  193-6?  618.40  118.62  165.01  6.95  2.69  36.39  843.45  54.01  486. ?8.  3  272.92  613.89  20.31  239.51  20.64  37.04  131.11  822.28  -50.95  573-90  4  144.35  6OI.38  24.55  140.86  25.03  159.69  30.89  802.06  64.54  566.34  5  100.94  506.99  50.69  111.34  21.52  17.80  202.11  707.34  61.83  521.60  6  116.42  518.75  60.81  103.25  8.30  59.48  69.95  721.24  -50-39  413:81  7  30.75  633-39  57-51  73.01  4.99  86.01  15.05  855.18  68.84  510.59  9  20.54  453.08  24.19  90.42  17.44  207.42  102.61  666 44  82.97  455.37  10  87.43  639.42  106.15  75-56  4. 74  178.71  51.06  872.22  64.53  497.96  11  74.06  545.16  29.10  86.76  9.. 28  79-13  52.68  767.69  -56.87  522.78  12  95-98  582.18  18.86  74.61  14.96  158.15  56.57  803.88  96.09  610.95  13  151.36  540.24  24.43  131.60  12.47  221.60  172.85  765.80  -61.27  590.76  14  40.08  665.52  21.59  43.99  29.99  145.26  109.83  878.11  -55-52  735.62  15  78.89  660.43  25.14  74.99  61.76  164.33  194.21  888.29  47.63  675.50  16  130.25  663.77  43.11  139.83  17.92  288.88  258.81  885.78  96- 74  700.47  17  111.01  625.56  25.34  95-57  12.81  41.50  191-53  852.17  -56.16  674.23  muscle, ligament and j o i n t forces = pounds  t  j o i n t torque = pound-inches  the peak f o r c e s r e c o r d e d . he  The  l a r g e l y a t t r i b u t e d to the  ficult  f o r the  91  test subject  -  variance  f a c t t h a t i t was  Morrison  some v a r i a t i o n i n t h e m u s c l e and  Due istic  the  required  values  l i g a m e n t f o r c e s and  extremely  (1970)  f o r simple  ( F i g . 4.02)  level  be  antagon-  considered  external force  a l s o r e f l e c t e d i n the  articular  found  walking.  of muscle f o r c e c a l c u l a t e d are  are  dif-  simulated  also  a n a l y s i s , the  c o u l d not  f o r e q u i l i b r i u m of the  T h e s e minimum v a l u e s  can  j o i n t forces of a s i n g l e  l i m i t a t i o n s of the  muscle a c t i o n s  therefore mum  when t e s t e d t w i c e  to the  results  to e x a c t l y d u p l i c a t e the  s k a t i n g t h r u s t f o r each t r i a l .  test subject  i n the  and  the  mini-  system.  values  of  forces.  Muscle Forces The explained and  the  f o r c e s developed i n the with reference  a s s u m p t i o n s made i n t h e  ment o f t h e  4.03,  skating  thrust  analysis.  initial  move-  The  forward support or t h r u s t i n g foot.  f o r c e , Fzp,  on  the  p r o d u c e s a n e g a t i v e •'.•moment Mxk  on  the knee t h a t t e n d s  extend the  joint.  a c t i o n i n the  Since  hamstrings, to s t a b i l i z e  4.02  body w e i g h t .  Fig. 3-20,  support foot, F i g .  T h i s moment a c t i o n i s r e s i s t e d by  f o r w a r d l e g assumes t h e Fig.  the  s u p p o r t f o o t i s a n t e r i o r to the knee a t t h i s p o i n t , the v e r t i c a l  be  a c t i o n s of the  s k a t i n g t h r u s t i s a s h i f t of weight from  r e a r f o o t to the the  to the  three muscle groups can  to force  t h e k n e e j o i n t as The  shows t h a t b o t h q u a d r i c e p s and  electromyogram  the of  hamstrings muscle  - 92 groups a r e a c t i v e d u r i n g quadriceps force could  t h i s phase b u t t h e magnitude o f  n o t be e v a l u a t e d  minancy o f t h e a n a l y s i s .  Since  quadriceps i s antagonistic strings,  the value  definition  -  due t o t h e i n d e t e r -  the force action of the  t o t h e f o r c e a c t i o n o f t h e ham-  o f h a m s t r i n g s f o r c e c a l c u l a t e d i s by  t h e minimum m u s c l e f o r c e r e q u i r e d  e x t e r n a l moment, Mxk.  t o balance the  The a c t u a l f o r c e a c t i n g i n t h e ham-  s t r i n g s i s e q u a l t o t h e sum o f (a)  the force action required  to resist  the external  moment, Mxk, a n d (b)  the force action required istic Since  t o balance t h e antagon-  f o r c e a c t i o n o f t h e q u a d r i c e p s on t h e j o i n t .  the e l e c t r i c a l a c t i v i t y  g r o u p s was r e c o r d e d w i t h  surface  (EMG) o f t h e m u s c l e  electrodes,  muscle a c t i v i t y w i t h i n a muscle group c o u l d defined.  individual n o t be a c c u r a t e l y  I t i spossible that the quadriceps a c t i v i t y  orded f o r t h i s cular rectus  p h a s e was due t o c o n t r a c t i o n p f t h e b i a r t i -  femoris  m u s c l e , t h e o n l y member o f t h e q u a d r i -  ceps group t h a t c r o s s e s  the h i p joint  and t h a t c a n t h e r e f o r e  flex  t h e h i p a s w e l l a s e x t e n d the. k n e e ( B a s m a j i a n ,  This  deduction agrees with  the  rec-  the analysis o f Paul  1970).  (1966) o f  function of the h i p in.walking. As  t h e s k a t e r d r i v e s f o r w a r d and t h e k n e e moves a h e a d  o f t h e s u p p o r t f o o t , F i g . 4.03> p o s i t i v e Mxk due t o t h e v e r t i c a l erior  the joint  i s subject  to a  f o r c e , F z p , and t h e p o s t -  f o r c e , F y p , on t h e f o o t , F i g . 3-20.  Since  a positive  Mxk  93 -  tends t o f l e x t h e knee, e q u i l i b r i u m i s obtained  action i n the quadriceps femoris. records,  Fig. 4.02,  Although  by f o r c e  electromyogram  i n d i c a t e t h a t b o t h q u a d r i c e p s and g a s t r o -  cnemius muscle groups a r e a c t i v e i n t h e support phase, t h e f o r c e a c t i o n o f t h e gastrocnemius muscle i sn o t considered to a f f e c t t h e knee.  Being a b i a r t i c u l a r muscle, the gastro-  c n e m i u s c a n b o t h f l e x t h e k n e e and p r o d u c e p l a n t a r of the ankle. so  short  However, t h e f i b r e s o f t h e g a s t r o c n e m i u s a r e  t h a t t h i s m u s c l e , c a n n o t f l e x t h e k n e e and p l a n t a r  f l e x the ankle muscle. the  flexion  a t t h e same t i m e b e c a u s e o f t h e s l a c k i n t h e  (Basmajian,  1970).  I t i stherefore  assumed t h a t i n  support phase o f t h e s k a t i n g t h r u s t , t h e g a s t r o c n e m i u s  r e s i s t s d o r s i - f l e x i o n a s t h e shank moves f o r w a r d o v e r t h e f o o t and d o e s n o t c o n t r i b u t e  t o f o r c e a c t i o n s a t t h e knee.  A t p u s h o f f , moment Mxk becomes n e g a t i v e a n t e r i o r f o r c e F y p o n t h e f o o t , F i g . 3*20, inertial  forces  accelerates  due t o t h e  and t h e i n c r e a s e d  o f t h e shank a n d f o o t a s t h e l o w e r  forward,  F i g . 4.04.  Since  limb  the hamstrings are  i n a c t i v e a t push o f f and t h e f o r c e a c t i o n i n t h e q u a d r i c e p s femoris the  i s assumed t o i m p a r t t h e f o r w a r d s a c c e l e r a t i o n t o  l e g , the negative  extension  moment, Myk, d e v e l o p e d a t  p u s h o f f must be e q u i l i b r a t e d b y f o r c e a c t i o n i n t h e g a s t r o cnemius muscle. and  As t h e g a s t r o c n e m i u s c a n n o t f l e x t h e k n e e  p l a n t a r f l e x the ankle  of the ankle  a t t h e same t i m e p l a n t a r  a t p u s h o f f must be due t o f o r c e  soleus muscle, t h e great  flexion  action of the  p l a n t a r f l e x o r o f the ankle  and a  -  94  -  member o f t h e t r i c e p s s u r a e m u s c l e g r o u p o f t h e l o w e r l e g . Ligament Forces The  forces  c a l c u l a t e d , i n t h e l i g a m e n t s must be c o n -  sidered, i n c o n j u n c t i o n , w i t h  the l i m i t a t i o n s of the s i m p l i f i e d 3-12  m u s c l e and l i g a m e n t system o f F i g . used t o o b t a i n The  equilibrium  conditions,  anterior-posterior forces  ligaments.  For the duration  Section  3-  a c t i n g on t h e j o i n t  w e r e assumed t o be b a l a n c e d by f o r c e s ate  and t h e e q u a t i o n s  developed i n the c r u c i -  of the skating  thrust,  e x c e p t i n g push o f f , t h e r e i s a n e g a t i v e p o s t e r i o r imposed on t h e knee, F i g . 4 . 0 6 .  Fyk,  Equilibrium  a t t h e j o i n t a r e m a i n t a i n e d by a t e n s i l e f o r c e the  posterior  c r u c i a t e , F i g . 3'24.  of t h e hamstrings muscle f o r c e on  force, conditions  developed i n  The h o r i z o n t a l  also  component  imposes a p o s t e r i o r  t h e . j o i n t w h i c h must be b a l a n c e d b y a n i n c r e a s e d  force  i n the posterior  tensile'  This explains  the c o i n c i -  dence o f peak p o s t e r i o r  cruciate ligament force  a n d maximum  hamstrings muscle force  as mentioned i n t h e r e s u l t s  illustrated the  skater  Fyk,  thrusts  forward t o push o f f , the p o s t e r i o r  on t h e j o i n t d e c r e a s e s w h i l e  the horizontal  small  anterior force  tensile  force  As force,  component  o n t h e j o i n t becomes a n t e r i o r a s t h e  j o i n t moves ahead o f t h e k n e e , F i g . 4 . 0 3 .  a small  section;  i n F i g . 4 . 0 8 , and s u m m a r i z e d i n T a b l e No. 3 '  of the quadriceps force hip  cruciate.  force  The . r e s u l t i s  o n t h e k n e e w h i c h i s b a l a n c e d by a  acting i n the anterior cruciate.  Ina l l  tests,  the p o s t e r i o r  maximum f o r c e  icular  surfaces  -  c r u c i a t e c a r r i e d the greater  o f 240  anterior cruciate.  95  a  p o u n d s c o m p a r e d t o 62 p o u n d s i n t h e The f o r c e  of f r i c t i o n acting at the art-  o f t h e j o i n t was n o t c o n s i d e r e d when c a l -  culating the cruciate  forces.  Since the femoral  r o t a t e backward on t h e t i b i a d u r i n g force  force,  the skating  condyles thrust, the  o f f r i c t i o n on t h e j o i n t i s d i r e c t e d p o s t e r i o r l y and  would t h e r e f o r e cruciate.  increase  the tensile  A s s u m i n g a v a l u e o f 0.02  f r i c t i o n i n the i j o i n t  (Rydell,  force  i n the posterior  f o rthe coefficient  1966),  of  t h e maximum f o r c e o f  f r i c t i o n w o u l d be i n t h e o r d e r o f 18 p o u n d s a c t i n g a t t h e point  i n the skating  t h r u s t when t h e n o r m a l j o i n t f o r c e i s  maximum. Medial-lateral by  tensile  joint.  forces  s t a b i l i t y o f t h e knee i s m a i n t a i n e d  acting i n the c o l l a t e r a l ligaments of the  The v a l g u s - v a r u s moment, Myk, i s r e s i s t e d by a  force  i n e i t h e r t h e m e d i a l c o l l a t e r a l o r l a t e r a l c o l l a t e r a l whenever t h e c e n t r e o f p r e s s u r e o f t h e normal j o i n t falls As  outside  the skater  the  knee j o i n t  Fzp,  f o r c e , Rz,  t h e l i m i t i n g v a l u e Xo, a s shown i n F i g .  3-26.  moves f o r w a r d o n t o t h e s u p p o r t l e g , F i g . 4.03> i s l a t e r a l with  o n t h e f o o t , F i g . 3-20,  moment, Myk, o n t h e j o i n t .  respect to the v e r t i c a l  force,  and t h i s d e v e l o p s a p o s i t i v e T h i s p o s i t i v e moment t e n d s t o  s e p a r a t e t h e l a t e r a l c o n d y l e s o f t h e j o i n t and e q u i l i b r i u m is The  achieved through a t e n s i l e  force  i n the l a t e r a l  magnitude o f t h e l a t e r a l c o l l a t e r a l f o r c e  collateral.  i s directly  , related This  to the relative  _ 6 9  -  a n g l e o f t h e shank t o t h e v e r t i c a l .  accounts f o r t h e wide range i n t e n s i l e f o r c e s  i n the l a t e r a l  collateral  Minimum v a l u e s  correspond to upright  w h i l e maximum v a l u e s  as r e p r e s e n t e d  i n T a b l e No.  to the foot.  vertical  and i n s i d e  f o r c e , F z p , o n t h e f o o t , F i g . 3*20,  ject to a negative  moment, Myk.  a signifi^  Approaching push o f f  i n t h e s k a t i n g t h r u s t , t h e k n e e moves m e d i a l l y the  J.  a n g l e s o f t h e shank  a c t when t h e k n e e i s l a t e r a l  cant degree w i t h r e s p e c t  calculated  This negative  and i s s u b -  Myk t e n d s t o  s e p a r a t e t h e m e d i a l c o n d y l e s o f t h e j o i n t and i s r e s i s t e d by a t e n s i l e force i n themedial c o l l a t e r a l . nitude the  A g a i n t h e mag-  o f t h e f o r c e i n the- m e d i a l c o l l a t e r a l  a n g l e o f t h e shank w i t h maximum v a l u e s  i s dependent on  a c t i n g when t h e  k n e e i s m e d i a l a maximum amount w i t h r e s p e c t  to the foot.  T a b l e No. 3 i n d i c a t e s t h a t when a l a r g e m e d i a l force i sdeveloped during lateral  collateral  a skating thrust, the force i n the  c o l l a t e r a l i s m i n i m a l and v i c e  versa.  P a r t o f t h e v a l g u s - v a r u s moment, Myk, may be r e s i s t e d by  the cruciates.  Brantigan  and V o s h e l l  (1941)  demonstrated  t h a t when t h e k n e e i s i n f l e x i o n some c r u c i a t e l i g a m e n t sion i s required  to assist medial-lateral i n s t a b i l i t y  j o i n t due t o a s l a c k e n i n g ever, the  F i g . 4.06  of the l a t e r a l  collateral.  o f the How-  i n d i c a t e s t h a t moment Myk i s n e g a t i v e f o r  f l e x i o n p o r t i o n o f t h e s k a t i n g t h r u s t and no f o r c e  i n t h e c o l l a t e r a l s ' d u r i n g t h i s phase, F i g . 4.08. other  ten-  acts  On t h e  h a n d some o f t h e f o r c e a t t r i b u t e d t o t h e l a t e r a l c o l -  - 97 l a t e r a l ligament i s probably carried tibial  tract.  A l s o , McCloy  as t e n s i o n i n t h e i l i o -  (1959) h a s s t a t e d t h a t i t i s  possible that a portion of the forces ascribed to the c o l l a t e r a l l i g a m e n t s may be t a k e n b y t h e q u a d r i c e p s m u s c l e g r o u p s i n c e t h e v a s t u s m e d i a l i s and v a s t u s l a t e r a l i s b l e n d orly  w i t h the c o l l a t e r a l s through  r e c t i n a c u l u m p a t e l a e and i t s ' ligament o f the j o i n t .  M o r r i s o n (1970)  force action of the l a t e r a l  lateral  f u r t h e r suggests  and m e d i a l h a m s t r i n g s These  or the state-  i f one a c c e p t s t h e t h e o r y o f s e v e r a l  such as S m i l l i e  (1951)  that tension receptors i n the  a r t i c u l a r l i g a m e n t s , when a c t i v i a t e d , p r o d u c e a r e f l e x t r a c t i o n i n t h e a s s o c i a t e d muscle groups. not been proven (1959)  that  e q u i l i b r a t e d hy d i f f e r e n -  and m e d i a l heads o f t h e g a s t r o c n e m i u s .  ments a r e n o t e w o r t h y authors  their insertion i n the  association with the capsular  t h e v a l g u s - v a r u s moment i s p a r t l y tial  posteri-  con-  This theory has  and i n f a c t i s c o n t r a d i c t e d by S t e n e r ' s  experiments  f o r the medial  c o l l a t e r a l ligament o f the  knee. Articular The  Forces j o i n t f o r c e , Rz, which  a c t s normal t o t h e a r t i -  c u l a r s u r f a c e o f t h e knee j o i n t a t t a i n s a peak v a l u e a t a p o i n t i n t h e support phase o f t h e s k a t i n g t h r u s t , F i g . 4 . 0 9 , when t h e sum o f t h e . n o r m a l  component o f t h e q u a d r i c e p s  muscle f o r c e p l u s t h e e x t e r n a l f o r c e , Fzk, i s maximal, Equation 3-17.  The maximum v a l u e o f Rz d e v e l o p e d  i n the  - 98  -  s k a t i n g t h r u s t was 888 p o u n d s o r 5 - 6 0 of t h e t e s t  t i m e s t h e body  weight  subject.  Test r e s u l t s i n d i c a t e that during  the support  phase  of t h e s k a t i n g t h r u s t t h e centre o f pressure o f j o i n t Rz, i s p o s i t i o n e d shifts  initially  to the l a t e r a l  force,  over t h e medial condyles but then  condyles a t push o f f , F i g . 4 . 1 0 .  Since  t h e m e d i a l c o n d y l e h a s a l a r g e r a n a t o m i c a l b e a r i n g a r e a compared  condyle, F i g . 3.02,  to the l a t e r a l  i tfollows that the  compressive s t r e s s imposed a t t h e m e d i a l a r t i c u l a r of the j o i n t  i s smaller  cular surface.  Also,  surface  than the stress o f the l a t e r a l  as M o r r i s o n (1970)  has noted,  arti-  the stres-  s e s a c t i n g i n t h e s h a f t o f t h e t i b i a w o u l d be l o w e r o n t h e medial s i d e because t h e medial condyle overhangs t h e s h a f t o f the t i b i a l e s s than t h e l a t e r a l The tively  condyle.  '  s i d e o r . s h e a r f o r c e , Rx, o n t h e j o i n t  small,  a p p r o x i m a t e l y 0.10  normal a r t i c u l a r  i s rela-  times t h e magnitude o f t h e  f o r c e , Rz, F i g . 4 . 0 9 .  The m e d i a l o r l a t e r a l  movement o f t h e f e m u r o n t h e t i b i a i s c o n s i d e r e d t o be r e s isted  by t h e t i b i a l  force  between t h e c o n d y l e s and by t e n s i o n  structures  intercondylar  (Brantigan  t o move l a t e r a l l y  and V o s h e l l ,  eminence, by a f r i c t i o n  1941).  on t h e t i b i a d u r i n g  the s k a t i n g t h r u s t and m e d i a l l y  i n the ligament The f e m u r  tends  t h e support phase o f  a t push o f f .  The m a g n i t u d e a n d d i r e c t i o n o f t h e a n t e r i o r - p o s t e r i o r f o r c e , Ry, o n t h e j o i n t in  i s r e f l e c t e d by t h e f o r c e s  the cruciate ligaments.  For the greater  acting  portion of the  skating  thrust  t h e femur t e n d s t o g l i d e f o r w a r d on t h e t i b i a  and i s c o n t r o l l e d cruciate forced  by a t e n s i o n  ligament, F i g . 4.08.  previously,  A t push o f f t h e femur i s  i nthe anterior  and t h i s m o t i o n i s  cruciate.  d i r e c t i o n were n e g l e c t e d .  Torque Fig.  4.09 i n d i c a t e s  a p o s i t i v e i n w a r d t o r q u e , Mz, ,  v  on t h e knee d u r i n g t h e s k a t i n g  produces medial r o t a t i o n o f the t i b i a r e s i s t e d by t h e c o l l a t e r a l l i g a m e n t s . A c c o r d i n g t o M o r r i s o n (1970)  thrust.  on i n t a c t knee  b a l a n c e d by t e n s i o n  (Steindler,  therefore  1955)  f i b r e s o f the medial (1941)  dem-  j o i n t s that medial r o t a t i o n i s  i na tightening  ment a n d t h e c r u c i a t e s  torque  on t h e femur w h i c h i s  c o l l a t e r a l l i g a m e n t w h i l e B r a n t i g a n and V o s h e l l onstrated  This  an inward torque on t h e j o i n t  i s r e s i s t e d by t h e o b l i q u e p o s t e r i o r  lateral  collateral liga-  as they t w i s t on themselves.  I t i s  a p p a r e n t t h a t moment a c t i o n , Mz, a b o u t t h e l o n g  a x i s o f t h e t i b i a must be b a l a n c e d b y f o r c e a r t i c u l a r l i g a m e n t s and w i l l ligament forces  as c a l c u l a t e d  1970) t h a t  actions  i n the  a l t e r the d i s t r i b u t i o n o f the i nthe analysis.  suggested by c e r t a i n a u t h o r s ( S t e i n d l e r , Paul,  As s t a t e d  the effects of f r i c t i o n i nthe j o i n t i n the  anterior-posterior  acting  developed i n the p o s t e r i o r  backward r e l a t i v e t o t h e t i b i a  r e s i s t e d by t e n s i o n  Joint  100 -  I t i s also  1965; R a d i n and  t h e m e n i s c i and t e n s o r f a s c i a l a t a e  r e s i s t i n g t h e e f f e c t s o f a t o r q u e on t h e knee  joint.  aid i n  Forces  101  a t t h e Knee i n V a r i o u s The  relative  preceding  -  Activities  results reveal l i t t l e  s t r a i n imposed on t h e l i g a m e n t s  knee s i n c e t h e a c t u a l t e n s i l e characteristic  concerning the  and m u s c l e s o f t h e  s t r e n g t h and s t r e s s - s t r a i n  o f human l i g a m e n t  and m u s c l e t i s s u e h a s n o t  been e x p e r i m e n t a l l y determined t o t h i s date.  Considerable  r e s e a r c h h a s b e e n done by T i p t o n a n d a s s o c i a t e s and  Zuckerman (1969.  animals  1973)  but i t i s d i f f i c u l t  (1967,  1975)  on t h e s t r e n g t h o f l i g a m e n t s i f not impossible  to relate  r e s u l t s t o t h e s t r e n g t h o f human l i g a m e n t o u s t i s s u e . f o r e we a r e f o r c e d t o e v a l u a t e ent  study  other  The  (Morrison,  mean maximum m u s c l e a n d l i g a m e n t  i n T a b l e No. 4 .  t h e mean o f f i v e for walking  trials  represent  Upon e x a m i n a t i o n  studies f o r  forces calculated activities  The p e a k s k a t i n g f o r c e s  of the tabulated r e s u l t s ,  test  subjects.  i t i s apparent  t h a t t h e maximum f o r c e s d e v e l o p e d i n t h e c o l l a t e r a l collateral,  ligaments,  are s i g n i f i c a n t l y  g r e a t e r d u r i n g a s k a t i n g t h r u s t a s compared t o l e v e l clined walking.  represent  on a s i n g l e s u b j e c t w h i l e t h e f o r c e s  t h e mean f r o m t h r e e  i n p a r t i c u l a r the medial  There-  1969)  f o r t h e s k a t i n g t h r u s t and f o r v a r i o u s w a l k i n g are l i s t e d  these  the s i g n i f i c a n c e of the pres-  "by c o m p a r i s o n w i t h r e s u l t s o f s i m i l a r  activities.  from  or i n -  The a n t e r i o r c r u c i a t e f o r c e f o r t h e s k a t i n g  t h r u s t i s comparable t o t h a t developed i n l e v e l w a l k i n g b u t only 0.3  times  the t e n s i l e  c r u c i a t e when w a l k i n g  force acting i n the anterior  down a n i n c l i n e d ramp.  The f o r c e  acting i n the posterior cruciate during the skating thrust i s  102  -  -  TABLE NO. 4 THE MAXIMUM MUSCLE AND LIGAME'NT FORCES OF VARIOUS A C T I V I T I E S  Muscle Force , l b s Ligament Force, l b s Activity H  Q  G  pc  ac  mc  1c  309  191  262  79  38  17  50  W a l k 1 ng\" Up V R amp  240  176  335  144  15  16  158  W a l k i n g Down Ramp  189  430  -  59  100  19  62  W a l k i n g Up S t a i r s  177  433  79  273  6  9  156  88  380  155  101  21  19  179  652  79  164  32  212  Level  Walking  W a l k i n g Down S t a i r s Skating  Thrust  .posterior  quadriceps  ac  anterior  G  gastrocnemius  mc  medial  lc  lateral  80 204  PC Q  .  cruciate cruciate  collateral collateral  twice  as great  as t h e f o r c e  -  for l e v e l walking but l e s s  the p o s t e r i o r c r u c i a t e f o r c e stairs.  103  c a l c u l a t e d when w a l k i n g up  The p e a k m u s c l e f o r c e  652  f o r the skating thrust,  p o u n d s i n t h e q u a d r i c e p s , i s d o u b l e t h e maximum m u s c l e recorded i n l e v e l walking,  than  force  309 p o u n d s i n t h e h a m s t r i n g s .  A d i r e c t comparison o f a c t i v i t i e s suggests that the s k a t i n g t h r u s t i s comparable t o w a l k i n g u p s t a i r s i n t h a t t h e q u a d r i c e p s muscle group e x e r t s case, while  the forces  t h e maximum f o r c e  a c t i n g i n t h e g a s t r o c n e m i u s a n d ham-  s t r i n g s m u s c l e g r o u p s a r e much s m a l l e r . forces  i n each  However, t h e l a r g e  d e v e l o p e d i n t h e q u a d r i c e p s m u s c l e g r o u p and t h e  c o l l a t e r a l ligaments during  a s k a t i n g t h r u s t makes i t u n i q u e  when c o m p a r e d t o e i t h e r s t a i r o r ramp Peak a r t i c u l a r  forces  walking.  i n c l u d i n g j o i n t torque  a t t h e k n e e f o r t h e s k a t i n g t h r u s t and t h e v a r i o u s activities No.  5-  five  studied  by M o r r i s o n ( 1 9 6 9 ) a r e l i s t e d  on a s i n g l e s u b j e c t  t h e maximum mean f r o m t h r e e  i n Table  or v e r t i c a l skating,  f o r t h e s k a t i n g t h r u s t and  test subjects  f o rthe walking  From T a b l e No. '5 i " t i s e v i d e n t  activities.  t h a t t h e normal  j o i n t f o r c e , Rz, i s s i g n i f i c a n t l y  5-^8  larger f o r  t i m e s b o d y w e i g h t compared t o 4 . 2 5  w e i g h t f o r w a l k i n g u p s t a i r s and 3 . 4 0  t i m e s body  t i m e s body w e i g h t f o r  walking. Probably the severest  during  walking  A g a i n t h e s e r e s u l t s r e p r e s e n t t h e maximum mean o f  trials  level  acting  force  imposed o n t h e knee  the skating thrust i s the j o i n t torque.  joint  I n the skating  - 104 TABLE NO. 5 MAXIMUM JOINT FORCES AND TORQUES OF VARIOUS A C T I V I T I E S  Max. J o i n t  Activity  Rz/bw  Force Rx/bw  Mz lb-ins  3.40  0.26  239  W a l k i n g Up Ramp  3-97  -  -  W a l k i n g Down Ramp  3-95  -  -  W a l k i n g Up S t a i r s  4.25  0.89  -  W a l k i n g Down S t a i r s  3.83  Skating Thrust "  5.48  Level  Walking  -  0.51  Rz/bw  R a t i o normal  Rx/bw  Ratio  s h e a r f o r c e t o body  Mz. . .  Joint  torque  -  696  j o i n t f o r c e t o body weight  weight  -  10'5 -  t h r u s t a mean maximum t o r q u e o f 696 p o u n d - i n c h e s was d e v e l o p e d c o m p a r e d t o a maximum o f 239 p o u n d - i n c h e s f o r l e v e l This  l a r g e t o r q u e on t h e j o i n t has s e r i o u s  when i t i s c o n s i d e r e d vertical the  joint  implications  t h a t t h e maximum v a l u e s  o f t o r q u e and  f o r c e a c t a t t h e same p o i n t i n t i m e  skating thrust, Fig.  4.09.  walking.  during  -  106  -  CHAPTER V SUMMARY AND The  CONCLUSIONS  k n e e i s p r o b a b l y s u b j e c t t o more s t r e s s and. s t r a i n  t h a n a n y o t h e r j o i n t o f t h e body. i s m a i n t a i n e d by t h e l i g a m e n t o u s articular and  cartilage  femur.  thrust,  The s t a b i l i t y o f t h e k n e e structure of the j o i n t , the  and t h e bone a r c h i t e c t u r e o f t h e t i b i a  D u r i n g an a t h l e t i c  movement s u c h a s t h e s k a t i n g  c o n t r a c t i l e muscle f o r c e s p l u s e x t e r n a l f o r c e s o f  r e a c t i o n impose a c o n s i d e r a b l e s t r e s s on t h e knee. f o r c e s a r e n e c e s s a r i l y b a l a n c e d by t h e a r t i c u l a r the to  j o i n t and by t h e t e n s i l e prevent r e l a t i v e The  tude  f o r c e s developed  surfaces of  i n the ligaments  displacements of the j o i n t .  p r e s e n t s t u d y was d e s i g n e d  and t e m p o r a l  sequence o f muscle,  to determine  One m a l e t e s t  s u b j e c t , an accomplished  made 15 s i m u l a t e d s k a t i n g t h r u s t s .  t h e magni-  l i g a m e n t and a r t i c u l a r  f o r c e s a c t i n g a t t h e knee j o i n t d u r i n g a s i m u l a t e d thrust.  These  skating  hockey p l a y e r ,  The r e a c t i o n f o r c e s and  p o i n t o f a p p l i c a t i o n o f t h e s e f o r c e s d u r i n g t h e t h r u s t were recorded with the K i s t l e r force plate at the l a b o r a t o r y of the U n i v e r s i t y o f Washington. each and  trial  A synchronized cine f i l m record of  was o b t a i n e d f r o m  l a t e r a l planes.  16 mm f i l m i n b o t h t h e f r o n t a l  Electromyographic' data f o r the three  main muscle groups (hamstrings, gastrocnemius  and q u a d r i c e p s )  -  active during conducted  and  -  t h e s k a t i n g t h r u s t was o b t a i n e d  on-ice  Columbia.  107  from  tests  and o f f - i c e a t t h e U n i v e r s i t y o f B r i t i s h  A n t h r o p o m e t r i c d a t a a f t e r Dempster (1955)>  Fischer  (I889)  and M o r r i s o n  (1968)  g r a v i t a t i o n a l limb  forces while  a c c e l e r a t i o n data determined  from the d i g i t i z e d  f i l m r e c o r d s was u s e d t o c a l c u l a t e  inertial  forces.  allowed  Braune  calculation of  U s i n g D'Alembert's p r i n c i p l e o f e q u i l i -  brium of bodies i nmotion, the j o i n t forces  and moments a t  the knee were d e t e r m i n e d from t h e f o r c e p l a t e r e a c t i o n limb  gravitational forces  forces  and l i m b  inertial  forces,  f o r c e s . . The  i n e a c h m u s c l e g r o u p and l i g a m e n t were d e t e r m i n e d  from the c a l c u l a t e d e x t e r n a l and  limb  the required Results  force  system a c t i n g a t t h e knee  s t a b i l i t y conditions  showed t h a t f o r c e  i n the hamstrings to s t a b i l i z e  of the joint.  a c t i o n developed  initially  t h e j o i n t as t h e s k a t e r  s h i f t e d h i s weight t o the support l e g .  As t h e s u p p o r t l e g  assumed t h e b o d y w e i g h t , p o w e r f u l f o r c e a c t i o n d e v e l o p e d i n the  q u a d r i c e p s muscle t o e x t e n d t h e knee and d r i v e t h e s k a t e r  forward past the support foot. small  force  to plantar  The g a s t r o c n e m i u s e x e r t e d  a  f l e x o r extend the ankle f o r the.  f i n a l push o f f t h a t i s c h a r a c t e r i s t i c o f a l l accomplished skaters.  The p o s t e r i o r c r u c i a t e l i g a m e n t d e v e l o p e d  tension  i n o r d e r t o r e s i s t t h e a n t e r i o r d i s p l a c e m e n t o f t h e femur r e l a t i v e to the t i b i a during force The  as t h e s k a t e r  forces  the thrust reaching  a maximum  s h i f t e d h i s weight to the support  d e v e l o p e d i n t h e a n t e r i o r c r u c i a t e were  foot.  relatively  small  108  -  and u n i m p o r t a n t i n t h e s k a t i n g t h r u s t .  Tensile  d e v e l o p e d i n t h e c o l l a t e r a l l i g a m e n t s was r e q u i r e d medio-lateral  s t a b i l i t y w i t h t h e peak l a t e r a l  force  to assure  collateral  f o r c e s d e v e l o p e d a t t h e o n s e t o f t h e s u p p o r t p h a s e and m a x i mum m e d i a l c o l l a t e r a l extension  forces developed during  o f the l e gthrough push o f f .  Although the current the  the f i n a l  relative  stability  i n v e s t i g a t i o n c a n n o t comment o n  o f t h e k n e e i t c a n be s t a t e d t h a t t h e  j o i n t i s most s u s c e p t i b l e t o i n j u r y  i n s k a t i n g when t h e e x -  t e r n a l f o r c e s and t o r q u e s o f a t h l e t i c imposed on t h e c r i t i c a l  values  competition  a r e super-  o f l i g a m e n t and a r t i c u l a r  f o r c e s d e v e l o p e d by t h e t h r u s t i t s e l f .  I t therefore  t h a t t h e l a t e r a l c o l l a t e r a l l i g a m e n t w o u l d be m o s t tible •while the  to a tensile  strain  d r i v e s forward a t push o f f .  d e n c e o f a maximum j o i n t f o r c e , joint  suscep-  a t t h e onset o f t h e s u p p o r t phase  t h e m e d i a l c o l l a t e r a l i s most v u l n e r a b l e  skater  appears  Also,  to injury  as  the c o i n c i -  s i x t i m e s body w e i g h t , and a  t o r q u e a p p r o a c h i n g 700 p o u n d - i n c h e s d u r i n g  phase p l a c e d  a considerable  of the j o i n t  and t h e ; j o i n t m e n i s c i .  the support  s t r e s s oh the a r t i c u l a r  surfaces  Damage t o t h e m e n i s c i  o f t h e k n e e i n t h e f o r m o f t e a r i n g i s a common i n j u r y  i n the  game o f i c e h o c k e y . The  m a g n i t u d e o f t h e m u s c l e , l i g a m e n t and j o i n t  f o r c e s d e v e l o p e d i n t h e s k a t i n g t h r u s t were greater  than respective  forces  exerted  during  significantly level  walking  '.while t h e c y c l i c p a t t e r n o f t h e s k a t i n g f o r c e s was c o m p a r a b l e  -  109  -  to w a l k i n g u p s t a i r s i n d i c a t i n g a temporal s i m i l a r i t y i n these a c t i v i t i e s . Conclusions The  f o l l o w i n g s t a t e m e n t s a r e made w i t h r e s p e c t t o t h e  biomechanics (1)  The  of the s k a t i n g  thrust.  q u a d r i c e p s a r e t h e most i m p o r t a n t m u s c l e  i n the s k a t i n g t h r u s t d e v e l o p i n g c o n t r a c t i l e of  t h e o r d e r o f 700  group forces  p o u n d s when e x t e n d i n g t h e k n e e  joint. (2)  The  h a m s t r i n g s and g a s t r o c n e m i u s m u s c l e  e x e r t f o r c e s l e s s t h a n 200  groups  100  p o u n d s and  pounds  r e s p e c t i v e l y t o s t a b i l i z e the knee d u r i n g the s h i f t and p u s h o f f p h a s e s o f t h e s k a t i n g (3)  c o l l a t e r a l l i g a m e n t s and t h e p o s t e r i o r  are  important i n m a i n t a i n i n g s t a b i l i t y of the  and  tensile  these (4)  thrust.  The  The of  f o r c e s i n e x c e s s o f 250  weight  cruciate joint  pounds a c t i n  structures.  knee j o i n t i s s u b j e c t to the combined a joint force  s i x t i m e s body w e i g h t and  t o r q u e a p p r o a c h i n g 700  pound-inches  effects, a  joint  superimposed  upon each o t h e r d u r i n g the s u p p o r t phase o f the skating (5)  thrust.  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K i n e m a t i c s o f n o r m a l l o c o m o t i o n f r o m TV d a t a . J . Biomechanics. 7:479Z u c k e r m a n , J . and S t u l l , G. A. I 9 6 9 . Effects o f exercise on k n e e l i g a m e n t s e p a r a t i o n f o r c e i n r a t s . J . Applied Physiology. 26:716-719. 1973Ligamentous s e p a r a t i o n f o r c e i n r a t s as i n f l u e n c e d b y t r a i n i n g , d e t r a i n i n g and cage r e s t r i c t i o n . M e d i c i n e and S c i e n c e i n S p o r t s .  -  117  -  APPENDICES  -  118 -  APPENDIX  ANTHROPOMETRIC  A  MEASUREMENTS  -  119  -  APPENDIX A ANTHROPOMETRIC MEASUREMENTS 1.  Body Segment P a r a m e t e r s The f o l l o w i n g b o d y segment p a r a m e t e r s r e p r e s e n t t h e  average o f f i v e Segment  i n d e p e n d e n t measurements.  Circumference,  in  Radius, i n  Length, i n  shank  14. 50  2.  foot  13.  2.07  ankle  12.80  2.02  -  knee  15.30  2.43  -  30  r a d i u s o f segment = c i r c u m f e r e n c e  31  16.50 10.50  of limb  2 it«  The l e n g t h o f a segment was m e a s u r e d joint at  c e n t r e and t h e c i r c u m f e r e n c e  the, j o i n t  2.  centre to  o f a segment was m e a s u r e d  c e n t r e a n d c e n t r e o f g r a v i t y o f t h e segment.  C a l c u l a t i o n o f Segment W e i g h t s Dempster  (1955)  expressed  segment a s a p e r c e n t a g e measurements  the weight  of the t o t a l  o f e a c h "body  body w e i g h t , b a s e d o n  f r o m l i v i n g male s u b j e c t s o f v a r i o u s body  and a g e . Test  from j o i n t  s u b j e c t body w e i g h t  = 165 l b s  types  -  120  -  D e m p s t e r fo  Weight l b s  thigh  9.65  16.00  shank  4.50  7.43  foot  1.40  2.31  Segment  segment w e i g h t 3.  Centre  = D e m p s t e r fo x b o d y  o f G r a v i t y o f Body  Dempster determined of  weight  Segments  t h e d i s t a n c e o f t h e mass c e n t r e  e a c h b o d y segment f r o m t h e p r o x i m a l end e x p r e s s e d  as a  p e r c e n t o f t h e l e n g t h o f t h e segment Segment  Length,  D e m p s t e r fo  in  Centre G r a v i t y , i n  shank  16.5  0.433  7-15  foot  10.5  0.429  ^.50  d i s t a n c e o f e.g. f r o m p r o x i m a l end o f segment = D e m p s t e r fo x segment l e n g t h In  the case o f the f o o t ,  the centre of g r a v i t y  at  the i n t e r s e c t i o n of a v e r t i c a l  to  t h e h e e l - and a l i n e  l i n e 4.50 inches proximal  j o i n i n g the ankle a x i s to the b a l l o f  the  foot.  4.  Moment o f I n e r t i a o f Segment The mass moment o f i n e r t i a  equal to the product  lies  ( I ) o f a body segment i s  o f t h e s e g m e n t ' s mass and t h e r a d i u s o f  gyration  121  ( r ) o f t h e segment.  determined  (I889)  B r a u n e and. F i s c h e r  c o - e f f i c i e n t s to allow  c a l c u l a t i o n of the radius  o f g y r a t i o n o f a segment. Segment  Length,  i n  Diameter,  i n  rx  ry  rz  shank  16.5  4,62  0.25  O.35  4.13  ^.13  1-62  foot  10.5  4.14  0.30  O.35  1.45  3.15  3.15  radius C^is  of gyration  the F i s c h e r  rotation dicular radius  about  ( r ) i s expressed i n inches  c o e f f i c i e n t f o r the radius  of gyration f o r  t h e a x i s t h r o u g h t h e mass c e n t r e and p e r p e n -  to the l o n g i t u d i n a l of gyration =  a x i s o f t h e segment  x length  o f segment  For r o t a t i o n  o f t h e segment a b o u t  F i s c h e r used  t h e c o e f f i c i e n t C^ a n d t h e d i a m e t e r o f t h e s e g -  ment t o c a l c u l a t e radius Segment  the radius  of gyration = Weight,  the l o n g i t u d i n a l  axis,  of gyration  x d i a m e t e r o f segment lbs  Ix  Iy  Iz  shank  7-^3  3-92  3-92  0.60  foot  2.31  0.15  0.71  O.71  moment o f i n e r t i a and  is  ( I ) = mass o f segment x ( r a d i u s o f p  expressed i n s l u g - i n  gyration)  -  122  -  The c o e f f i c i e n t s o f F i s c h e r a n d D e m p s t e r a r e t a k e n f r o m a r e v i e w o f body segment p a r a m e t e r s b y D r i l l i s , and  B l u e s t e i n (1964)  5.  Anthropometric  Contini  Scaling Factors  S c a l i n g f a c t o r s were r e q u i r e d t o o b t a i n t h e t e s t s u b j e c t ' s c o - o r d i n a t e s o f m u s c l e and l i g a m e n t  attachment  from t h e . . r e s p e c t i v e b a s i c c o - o r d i n a t e s o f M o r r i s o n as l i s t e d in  Table  No. 1 o f t h e t e x t .  The d i m e n s i o n s  used t o o b t a i n  the s c a l i n g f a c t o r s f o r t h e knee a r e , X - the breadth lateral  c o n d y l e s measured from t h e  epicondyle to the medial  Y - t h e depth terior  of the femoral  condyle  o f t h e f e m o r a l c o n d y l e s measured from t h e an-  surface of the l a t e r a l  surface of the medial  condyle  to the p o s t e r i o r  condyle.  Z - t h e l e n g t h o f t h e t i b i a measured from t h e c e n t r e o f t h e knee j o i n t  to the centre of the ankle  joint.  F o r t h e p e l v i s a common s c a l i n g d i m e n s i o n for  was u s e d  male s u b j e c t s .  X - t h e d i s t a n c e between t h e a n t e r i o r s u p e r i o r i l i a c  spines  of the p e l v i s Therefore,  a common s c a l i n g f a c t o r i s c a l c u l a t e d f o r  the p e l v i s which i s a p p l i e d t o t h e three c o - o r d i n a t e s o f  muscle attachment  at the  123  -  pelvis.  Joint  Co-ordinate  knee  X  3.50  3-78  1.07  knee  Y  3.55  3.64  1.03  knee Z  Z  16.00  16.16  1.01  pelvis  X  8.70  Scaling Basic  Dimension Subject  Scaling  8. 20  Factor  0.94  s c a l i n g dimensions expressed i n inches s c a l i n g f a c t o r = dimension from t e s t s u b j e c t b a s i c dimension from d i s s e c t i o n The  c o - o r d i n a t e of a muscle or ligament attachment  the s k e l e t o n o f the t e s t s u b j e c t i s then c o n s i d e r e d to t h e b a s i c d i m e n s i o n as m e a s u r e d f r o m d i s s e c t i o n by t h e a p p r o p r i a t e s c a l i n g f a c t o r .  multiplied  F o r example the Xs  o r d i n a t e of the p a t e l l a r ligament attachment to the Xsq, i s c a l c u l a t e d  as  follows  Xsq = (Xs c o - o r d i n a t e measured) x  (scaling factor i n dissection)  be  Co-  tibia,  to  - 124 -  APPENDIX B INSTRUMENTATION  \  -  125  -  APPENDIX B INSTRUMENTATION 1.  F i l m i n g Equipment Two  c a m e r a s were r e q u i r e d  d a t a i n the 16  mm  ,  two  Locam:  motor  driven  internal mm  Bolex:  spring  f o r a t i o n s was  film  speed  pulse  light  loaded  set f i l m Kodak 4X  cinematographic  p l a n e s o f movement.  adjustable  16  to o b t a i n  speeds "  Reversal  320  ASA  f i l m w i t h d o u b l e edge p e r -  used w i t h both cameras. A 35  F i l m i n g s p e e d was  mm  Tektronix  c a m e r a and  a 35  c a m e r a were u t i l i z e d  to record  the  oscilloscope  frames/sec.  of the 2.  force plate  stored  mm  64  Nikkormat traces  output.  Data Reduction The  Vanguard M o t i o n A n a l y z e r  of the  Institute  Animal Resourses (I.A.R.E.) capable of r e a d i n g s nearest data.  0.001  i n c h was  u s e d t o r e d u c e c i n e m a and  to  of the  force  plate  3.  126  -  Electromyography B i p o l a r e l e c t r o d e s p l a c e d o n t h e b e l l y o f two  g r o u p s were c o n n e c t e d t o s e p a r a t e c h a n n e l s o f a Sanborn Recorder. muscle  groups  T h i s allowed the e l e c t r i c a l  t o be m o n i t o r e d  muscle  two-channel output of  s i m u l t a n e o u s l y as a t r a c e  two on  paper. paper  speed  - 100 mm/sec  g a i n - same f o r b o t h 4.  Force Measuring  channels Platform  The m u l t i - c o m p o n e n t d e s i g n e d by t h e K i s t l e r  m e a s u r i n g p l a t f o r m Type 9261A  Instruments i s a p i e z o e l e c t r i c  trans-  d u c e r w h i c h m e a s u r e s any f o r c e a p p l i e d t o i t i n t h r e e o r t h o g o n a l components.  I n a d d i t i o n t h e moment a p p l i e d t o t h e  p l a t f o r m and t h e c o - o r d i n a t e s o f t h e p o i n t o f a p p l i c a t i o n  of  the  f o r c e are recorded.  are  f i t t e d t o t h e c o r n e r s o f t h e p l a t f o r m w h i c h has a h i g h  rigidity  Four q u a r t z force-measuring-elements  a l l o w i n g o p e r a t i o n w i t h a minimum a  measuring  d i s p l a c e m e n t as w e l l a s a w i d e f r e q u e n c y r a n g e . The  electrical  c h a r g e s y i e l d e d by t h e p l a t f o r m  s t r i c t l y p r o p o r t i o n a l t o t h e m e a s u r a n d s ; by means o f a m p l i f i e r s they are converted i n t o t h e n c a n be r e c o r d e d , i n d i c a t e d required. six  are charge  a n a l o g dc v o l t a g e s ,  or otherwise processed  I n o u r c a s e t h e f o r c e p l a t e o u t p u t was  which as  stored  as  s e p a r a t e s t o r a g e t r a c e s on t h r e e d u a l c h a n n e l T e k t r o n i x  oscilloscopes.  -  127  -  K1STLER F O R C E P L A T F O R M ON P I E Z O E L E C T R I C E F F E C T OUARTZ CRYSTALS  BASED OF  - 128 -  I  (  APPENDIX C DATA REDUCTION  -  129 -  APPENDIX C DATA REDUCTION 1.  Cinema S c a l i n g F a c t o r s A s u r v e y o r ' s r a n g e p o l e was u t i l i z e d a s t h e r e f e r e n c e  image i n d e t e r m i n a t i o n o f t h e X a n d Y s c a l i n g f a c t o r s f o r reduction of cine film Co-ordinate  data.  Image, i n  Actual, i n  Scaling Factor  X  6.396  72.00  10,38  Y  5.592  72.00  12.88  The c a l c u l a t e d  s c a l i n g f a c t o r s represent the average  o f t e n measurements s c a l i n g f a c t o r = a c t u a l l e n g t h o f range p o l e image l e n g t h o f r a n g e p o l e 2.  Force P l a t e Data  Reduction  The s y n c h r o n i z e d  f o r c e p l a t e t r a c e s , recorded on  § 5 mm f i l m ,  were d i g i t i z e d  traces into  50 d i v i s i o n s c o r r e s p o n d i n g  the  by h o r i z o n t a l l y i n c r e m e n t i n g t h e t o t h e 50 f r a m e s o f  16 mm f i l m r e c o r d t h a t d e s c r i b e d t h e s k a t i n g t h r u s t .  The a c t u a l v a l u e s o f t h e o u t p u t c o m p o n e n t s were d e t e r m i n e d hy a p p l y i n g t h e f o r c e p l a t e and o s c i l l o s c o p e c a l i b r a t i o n f a c t o r s t o each o f t h e v e r t i c a l  c o - o r d i n a t e s d e f i n e d by t h e  50 h o r i z o n t a l d i v i s i o n s .  130 -  The c a l i b r a t i o n f a c t o r s f o r t h e  o u t p u t v a r i a b l e s i n terms o f measurand u n i t s p e r v e r t i c a l d i v i s i o n are, Variable  Force  Fx  100  N/V  X  2 V/div.  =  200, N / d i v .  Fy  100  N/V  X  1 V/div.  =  100 N / d i v .  Fz  100  N/V  X  5 V/div.  =  500 N / d i v .  Mz  100  Nm/V  X  0.02V/div.  =  2 Nm/div.  Ax  .5 Cm/V  X  0.5  V/div.  = 2.5 cm/div.  Ay  5 Cm/V  X  0.5  V/div.  = 2.5 cm/div.  Plate  Oscilloscope  i : N (Newton) = 0.2248 l b s 1 Nm (Newton-meter) = (0.2248 x 39-37)  lb-ins  1 cm (centimeter) = O . 3 9 3 7 i n F x = (200) (0.2248)  = 44.96 lb/div,.  F y = (100)(0.2248)  = 22.48 l b / d i v .  F z = (500)(0.2248)  =112.40  Mz = (2)(0.2248 x 39-37)  = 15-50 l b - i n / d i v .  Ax = (2.5) (0.,3937)  = 0.984 i n / d i v .  Ay = (2.5)(0.3937)  = 0.984 i n / d i v  lb/div.  M.U-./div.  -  131 -  APPENDIX D LIMB AND JOINT CO-ORDINATES  - 132 -  APPENDIX D LIMB AND JOINT CO-ORDINATES 1.  Orthogonal  Co-ordinates  The l i m b and j o i n t c o - o r d i n a t e s were d e t e r m i n e d  with  r e s p e c t t o t h e c e n t r e a x i s o f t h e f o r c e p l a t f o r m and f o r t h e f o l l o w i n g s i g n convention. X - p o s i t i v e medial  to centre of platform  Y - positive  forward  Z - positive  above p l a t f o r m  The o r t h o g o n a l are  ( i n inches)  of centre of platform  c o - o r d i n a t e s o f t h e l i m b s and j o i n t s  shown i n F i g . DI f o r t h e k n e e a h e a d o f and m e d i a l  centre axis of the force platform.  Ygf i  FIG.  DI  Xgf  i  LIMB AND JOINT CO-ORDINATES  to the  The o r t h o g o n a l  133  -  c o - o r d i n a t e s o f F i g . DI r e p r e s e n t t h e  c o - o r d i n a t e s o f t h e j o i n t c e n t r e o f t h e knee and a n k l e and t h e mass c e n t r e o f t h e shank a n d f o o t .  These  co-ordinates  were d e t e r m i n e d b y c o r r e c t i n g t h e c o - o r d i n a t e s o f l i m b and joint 2.  s u r f a c e m a r k e r s f o r l i m b a n g l e and l i m b  A n g u l a r Limb  radius.  Co-ordinates  The a n g u l a r  limb co-ordinates  expressing limb  were d e t e r m i n e d f r o m t h e c o - o r d i n a t e s  of the j o i n t  angles  surface  markers. The a n g u l a r and  c o - o r d i n a t e s f o r r o t a t i o n o f t h e shank  f o o t w i t h r e s p e c t t o t h e X a x i s i s shown i n F i g . D2.  ( Yk,Zk)  DYS= Yk-Ya DZS= Zk-Za DZS DYF= Yt-Ya DZF = Za-Zt ( Ya,Za)  ( Yt.Zt)  FIG. 9XS  D2  = arctan  ANGULAR LIMB CO-ORDINATES DYS DZS  9XF  = arctan  'DYF DZF  -  134  -  (Xk,Zk)  DXS=Xk-Xa DZS = Zk-Za DZS DXF = X a - X t DZF= Z a - Z t  (Xa,Za) (Xt,Zt)  FIG. 9YS  Fig.  axis,  D3.  9 Y F = arctan  co-ordinate  9 Y F , was d i r e c t l y  The a n g u l a r  longitudinal  ANGULAR LIMB CO-ORDINATES  = arctan  The a n g u l a r tudinal  D3  axis,  ^||  o f t h e f o o t about i t s l o n g i d e t e r m i n e d a s shown above i n  c o - o r d i n a t e o f t h e shank a b o u t i t s  9 Z S , was c a l c u l a t e d  from a knowledge o f  t h e r a d i u s o f t h e shank and t h e l o c a t i o n o f t h e mass  centre  m a r k e r o f t h e shank a s shown i n F i g . D4. Angular co-ordinate the f o o t t h e v e r t i c a l 9ZF  axis  9 Z F represents  the r o t a t i o n o f  and i s c a l c u l a t e d  as  = arctan  The a n g u l a r  r o t a t i o n of the thigh  about t h e X and Y  135 a x e s were c a l c u l a t e d GXT = a r c t a n  DYT DZT  9YT = arctan  DXT DZT  -  as f o l l o w s  Rs - r a d i u s  of  YSA-anterior  shank c o - o r d i n a t e of s h a n k  YSP-posterior YS  c o - o r d i n a t e of  - co-ordinate  DYS  =  DS=  YS-YSP  of s h a n k  shank  marker  YSA-YSP  DYS/2  FIG.  D4  ROTATION OF SHANK ABOUT LONG A X I S  where t h e a n g u l a r r o t a t i o n o f t h e shank 9 Z S i s c a l c u l a t e d follows . 9ZS = a r c s m n ( 7 C  3.  DYS/2 - DS  Limb and J o i n t C e n t r e  Co-ordinates  The YZ p l a n e was c h o s e n a s the- r e f e r e n c e plane  measuring  i n c a l c u l a t i o n of the co-ordinates o f j o i n t  and mass c e n t r e s .  centres  'Z'  I36 -  Co-ordinate  S i d e V i e w , YZ P l a n e FIG.  D5  A'Zk =. Rxk • s i n  F r o n t V i e w , XZ P l a n e  'Z' CO-ORDINATE OF KNEE AND ANKLE 9YT  Zk = Z k y z - Rxk • S i n 9 Y T WHERE Zk r e p r e s e n t s t h e a c t u a l c o - o r d i n a t e a n d h e i g h t o f t h e knee X AZa  j o i n t c e n t r e a n d Rxk i s t h e r a d i u s o f t h e knee  joint i n  direction. = Ra • s i n  9YS  Z a = Z a y z - Ra • 9 Y S where Z<a. r e p r e s e n t s t h e a c t u a l c o - o r d i n a t e a n d h e i g h t o f t h e  - 137 ankle The  joint  vertical  lated  and Ra i s  co-ordinate  of  the the  r a d i u s of  the  ankle  shank mass c e n t r e  is  joint. calcu-  similarily.  A Z s = Rs Zs  centre  • s i n 9YS .  v  = Zsyz -  Rs  Side  • s i n 9YS. "  View, FIG.  YZ P l a n e D6  F r o n t View,  XZ P l a n e  'Z* CO-ORDINATE OF FOOT  A . Z f = R f • s i n 9YF Zf  = Zfyz  -  where R f i s  R f • s i n 9YF  the  width of  the  foot  at  the  mass c e n t r e  of  the  foot. 'Y'  Co-ordinate The  Y co-ordinate  of  the  joint  centres  and l i m b mass  - 138 c e n t r e s i s determined by c o r r e c t i n g s u r f a c e marker measured  the Y co-ordinate  i n t h e YZ p l a n e  o f the  f o r rotation of the  l i m b about i t s l o n g a x i s , - F i g . D ? .  Ykyz  S i d e V i e w , YZ P l a n e FIG. AYs  D7  Vertical  V i e w , XY P l a n e  'Y' CO-ORDINATE OF KNEE AND SHANK  = Rs • s i n 9ZS  Ys = Y s y z + Rs • s i n OZS where Y s i s t h e a c t u a l  co-ordinate  o f t h e mass c e n t r e o f t h e  shank a n d Rs i s t h e r a d i u s o f t h e shank a t t h e mass c e n t r e . The Yf. c o - o r d i n a t e o f t h e k n e e i s d e t e r m i n e d s i m i l a r i l y f r o m shank r o t a t i o n a s  -  139  -  A Yk = Rxk • s i n 9ZS Yk = Y k y z + Rxk • s i n 9ZS  where Rxk r e p r e s e n t s t h e c a l c u l a t e d , r a d i u s o f t h e k n e e a t the  j o i n t marker i n X d i r e c t i o n . The Y c o - o r d i n a t e o f t h e a n k l e  j o i n t c e n t r e and t h e  f o o t mass c e n t r e was c a l c u l a t e d f r o m t h e 9ZF. f o o t r o t a t i o n a p p l i e d t o t h e YZ c o - o r d i n a t e o f t h e r e s p e c t i v e s u r f a c e m a r k e r s shown i n F i g . D6 S O t h a t Y a = Y a y z + R a • s i n 9ZF Y f = Y f y z + R f • s i n 9ZF ' 'X' C o - o r d i n a t e The X c o - o r d i n a t e o f t h e k n e e  j o i n t c e n t r e and shank  mass c e n t r e w e r e d e t e r m i n e d f r o m t h e X c o - o r d i n a t e o f t h e s u r f a c e m a r k e r s m e a s u r e d i n t h e XZ p l a n e and t h e shank  rot-  ation. Xk = X k x z + Ryk • s i n 9ZS  1  X s = X s x z + Rs • s i n 9ZS while the X co-ordinate of the ankle  j o i n t c e n t r e and t h e  f o o t mass c e n t r e was c a l c u l a t e d f r o m t h e r o t a t i o n o f t h e f o o t about i t s v e r t i c a l  axis,  X a = X a x z + R a • s i n 9ZF X f -= Y f x z + R f • s i n 9ZF  9ZF  - 140 -  APPENDIX E MUSCLE AND LIGAMENT CO-ORDINATES  V  -  -  APPENDIX E MUSCLE AND LIGAMENT  CO-ORDINATES  The c o - o r d i n a t e s o f a l l m u s c l e and l i g a m e n t  attach-  m e n t s were d e t e r m i n e d i n t e r m s o f t h e same a x e s -- t h e g r i d axes w i t h o r i g i n a t t h e c e n t r e o f t h e f o r c e p l a t f o r m . 1.• M e d i a l C o l l a t e r a l  Ligament  Zs  Ys  Zsm'  exs  FIG. E l  t a n 9xm = 9xm  1  Ysm Zsm  = 9xm + 9 x s  MEDIAL COLLATERAL ATTACHMENT TO T I B I A I N YZ PLANE FOR ROTATION 9XS Rmyz  2  = Ysm  2  + Zsm'  - 142 Zsm' = Rrayz • c o s 9xm' f o r r o t a t i o n i n t h e XZ p l a n e plane  Ysm' = Rmyz • s i n 9xm  1  ( 9 Y S ) and. r o t a t i o n i n t h e XY  (9ZS) t h e c o - o r d i n a t e s o f attachment reduce t o  Zsm = Zsm* - c o s 9YS Ysm = Ysm' - c o s 9ZS  Xsm'  FIG.  E2  MEDIAL COLLATERAL ATTACHMENT TO T I B I A I N XZ PLANE FOR ROTATION 9YS  t a n 9ym =  Rmxz = X s m  2  + Zsm  9ym' = 9ym + 9;YS ^ Xsm' = Rmxz  • s i n Gym'  f o r r o t a t i o n o f t i b i a i n XY p l a n e  (9ZS) t h e c o - o r d i n a t e o f  2  -  143 -  attachment reduces t o Xsm = Xsm' - c o s 9ZS'- : The c o - o r d i n a t e s o f m e d i a l  ligament  attachment t othe  t i b i a w i t h r e s p e c t t o t h e g r i d axes a r e t h e r e f o r e  Xgm = Xgk + Rmxz • s i n 9ym• . c o s 9ZS Ygm = Ygk - Rmyz • s i n 9xm' • c o s 9ZS Zgm = Zgk - Rmyz • c o s 9 x m ' y  • c o s 9YS  where X g k , Y g k , Zgk a r e t h e g r i d c o - o r d i n a t e s o f t h e t i b i a l axes o f t h e knee  FIG.  E3  MEDIAL COLLATERAL ATTACHMENT TO FEMUR I N YZ PLANE FOR ROTATION 9XT  - 144 tan  9xfm =  Zffm Yffm  Rfmyz  2  = Yffm  2  + Zffm  2  9xfm' * 9xfm - 9XT Z f f m ' = Rfmyz  • s i n 9xfm'  f o r r o t a t i o n o f f e m u r i n XZ p l a n e plane  • c o s 9xfm'  ( 9 Y T ) a n d r o t a t i o n i n XY  (9ZT) t h e c o - o r d i n a t e s o f attachment reduce t o  Zffm = Zffm'  . c o s 9YT  Y f f m =.' Y f f m '  . cos. 9ZT  F I G . E4  . tan  Y f f m ' = Rfmyz  MEDIAL COLLATERAL ATTACHMENT TO FEMUR I N XZ PLANE FOR ROTATION 9YT  u  „ Zffm 9yfm =  n  9yfm' = 9yfm - 9YT X f f m ' = Rfmxz  • c o s 9yfm'  Rfmxz  2  = Xffm  2  + Zffm  2  corrected for rotation Xffm  = Xffm» The  • cos  145  -  o f t h e f e m u r i n t h e XY p l a n e  9ZT  co-ordinates of medial  femur w i t h r e s p e c t t o the g r i d  ligament  + Rfmxz • c o s  Ygfm = Y g f  - Rfmyz • c o s 9 x f m ' • c o s 9ZT  9yfm' • cos  Zgfm = Z g f + Rfmyz • s i n i O x f m ' • c o s  Ygf,  axes o f the The  .  9YT  Zgf, a r e t h e g r i d c o - o r d i n a t e s o f t h e  co-ordinates of l a t e r a l  Lateral  femur are c a l c u l a t e d  Collateral  femoral  ligament  attachment to  similarily.  Ligament  Zsl  FIG.  E5  the  9ZT  knee  t h e f i b u l a and 2.  attachment to  axes are t h e r e f o r e  Xgfm = X g f  where Xgf,  (9ZT)  LATERAL COLLATERAL ATTACHMENT TO F I B U L A I N YZ PLANE FOR ROTATION 9XS  t a n 9x1 = | g  146 Rlyz^ = Y s l ^ + Z s l ^  9x1'  = 9x1 + 9XS  Zsl'  = Rlyz  • cos 9x1'  Ysl•  = Rlyz  • s i n 9x1'  c o r r e c t e d f o r r o t a t i o n o f t h e t i b i a i n t h e XZ p l a n e and  t h e XY p l a n e  Zsl  = Z s l ' • c o s 9YS  Ysl  = Y s l ' • c o s 9ZS  FIG.  E6  t a n 9 y l = ||± 9yl'  = 9 y l - 9;YS  (9YS)  (9ZS) t h e c o - o r d i n a t e s r e d u c e t o  LATERAL COLLATERAL ATTACHMENT TO .FIBULA I N XZ PLANE FOR ROTATION 9YS Rlxz  2  = Xsl  2  +  Zsl  2  - 14? Xsl'  = Rlxz  • sin 9yl'  c o r r e c t e d f o r r o t a t i o n o f t h e t i b i a i n t h e XY p l a n e ( 9 Z S ) Xsl  = X s l ' • c o s 9ZS The  to  co-ordinates of the l a t e r a l  the f i b u l a  ligament  attachment  w i t h r e s p e c t t o t h e axes a r e t h e r e f o r e  Xgl  = Xgk - R l x z  • s i n 9 y l ' • c o s 9ZS  Ygl  = Ygk - R l y z - • s i n 9x1'  Zgl  = Zgk - R l y z  • c o s 9ZS  • c o s 9 x 1 ' • c o s 9YS  Zf  Yf ZffI  YffI  FIG.  E7  LATERAL COLLATERAL ATTACHMENT TO FEMUR I N YZ PLANE FOR ROTATION 9XT  tan Qxfl = | 9xfl'  = 9xfl  Yffl'  = Rflyz  Rflzy  2  = Yffl  2  +  Zffl  2  - 9XT • cos 9 x f l '  Zffl'  = Rflyz  . s i n 9xf1'  c o r r e c t e d f o r r o t a t i o n o f t h e f e m u r i n t h e XZ p l a n e ( 9 Y T ) and  r o t a t i o n i n t h e XY p l a n e  Zffl  = Zffl'  • c o s 9YT  Yffl  = Yffl'  • c o s 9ZT  (9ZT) t h e c o - o r d i n a t e s reduce t  ff  FIG.  tan 9yfl 9yfl' Xffl  E8  LATERAL COLLATERAL ATTACHMENT TO FEMUR I N XZ? PLANE FOR ROTATION 9YT  =  = 9yfl = Rflxz  i'  Rflxz + 9YT • cos 9 y f l '  2  = Xffl  2  +  Zffl  2  - 14,9 c o r r e c t e d , f o r r o t a t i o n o f f e m u r i n XY p l a n e ordinate Xffl  reduces to  = Xffl' The  the  3-  (9ZT) t h e c  • c o s 9ZT  co-ordinates of l a t e r a l ligament  femur w i t h  r e s p e c t t o t h e g r i d axes a r e  Xgfl = Xgf - Rflxz  • cos 9 y f l '  • c o s 9ZT  Y g f l = Ygf - Rflyz  • cos 9xf1'  • c o s 9ZT  Zgfl = Zgf + Rflyz  • s i n9xf1'  • c o s 9YT  Anterior  FIG.  Cruciate  E9  attachment  Ligament  ANTERIOR CRUCIATE ATTACHMENT TO T I B I A I N YZ PLANE FOR ROTATION 9XS  tan  150  -  Oxa = f | f  Qxa'  = 9xa  Zsa'  = Rayz  corrected plane  Rayz  -  2  = Ysa  + Zsa  2  9XS • sin  for  9xa'  rotation  Ysa' of  tibia  i n XZ p l a n e  = Rayz (9YS)  • cos  9xa'  and t h e XY  (9ZS)  Zsa  = Zsa'  • cos  9YS  Ysa  = Ysa'  • cos  9ZS  Zs  Xsa'  FIG.  tan 9ya'  9ya = = 9ya  corrected  2  E10  ANTERIOR CRUCIATE ATTACHMENT TO T I B I A IN XZ PLANE FOR ROTATION 9YS Raxz  Asa  + 9YS for  rotation  Xsa' of  the  tibia  i n the  2  = Xsa  = Raxz  2  + Zsa  • cos  XY p l a n e  2  9ya'  (9ZS)  Xsa  151  -  = X s a ' • c o s 9ZS The c o - o r d i n a t e s  o f a n t e r i o r c r u c i a t e ligament  ment t o t h e t i b i a w i t h r e s p e c t  attach-  t o t h e g r i d axes a r e t h e r e f o r e  X g a = Xgk + R a x z • c o s 9 y a ' • c o s 9ZS Y g a = Ygk + R a y z • c o s 9 x a ' * c o s 9ZS Z g a = Zgk + R a y z " s i n 9 x a ' • c o s 9YS  exfa'  Yf  =k  FIG.  tan  9sfa  E l l  ANTERIOR CRUCIATE ATTACHMENT TO FEMUR IN YZ PLANE FOR ROTATION 9XT  Zffa Yffa  9xfa'  = 9xfa  Zffa'  = Rfayz  Zffa'  Rfayz  2  = Yffa  2  + Zffa  2  - 9XT • s i n 9xfa'  Yffa'  = Rfayz  • cos 9xfa'  corrected  152 -  f o r r o t a t i o n o f the femur i n the XZ plane (QYT)  and r o t a t i o n i n the XY plane (9ZT) Yffa = Yffa'  • cos 9ZT  Zffa = Zffa'  • cos 9YT  Xf  FIG. E12  ANTERIOR CRUCIATE ATTACHMENT TO FEMUR IN XZ PLANE FOR ROTATION 9YT  tan 9 y f a = | | | |  Rfaxz  2  = Xffa  2  + Zffa  9yfa' = 9 y f a + 9YT X f f a ' = Rfaxz corrected  ; cos Qyfa'  f o r r o t a t i o n o f the femur i n the XY plane (9ZT)  Xffa = Xffa'  • cos 9ZT  The c o - o r d i n a t e s o f a n t e r i o r  cruciate  ligament  attachment  153  -  t o t h e femur w i t h r e s p e c t t o t h e grid, axes  Xgfa = Xgf - Rfaxz  • cos Qyfa'  • cos 9 Z T  Ygfa = Ygf - Rfayz  • cos  • cos  Zgfa = Zgf + Rfayz  • s i nQxfa'  4.  Posterior Cruciate  FIG. E13  9 x f a '  9ZT  • cos',9YT  Ligament  POSTERIOR CRUCIATE ATTACHMENT TO I N YZ PLANE FOR ROTATION 9 X S  tan  Rpyz  9xp'  =  9xp-  -  Zsp'  = Rpyz • s i n 9 x p '  2  = Ysp  TIBIA  2  + Zsp  2  9XS"  Ysp'  = Rpyz • c o s 9 x p '  -  15^  -  corrected f o r r o t a t i o n of the t i b i a  i n t h e XZ p l a n e (GYS)  and r o t a t i o n i n t h e XY p l a n e ( 9 Z S ) Ysp  = Y s p ' • c o s 9ZS  Zsp  = Z s p ' • s i n 9YS  FIG.  El4  POSTERIOR CRUCIATE ATTACHMENT TO T I B I A I N XZ PLANE FOR ROTATION 9YS  Rpxz = Zsp  Xsp'  9yp'  = 9YS  = Z s p • s i n 9YS  c o r r e c t e d f o r r o t a t i o n o f t h e t i b i a i n t h e XY p l a n e ( 9 Z S ) Xsp  = X s p ' • c o s 9ZS The  co-ordinates of posterior  cruciate  ligament  -  155  -  attachment to the t i b i a with respect the grid, axes  Xgp = Xgk + Zsp • 9YS • cos 9ZS Ygp = Ygk - Rpyz • cos 9xp' •• cos 9ZS Zgp = Zgk - Rpyz • s i n 9xp' • cos 9YS  Oxfp' = 9 x f p - 9XT Zffp* = Rfpyz • s i n 9 x f p '  Yffp' = Rfpyz • cos 9xfp'  corrected f o r r o t a t i o n of the femur i n the XZ plane (9YT) and the XY plane (9ZT)  -  Yffp  = Yffp'  • c o s 9ZT  Zffp = Zffp'  • c o s 9YT  FIG.  E16  156  -  POSTERIOR CRUCIATE ATTACHMENT TO FEMUR I N XZ PLANE FOR ROTATION 9YT  tan 9yfp = 9xfp*  Rfpxz  = 9 y f p + 9YT  Xffp'  2  = Xffp  = Rfpxz  2  + Zffp  2  • c o s Oyfp*  c o r r e c t e d f o r r o t a t i o n o f t h e f e m u r i n t h e XY p l a n e ( 9 Z T ) Xffp  = Xffp'  •• c o s 9ZT  The c o - o r d i n a t e s o f p o s t e r i o r  cruciate ligament  ment t o t h e f e m u r w i t h r e s p e c t t o t h e g r i d a x e s a r e  attach-  - 157. Xgfp = Xgf + Rfpxz • cos Oyfp  1  . cos 9 Z T  Ygfp = Ygf + Rfpyz • cos Qxfp'  • cos 9 Z T  Zgfp = Zgf - Rfpyz • s i n Qxfp*  " cos 9 Y T  -  158  -  MUSCLE CO-ORDINATES The muscle  a t t a c h m e n t s were c a l c u l a t e d t o a l l o w d e t e r m i n a t i o n o f  respective The  c o - o r d i n a t e s o f t h e h a m s t r i n g and g a s t r o c n e m i u s  l i n e s o f f o r c e a c t i o n f o r these muscle  l i n e o f f o r c e a c t i o n f o r t h e q u a d r i c e p s g r o u p was  d e t e r m i n e d f r o m e q u a t i o n 3-01 1.  groups.  Hamstrings Muscle  FIG. E17  t a n 9xh = | | | 9 x h ' = 9 x h + 9XS  o f s e c t i o n No. 3 .  Group  HAMSTRINGS ATTACHMENT TO T I B I A I N YZ PLANE FOR ROTATION 9XS Rhyz  2  = Ysh  2  + Zsh  2  -  Ysh'  159  -  = Rhyz ' s i n 9 x h '  c o r r e c t e d f o r r o t a t i o n i n t h e XZ p l a n e  Z s h ' = Rhyz • c o s 9xh ( 9 Y S ) and f o r r o t a -  t i o n i n t h e XY p l a n e ( 9 Z S ) Y s h = Y s h ' • c o s 9YS  Xsh'  F I G . E18  HAMSTRINGS ATTACHMENT TO T I B I A I N XZ PLANE FOR ROTATION 9YS  Rhxz = Z s h Xsh'  9 y h ' = 9YS-  = Z s h • s i n 9YS  c o r r e c t e d f o r r o t a t i o n o f t h e t i b i a i n t h e XY p l a n e  (9ZS) t h e  co-ordinate reduces to X s h = X s h ' • c o s 0ZS The c o - o r d i n a t e s o f h a m s t r i n g a t t a c h m e n t  to the t i b i a  -  160  -  with r e s p e c t to the grid, axes are Xgh = Xgk + Zsh • s i n 9YS . cos 9ZS Ygh = Ygk - Rhyz • s i n 9xh'  • cos 9ZS  Zgh = Zgk - Rhyz • cos 9xh' • cos 9YS The hamstrings being a b i a r t i c u l a r muscle group c r o s s the  knee j o i n t and. h i p j o i n t to i n s e r t i o n i n the p e l v i s . To determine the c o - o r d i n a t e s o f attachment to the  p e l v i s with r e s p e c t to the g r i d axes, the b a s i c with r e s p e c t to M o r r i s o n ' s p e l v i c c  co-ordinates  o r i g i n a t the a n t e r i o r  ilia's) spine (p) are transposed to the femoral head  origin  (fh). The c o - o r d i n a t e s o f hamstring muscle group attachment to p e l v i s w i t h r e s p e c t to the g r i d axes are Xgph = Xgfh + (Xph - Xpfh) Xgph = Ygfh - (Yph - Ypfh) Zgph = Zgfh - (Zph - Zpfh)  The c o - o r d i n a t e s o f hamstrings attachment to the p e l v i s r e p r e s e n t a common o r i g i n o f i n s e r t i o n f o r the muscles which make up the hamstrings muscle group. The c a l c u l a t i o n s  f o r hamstrings attachment to the  -  161  -  Xfhh  FIG. E 1 9  HAMSTRINGS ATTACHMENT TO P E L V I S I N XZ PLANE WITH RESPECT TO FEMORAL HEAD  Zp Yfhh z Yph -Ypfh  Yp  F I G . E'20  HAMSTRINGS ATTACHMENT TO P E L V I S I N YZ PLANE WITH RESPECT TO FEMORAL HEAD  - 1-6-2 pelvis 9XP,  have n o t b e e n c o r r e c t e d f o r r o t a t i o n s  9YP and 9 Z P , as t h e s e  rotations  from the s u r f a c e markers u s e d . assumed  2.  pelvis,  c o u l d n o t be d e t e r m i n e d  However t h e s e  rotations  are  small.  G a s t r o c n e m i u s M u s c l e Group  Ysfg  FIG.  tan  o f the  E21  9xfg = | | | |  9xfg'  = 9xfg  Ysfg'  = Rfgyz  Ysfg'  GASTROCNEMIUS ATTACHMENT TO FEMUR IN YZ PLANE FOR ROTATION 9XT ,  Rfgyz  2  = Ysfg  2  + Zsfg  2  - 9XT  • cos 9xfg  Zsfg'  c o r r e c t e d f o r r o t a t i o n i n t h e XZ p l a n e  = Rfgyz  • s i n 9xfg*  (9YT) and r o t a t i o n i n  -  163  -  t h e XY p l a n e (QZT) Ysfg = Ysfg'  • c o s QZT  Asfg = Zsfg'  • c o s 9YT  Xsfg'  FIG.  E22  GASTROCNEMIUS ATTACHMENT TO FEMUR I N XZ PLANE FOR ROTATION 9YT  Rfgxz = Zsfg Xsfg'  = Zsfg  9yfg'  = 9YT  • s i n 9YT  c o r r e c t e d , f o r r o t a t i o n o f t h e f e m u r i n t h e XY p l a n e ( 9 Z T ) Xsfg = Xsfg* The  c o s 9ZT  co-ordinates  o f gastrocnemius muscle group  attachment t o t h e femur w i t h r e s p e c t  to the g r i d  axes  - 164 X g f g = Xgk + Z s f g  • s i n 9YT . c o s 9ZT  Y g f g = Ygk - R f g y z  • cos 9xfg'  Z g f g = Zgk + Rgxz • s i n 9 x f g '  FIG. E 2 3  . c o s 9YT  GASTROCNEMIUS ATTACHMENT TO T I B I A I N YZ PLANE FOR ROTATION 9XS  t a n oxg = I § £ Zsg &  9xg'  • c o s 9ZT  Rgyz  2  = Ysg  2  + Zsg  2  = 9 x g + 9XS  Ysg' = Rgyz • s i n 9xg'  Z s g ' = Rgyz • c o s 9xg'  c o r r e c t e d f o r r o t a t i o n o f t h e t i b i a i n t h e XY p l a n e ( 9 Z S )  - 166 and t h e p l a n e ( 9 Y S ) Y s g = Y s g ' • c o s 9ZS  Z s g = Z s g ' • c o s 0YS  Zs Xs  Zsg  FIG. E24  GASTROCNEMIUS ATTACHMENT TO T I B I A I N XZ PLANE FOR ROTATION 9YS  Rgxz = Z s g Xsg'  9 x g ' = 9YS  = Z s g • s i n 9YS  c o r r e c t e d f o r r o t a t i o n o f t h e t i b i a i n t h e XY p l a n e ( 9 Z S ) X s g = X s g ' • c o s 9ZS The  c o - o r d i n a t e s o f gastrocnemius attachment  to the  166  -  -  t i b i a with r e s p e c t to the grid, axes are  Xgg = Xgk + Zsg . s i n 9YS  . cos 9ZS  Ygg = Ygk - Rgyz • s i n 9 x g '  • cos 9ZS  Zgg = Zgk - Rgyz • cos 9 x g '  • cos 9YS  -  16?  -  APPENDIX F MUSCLE AND LIGAMENT FORCES  -  168  -  APPENDIX F MUSCLE AND LIGAMENT FORCES 1•  Quadriceps  Muscle  Group  Zs Ysq  t  Ys  FIG.  Mxk  F l  FORCE ACTION OF QUADRICEPS MUSCLE GROUP I N THE YZ PLANE  = P q • c o s 9q • Y s q + P q • s i n 9q • Z s q  Pq = Mxk / ( c o s 9q • Y s q + s i n 9 q • Z s q ) where 9q i s t h e a n g l e o f t h e q u a d r i c e p s t o t h e Zs a x i s i n t h e Y s Z s p l a n e a n d Mxk i s t h e moment o n t h e k n e e i n t h e Y s Z s plane  \  - 169' -  FIG.  F2  ANGLE OF SHANK IN Y s Z s PLANE 9XS (+/ ARCTAN (DYS ' / D Z S ' )  - 1?0  -  i  w  Ys  sin(GYS- ©YT)- DZT  FIG.  F3  ANGLE OF THIGH IN Y s Z s PLANE 9XT .= ARCTAN ( D Y T " / D Z T " )  -  9q = 0.31 + O.37  x 10"^ x 10"  ( p h i ) - 8.4 2  (phi) +  17-1  x 10"  3  (phi)  2  15  P h i = 9XS + 9XT where 9XS and 9XT are c a l c u l a t e d i n the YsZs p l a n e as i n F i g . F2 and F3 2.  Hamstrings Muscle Group  -  sin G y h - D Z H  FIG. F5  172  -  1  ANGLE OF HAMSTRINGS IN YsZs PLANE 9X = ARCTAN (DYH"/l)ZH")  - 173 Mxk  = Ph • c o s 9xh . Y s h + Ph • s i n 9xh • Z s h  Ph = Mxk / ( c o s 9 x h • Y s h + s i n 9 x h • Z s h ) 9xh = 9 x + 9XS. i s t h e a n g l e o f t h e h a m s t r i n g s t o t h e Z s a x i s i n t h e YsZs p l a n e w i t h 9x c a l c u l a t e d  a s i n F i g . F 5 a n d 9XS  as i n F i g . F 2 3.  Gastrocnemius  Muscle  Group  Zs  DYG=Ygfg-Ygg Ys DZG = Z g f g - Z g g  ©xg - e x s - e x  tan 9x= DYG/DZG  exs  F I G . F6  FORCE ACTION.OF GASTROCNEMIUS MUSCLE GROUP I N THE YZ PLANE  Mxk  = Pq  Pg = Mxk 9xg = 9XS  • s i n 9xg / ( s i n 9xg  • Zsg + Pq  17k  -  • cos 9 x g  • Ysg  • Zsg + Fg . cos 9xg  - 9X i s the angle of the gastrocnemius  a x i s i n the YsZs plane with 9X c a l c u l a t e d 9XS  • Ysg)  from F i g . F2  to the Zs  as i n F i g . F7  and  -  FIG. F7  175  -  ANGLE OF GASTROCNEMIUS I N Y s Z s PLANE 9X = ARCTAN (DYG'/DZG')  -  176 -  LIGAMENT FORCES 1.  Anterior  Cruciate  Ligament  DYA: Yga-Ygfa  DZA:Zgfa - Z g a  t a n G x : DZA/DYA  FIG.  F8  FORCE ACTION OF ANTERIOR CRUCIATE LIGAMENT I N YZ PLANE  Fym + F y k = P a • c o s 9 x a P a = (Fym + F y k ) / c o s 9 x a 9 x a - OX - 9XS i s t h e a n g l e o f t h e a n t e r i o r c r u c i a t e Ys a x i s i n t h e YsZs p l a n e w i t h and 9XS f r o m F i g . F2  9X c a l c u l a t e d  to the  a s i n F i g . F9  -  177 -  Zs'  Gyfa = Qyfa + GYS D Z F A ' = Rfaxz- s'mGyfa'  Gya'= 6ya - GYS D Z A ' = Raxz- sin 9 y a '  DZFA 9YS DZA = DZFA +Zsfc.cosGXS- DZA*  Gza - GZS - Gza DYA = Raxy cos Gza  Xs  0zfa'= GZS - Q z f a ' DYFA  DYA  D Y F A ' = Rfaxy • c o s G z f a '  D Y A = D Y A + D Y F A ' I Z S fC • si n 6XS  FIG. F 9  ANGLE OF ANTERIOR CRUCIATE I N Y s Z s PLANE 9X = ARCTAN (DZA"/DYA")  - 178' 2.  Posterior  Cruciate  Ligament  DYP= Ygf p - Ygp D 2 A = Zgfp - Zgp  tan G\x = DZP/DYP  FIG.  F10  FORCE ACTION OF POSTERIOR CRUCIATE LIGAMENT I N YZ PLANE  Fym + F y k = Pp • c o s 9xp Pp = (Fym + F y k ) / c o s Gxp 9xp = 9X + 9XS i s t h e a n g l e o f t h e p o s t e r i o r  cruciate  Ys a x i s i n t h e Y s Z s p l a n e w i t h  as i n F i g . F l l  and 9XS f r o m F i g . F2  9X c a l c u l a t e d  to the  -  179  -  e y f p = B Y S - eyfp DZFP'=Rfpxz-sineyfp'  t a n Gyfp = DZFP/DYFP  DZP =Zsp  DZP"= D Z P ' + Z s f c - c o s e X S - D Z F P '  eztp'  DYP"= DYP+ DYFP+ Zsfc-sin 0 X S  FIG.  Fll  ANGLE OF POSTERIOR CRUCIATE IN YsZs PLANE, 9X = ARCTAN (DZP"/DYP")"  - 180 3-  L a t e r a l C o l l a t e r a l Ligament  DXL  FIG.  F12  Rz = F z k + Fzm +  FORCE ACTION OF LATERAL COLLATERAL LIGAMENT.IN XZ PLANE Fzcr  P I = (Myk + Rz • X I ) / ( c o s 9 y l • X s l - s i n Q y l • Z s l - cos 9yl • Y l ) 9yT = 9YS  -• 9Y i s t h e a n g l e o f t h e l a t e r a l  Zs a x i s i n t h e Y s Z s p l a n e w i t h and 9YS f r o m F i g . F 2  collateral  9Y c a l c u l a t e d  to the  as i n F i g . F 1 3  /  - 181 -  9x1 = GXS + G x l DZ FL  DZL = R l y z - s i n G x l  9xfl = G X S t 9xfl DZFL'= R f l y z - C O S 9 x f  l'  DZL = D Z L +• DZ FL +• Zsf c • cos G Y S  9 z l = GZS  -Qzl  DXL = R l x y sin G z l  Gzfl = 6zfl - 0 Z S DXFL = RfIxy cosGzfl'  v D X L = DXL - D X F L t Z s f c - s i n G Y S  FIG. F 1 3  ANGLE OF LATERAL COLLATERAL IN XsZs PLANE, Qy = ARCTAN (DXL"/DZL")  - 182 4.  Medial Collateral  Ligament  D X M = Xgm - Xgfm DZM = Zgf m - Z g m  t a n e y = DXM/DZM  FIG.  F14  FORCE ACTION OF MEDIAL COLLATERAL LIGAMENT I N XZ PLANE  Rz = FZK + FZM + FZCR Pm = (Myk + Rz • X I ) / ( c o s 9ym • Xsm + s i n 9ym • Zsm - c o s 9ym • X I ) 9ym = 9YS - 9Y i s t h e a n g l e o f t h e m e d i a l c o l l a t e r a l Zs a x i s i n t h e X s Z s p l a n e w i t h 9Y c a l c u l a t e d and  9YS f r o m F i g . F 2  to the  as i n F i g . F15  - 183 -  FIG. F 1 5  ANGLE OF MEDIAL COLLATERAL IN XsZs PLANE, 9Y = ARCTAN (DXM"/DZM")  - 184 -  APPENDIX G RESOLUTION OF EXTERNAL FORCE SYSTEM  - 185 -  APPENDIX G RESOLUTION OF EXTERNAL FORCE XY  SYSTEM  Plane  Fxk = Fxk-cos9ZS + Fyk-si n9ZS Fyk'= Fyk-cosGZS - Fxk-sinGZS  Mxk'= Mxk cos GZS + M y k - s i n Q Z S Myk'= M y k - c o s 9 Z S - M x k - s i n e Z S  XZ  Plane  Fxk'= Fxk-cosGYS - F z k - s i n ©YS Fz k' = Fzk-cosGYS + Fxk-sin ©YS  Mxk' = M x k - c o s G Y S - Mzk-sinQYS Myk' - Mzk-cos9YS + M x k - s i n 9 Y S GYS  \  - 186 YZ  Plane  Fyk= F y k . c o s e x S Ys  Myk  -Fzk-sinGXS  Fzk': Fzk-.cos GXS + F y k i s i n G X S  \ ^  Myk'= M y k c o s G X S - M z k - s i n G X S Mzk'r  Equations  of Resolved  External  Force  Mzk-cos GXS + M y k - s i n G X S  System  Fxk"  = Fxk  • c o s 9ZS  • c o s 9YS  + Fyk  • s i n 9ZS  Fyk'  = Fyk  • c o s 9ZS  • c o s 9XS  - Fxk  • s i n 9ZS - F z k . s i n 9XS  Fzk'  = F z k • c o s 9YS  • c o s 9XS  + Fyk  • s i n 9XS  + Fxk  • s i n 9YS  Mxk'  = Mxk  • c o s 9ZS  • c o s 9YS + Myk  • s i n 9ZS  - Mzk  • s i n 9YS  Myk'  = Myk  • c o s 9ZS  • c o s 9XS  • s i n 9ZS  - Mzk  • s i n 9XS  Mzk'  = Mzk  • c o s GXS  • c o s 9YS + Mxk  • s i n 9YS + Myk  • s i n 9XS  - Mxk  - F z k • s i n 9YS  - 187 -  APPENDIX H LIMB ACCELERATIONS  - 188 -  APPENDIX H LIMB ACCELERATIONS 1.  L i n e a r Limb A c c e l e r a t i o n A n u m e r i c a l d i f f e r e n t i a t i o n t e c h n i q u e based on f i n i t e  differences  (Lanczos, 1957) was;used to determine t h e l i n e a r  l i m b a c c e l e r a t i o n s o f the f o o t and. shank.  The l i n e a r a c -  c e l e r a t i o n s o f the f o o t and shank i n the X, Y and Z d i r e c t i o n s were c a l c u l a t e d from the r e s p e c t i v e d i s p l a c e m e n t s o f the c e n t r e  o f mass o f t h e f o o t and shank.  Therefore the  l i n e a r a c c e l e r a t i o n s a r e c a l c u l a t e d as f o l l o w s : Xn = 4Xn - 4 + 4Xn - 3 + Xn - 2 - 4Xn - 1 - lOXn - 4Xn + 1 + Xn + 2 + 4Xn + 3 + 4Xn + 4 /  X  n  - displacement of centre  100t  2  o f mass o f segment i n X d i r e c t i o n  at time, n Xn - a c c e l e r a t i o n o f c e n t r e  o f mass i n X d i r e c t i o n a t time, n  n - p o i n t i n time t - time i n t e r v a l o f d i s p l a c e m e n t from n t o n + 1 S i m i l a r equations give the a c c e l e r a t i o n of centre of mass o f a segment i n t h e Y and Z d i r e c t i o n s  -  189  -  Yn = 4Yn - 4 + 4Yn - 3 + Yn - 2 - 4Yn - 1 - 4Yn  + 1 + Y n + 2 + 4Yn  + 3 + 4Yn  lOYn-  + 4 /  100t  2  Z n = 4 Z n - 4 + 4 Z n - 3 + Z n - 2 - 4 Z n - 1 - lOZn., - 4 Z n +,'.1 + Z n +• 2 + 4 Z n + 3 + 4 Z n +.4 3-  Angular Limb  determined, from t h e r e s p e c t i v e  about  100t  2  Acceleration  The a n g u l a r a c c e l e r a t i o n s  f o o t and s h a n k .  /  o f t h e f o o t and. shank were  angular displacements of the  The a n g u l a r a c c e l e r a t i o n s  are c a l c u l a t e d  t h e X, Y and Z a x e s p a s s i n g t h r o u g h t h e c e n t r e o f mass  o f t h e segment a s f o l l o w s : 9x = 4 9 X n - 4 + 4 9 X n - 3 + 9Xn - 2 - 4 9 X n - 1 - 109Xn - 4 9 X n + 1 + 9Xn + 2 + 4 9 X n + 3 + 4 9 X n + 4 / 9 x n - a n g u l a r d i s p l a c e m e n t o f segment a b o u t ,time,  2  the X axis at  n  9x - a n g u l a r a c c e l e r a t i o n o f segment a b o u t time,  100t  the X axis at  n  n - p o i n t i n time t - time i n t e r v a l o f displacement from n t o n + 1 S i m i l a r equations give the angular a c c e l e r a t i o n of the segment a b o u t  t h e Y and Z  axes  9Yn = 4 9 Y n - k + 4 9 Y n - 3 + 9Yn - 2 - 4 9 Y n - 1 - 109Yn - 4 9 Y n + 1 + 9Yn + 2 + 4 9 Y n + 3 + 4 9 Y n + 4 /  100t  2  -  19P  -  9Zn = 49Zn - 4 + 49Zn - 3 + 9Zn - 2 - 49Zn - 1 - 109Zn - 49Zn + 1 + 9Zn + 2 + 49Zn + 3 + 49Zn + 4 / 1 0 0 t  2  

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