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Work characteristics of standing broad and vertical jumping 1986

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WORK CHARACTERISTICS OF STANDING BROAD AND VERTICAL JUMPING by ROBERT DALE FLEMING B.P.E., The U n i v e r s i t y of B r i t i s h Columbia, 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF PHYSICAL EDUCATION i n THE FACULTY OF GRADUATE STUDIES (School of P h y s i c a l E d u c a t i o n and R e c r e a t i o n ) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA Augus t 1986 (c) Robert Dale Fleming, 1986 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r 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 c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by t h e head o f my department o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f 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 n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . The U n i v e r s i t y o f B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 )E-6 (3/81) i i ABSTRACT The purpose of t h i s study was to determine the c o n t r i b u t i o n s made by the l e g muscle groups to the work done i n standing broad and v e r t i c a l jumping. A secondary purpose was to examine the p r i n c i p l e s of summation and c o n t i n u i t y of j o i n t f o r c e s as they apply to these jumps. Twelve s u b j e c t s were f i l m e d while jumping from a f o r c e p l a t f o r m . They performed a minimum of three maximal standing broad and v e r t i c a l jumps, with countermovements and use of the arms permitted. The jumps were f i l m e d at a r a t e of 50 frames per second while, synchronously, ground r e a c t i o n f o r c e data were c o l l e c t e d at 50 Hz. Link segment a n a l y s i s and i n v e r s e dynamics methods were used to compute the net muscle moments of f o r c e and the power and work outputs created by these moments of f o r c e . The jumps were examined over two time p e r i o d s , during both the p r o p u l s i v e phase of jumping and the e n t i r e jump. The work-energy approach was used to determine the r e l a t i v e c o n t r i b u t i o n s of the muscles c r o s s i n g the ankle, knee and hip j o i n t s to the t o t a l work done at the l e g j o i n t s . A work-energy a n a l y s i s ( i . e . the r a t i o of net mechanical work done at 6 j o i n t s to the gain i n t o t a l mechanical energy) f o r the two types of jumps during the two time i n t e r v a l s of i n t e r e s t produced values a l l l e s s than 1.0. T h i s suggests that there were other sources of work that subjects were us i n g and which were not measured i n the a n a l y s i s . As w e l l , • • • 111 t h i s suggests that the l i n k segment model u t i l i z e d may not have been a p p r o p r i a t e f o r a l l s u b j e c t s . For the standing broad jump the c o n t r i b u t i o n s of the ankle, knee and hip muscles during the p r o p u l s i v e phase were 30.2, 18.6 and 51.2 percent, r e s p e c t i v e l y , while t h e i r c o n t r i b u t i o n s over the e n t i r e jump were 31.5, 17.0 and 51.5 percent, r e s p e c t i v e l y . The r e s p e c t i v e c o n t r i b u t i o n s of the ankle, knee and hip j o i n t s f o r the v e r t i c a l jump duri n g the p r o p u l s i v e phase were 33.0, 24.8 and 42.2 percent and over the e n t i r e jump the c o n t r i b u t i o n s were 39.2 ( a n k l e ) , 22.4 (knee) and 38.4 (hip) percent. T w o - t a i l e d c o r r e l a t e d t - t e s t s were done to check for d i f f e r e n c e s i n r e l a t i v e c o n t r i b u t i o n s of both the ankle and knee j o i n t s to the work done at the l e g j o i n t s i n standing broad and v e r t i c a l jumping. The only s i g n i f i c a n t d i f f e r e n c e (p<.01) occurred at the ankle j o i n t over the e n t i r e jump. R e l a t i v e l y , the muscles c r o s s i n g the ankle j o i n t d i d s i g n i f i c a n t l y more work i n v e r t i c a l jumping than i n standing broad jumping. One-way ANOVAs with repeated measures were u t i l i z e d to t e s t the d i f f e r e n c e s between r e l a t i v e j o i n t c o n t r i b u t i o n s f o r each type of jump during the two time periods examined. Neuman-Keuls post hoc method was used to evaluate the m u l t i p l e p a i r w i s e c o m p a r i s o n s . There were two main f i n d i n g s . F i r s t , over the e n t i r e jump, the muscles c r o s s i n g the hip j o i n t d i d s i g n i f i c a n t l y more work than those of the knee j o i n t during both standing broad (p<.01) and v e r t i c a l i v jumping (p<.05). Then f o r the p r o p u l s i v e phase, t h e r e was s i g n i f i c a n t l y more work g e n e r a t e d at the h i p j o i n t than at e i t h e r the knee j o i n t or the a n k l e j o i n t d u r i n g b oth v e r t i c a l jumping (knee: p<.01; a n k l e : p<.05) and s t a n d i n g broad jumping (knee: p<.01; a n k l e : p<.01). R e s u l t s f o r the e v a l u a t i o n of the summation and c o n t i n u i t y p r i n c i p l e s s u p p o r t e d the p r i n c i p l e of summation of j o i n t f o r c e s as the muscles of a l l t h r e e l e g j o i n t s , f o r a l l s u b j e c t s , were net g e n e r a t o r s of p o s i t i v e work d u r i n g the p r o p u l s i v e phase of s t a n d i n g broad and v e r t i c a l j u m p i n g . The c o n t i n u i t y of j o i n t f o r c e s p r i n c i p l e , however, was not f u l l y s u p p o r t e d as the s e q u e n c i n g of m u s c u l a r c o n t r a c t i o n s was not always from p r o x i m a l to d i s t a l as e x p e c t e d . V TABLE OF CONTENTS A b s t r a c t i i L i s t of Tables . . v i L i s t of F i g u r e s - . v i i Acknowledgement v i i i I n t r o d u c t i o n 1 Purpose 4 Methodology 5 Procedure 5 Subjects 5 Markers 5 Data C o l l e c t i o n and A n a l y s i s 6 J o i n t Power 8 J o i n t Work 9 Energy C a l c u l a t i o n s 10 Work-Energy A n a l y s i s . 11 J o i n t C o n t r i b u t i o n 11 S t a t i s t i c s 12 P r i n c i p l e E v a l u a t i o n 13 Performance A n a l y s i s . . . . . 14 Re s u l t s 1 5 D i s c u s s i o n 33 Leg J o i n t Work 33 Standing Broad Jump 33 V e r t i c a l Jump 36 S t a t i s t i c s 39 Summary. . 41 Other J o i n t Work 41 Work-Energy A n a l y s i s 42 Biomechanical P r i n c i p l e s 44 Summary 48 J o i n t K i n e t i c s 48 Hip K i n e t i c s 48 Knee K i n e t i c s 49 Ankle K i n e t i c s 49 Conc l u s i o n s Recommendations • • Ref er ences -*4 Appendix 1 - Review of L i t e r a t u r e 58 Standing Jumps 58 Work and Power i n Human Locomotion 68 Biomechancal P r i n c i p l e s 72 B i b l i o g r a p h y 80 v i LIST OF TABLES 1. Sex, age, mass, height and sport of s u b j e c t s . . . 6 2. Average r e l a t i v e c o n t r i b u t i o n of the l e g j o i n t moments to the t o t a l work done at the l e g j o i n t s d u r i n g the e n t i r e jump 20 3. Average r e l a t i v e c o n t r i b u t i o n of the l e g j o i n t moments to the t o t a l work done at the l e g j o i n t s d u r i n g the p r o p u l s i v e phase 20 4. Average absolute and r e l a t i v e j o i n t c o n t r i b u t i o n to the ga i n i n t o t a l body energy f o r the e n t i r e jump i n standing broad jumping 21 5. Average a b s o l u t e and r e l a t i v e j o i n t c o n t r i b u t i o n to the gain i n t o t a l body energy during the p r o p u l s i v e phase of standing broad jumping . . . 21 6. Average absolute and r e l a t i v e j o i n t c o n t r i b u t i o n to the gain i n t o t a l body energy f o r the e n t i r e jump i n v e r t i c a l jumping 22 7. Average ab s o l u t e and r e l a t i v e j o i n t c o n t r i b u t i o n to the gain i n t o t a l body energy during the p r o p u l s i v e phase of v e r t i c a l jumping 22 8. Comparison of the r e l a t i v e percent c o n t r i b u t i o n of the ankle and knee j o i n t s i n v e r t i c a l jumping to t h e i r c o n t r i b u t i o n s i n standing broad jumping . . 23 9. Comparison of r e l a t i v e j o i n t c o n t r i b u t i o n s . . . 23 10. Average work done by c o n t r a c t i o n s of the muscles c r o s s i n g the ankle, knee and hip j o i n t s . . . . 24 11. I n d i c a t i o n of the extent of support f o r the summation and c o n t i n u i t y p r i n c i p l e s 32 12. P r e d i c t e d performance of subj e c t s 32 v i i LIST OF FIGURES 1. Sequencing of muscular c o n t r a c t i o n s f o r standing broad and v e r t i c a l jumping 25 2. Ankle p l o t s f o r v e r t i c a l jumping 26 3. Knee p l o t s f o r v e r t i c a l jumping 27 4. Hip p l o t s f o r v e r t i c a l jumping . . . . . . . 28 5. Ankle p l o t s f o r standing broad jumping 29 6. Knee p l o t s f o r standing broad jumping 30 7. Hip p l o t s f o r standing broad jumping 31 v i i i ACKNOWLEDGEMENT I wish to thank the members of my committee, Dr. John M. G o s l i n e , Dr. Ken D. Coutts and Dr. D. Gord E. Robertson, f o r the time and input they gave to and the i n t e r e s t they showed i n the t h e s i s . A p a r t i c u l a r thanks goes to Dr. Robertson f o r h i s help i n s e l e c t i n g a t o p i c , f o r h i s f l e x i b i l i t y i n course s e l e c t i o n , f o r h i s guidance and, most i m p o r t a n t l y , f o r r e k i n d l i n g my i n t e r e s t i n biomechanics. A s p e c i a l thanks to Dr. Gary D. S i n c l a i r f o r h i s help i n so many ways over the ye a r s . A f i n a l thanks goes to those f e l l o w graduate students who have become my f r i e n d s . Your h e l p , concern, c r i t i c i s m and support have a l l been g r e a t l y a p p r e c i a t e d . 1 INTRODUCTION While there has been a l a r g e amount of r e s e a r c h devoted to the standing jumps, most of the s t u d i e s have been kinematic analyses. U n f o r t u n a t e l y , kinematic analyses only d e s c r i b e movement; they do not provide i n f o r m a t i o n about the f o r c e s which cause movement. The k i n e t i c i n v e s t i g a t i o n s which have been u n d e r t a k e n to study jumping have concentrated almost e x c l u s i v e l y on the v e r t i c a l jump. Despite t h i s f a c t the movement p a t t e r n i t s e l f i s s t i l l not w e l l understood because r e s e a r c h has mainly focused upon using v e r t i c a l jumping as a t o o l f o r examining t o t a l body work, energy or power i n s t e a d of determining where and how work and power are being generated or absorbed. Only a j o i n t power a n a l y s i s allows the work done by the muscles c r o s s i n g a j o i n t to be c a l c u l a t e d which enables the r o l e and importance of the muscles i n v o l v e d to be a s c e r t a i n e d . Elftman (1939a, 1939b), while l o o k i n g at walking, was the f i r s t to combine j o i n t r e a c t i o n f o r c e s and net j o i n t moments with segmental and j o i n t kinematics to c a l c u l a t e the r a t e of change of energy f o r the l e g segments, the rate of energy t r a n s f e r through the l e g j o i n t s due to j o i n t f o r c e s and the r a t e of work done by muscles c r o s s i n g the j o i n t s . He l a t e r extended t h i s work to running (Elftman, 1940). Since that time, j o i n t power a n a l y s i s has been used to examine the c o n t r i b u t i o n of the l e g j o i n t s to walking ( B r e s l e r and Berry, 1951; Cappozzo e_t a_l. , 1976 ; M o r r i s o n , 2 1970; Zarrugh, 1981), race walking (White and Winter, 1985), jog g i n g (Winter, 1983), running (Robertson, 1985), jumping (Hubley and W e l l s , 1983; Robertson and Fleming, 1986) and soccer k i c k i n g (Robertson and Mosher, 1985). Hubley and Wells (1983) used the work-energy approach to q u a n t i f y the amount of p o s i t i v e work c o n t r i b u t e d by the muscles c r o s s i n g the h i p , knee and ankle j o i n t s during the p r o p u l s i v e phase of v e r t i c a l jumping. They found s i m i l a r r e l a t i v e work c o n t r i b u t i o n s by the l e g j o i n t s f o r both countermovement and squat jumps. Robertson and Fleming (1986) looked at the p r o p u l s i v e phase of both standing v e r t i c a l and standing broad jumping. They showed that there was a d i f f e r e n c e between r e l a t i v e l e g j o i n t c o n t r i b u t i o n s f o r the two types of jumps. However, the s t r e n g t h of t h e i r f i n d i n g was lessened by the small number of s u b j e c t s i n v o l v e d , p a r t i c u l a r l y i n the v e r t i c a l j ump. Two biomechancal p r i n c i p l e s which are thought to apply to jumping are the p r i n c i p l e of summation of j o i n t f o r c e s or moments and the p r i n c i p l e of c o n t i n u i t y of j o i n t f o r c e s or moments. Simply s t a t e d , the p r i n c i p l e of summation of j o i n t f o r c e s says that to produce the f a s t e s t , most powerful movement p o s s i b l e , a l l the j o i n t s that can c o n t r i b u t e to the movement must be used and used to t h e i r f u l l e s t extent. T h i s p r i n c i p l e has been d e s c r i b e d by Broer and Z e r n i c k e (1979), Dyson (1962), Jensen and Schultz (1977), Luttgens and Wells (1982), Morehouse and Cooper (1950), Norman 3 (1975), N o r t h r i p et a l . (1974), Simonian (1981) and the L e v e l I Coaching Theory Manual of the N a t i o n a l Coaching C e r t i f i c a t i o n Program (1979a). The sequencing of muscular c o n t r a c t i o n s f o r a movement i s explained by the p r i n c i p l e of c o n t i n u i t y of j o i n t f o r c e s which says that the order of muscle c o n t r a c t i o n s should be from the proximal to the d i s t a l muscle groups (Broer and Z e r n i c k e , 1979; Dyson, 1962; Gowitzke and M i l n e r , 1980; Luttgens and Wells, 1982; N a t i o n a l Coaching C e r t i f i c a t i o n Program, 1979a; Norman, 1975; Plagenhoef, 1971). T h i s i m p l i e s that the muscle groups c o n t r a c t from the l a r g e s t to the s m a l l e s t , from the str o n g e s t to the weakest or from from the slowest to the f a s t e s t . The u s e f u l n e s s of a biomechanical p r i n c i p l e depends upon the ease with which the p r i n c i p l e can be d i r e c t l y a p p l i e d to p h y s i c a l a c t i v i t y . A problem that a r i s e s f o r the a t h l e t e and coach i s how to apply the p r i n c i p l e to a t h l e t i c performance when o f t e n there i s l i t t l e or no e s t a b l i s h e d c r i t e r i a f o r e v a l u a t i n g whether or not a p r i n c i p l e i s being f o l l o w e d . Luttgens and Wells (1982), the N a t i o n a l Coaching C e r t i f i c a t i o n Program (1979a, 1979b, 1981) and Norman (1975) a l l s t a t e that through o b s e r v a t i o n of a performance i t i s p o s s i b l e to determine i f an a t h l e t e i s adhering to the p r i n c i p l e s of summation and c o n t i n u i t y of j o i n t f o r c e s . T herefore, i f a movement i s as f a s t as p o s s i b l e , i f a l l the j o i n t s are used through as l a r g e a range of motion as p o s s i b l e and i f the movement i s continuous, then i t i s 4 thought that both the summation and c o n t i n u i t y p r i n c i p l e s w i l l be i n evidence. The problem with t h i s approach i s that simple o b s e r v a t i o n does not provide i n f o r m a t i o n concerning the f o r c e s i n v o l v e d i n a movement. This can only be e s t a b l i s h e d through a k i n e t i c a n a l y s i s of the movement. PURPOSE The main purpose of t h i s study was to determine the r e l a t i v e c o n t r i b u t i o n of the muscles c r o s s i n g the h i p , knee and ankle j o i n t s to the t o t a l ( r e s u l t a n t ) work done at the l e g j o i n t s during maximal standing v e r t i c a l jumping and standing broad jumping. A secondary o b j e c t i v e was to determine i f the p r i n c i p l e s of summation of j o i n t f o r c e s and of c o n t i n u i t y of j o i n t f o r c e s held true for maximal standing broad and v e r t i c a l jumping by e s t a b l i s h i n g c r i t e r i a to make the d e t e r m i n a t i o n p o s s i b l e . A f i n a l aim was to i d e n t i f y any common patte r n s of j o i n t energy gener a t i o n or a b s o r p t i o n , f o r the two types of jumps, among a t e s t group of jumpers. 5 METHODOLOGY PROCEDURE Subj ect s. Twelve students, who were e i t h e r c u r r e n t l y or formerly a c t i v e i n community c o l l e g e or u n i v e r s i t y sports which i n v o l v e d jumping, performed a minimum of three t r i a l s of both the standing v e r t i c a l and the standing broad jump. Sin c e the s u b j e c t s were encouraged to jump maximally, countermovements and use of the arms were permitted. One of each type of jump f o r every s u b j e c t was chosen f o r a n a l y s i s . Before jumping, anthropometric data of sex, age, mass, height and segment lengths were c o l l e c t e d on each s u b j e c t . Subject i n f o r m a t i o n i s presented i n Table 1. Markers. Because both the standing v e r t i c a l and s t a n d i n g broad jumps were assumed to be b i l a t e r a l l y symmetric motions, one s i d e of the body was used to represent both s i d e s . The su b j e c t s had markers placed on the r i g h t s i d e of t h e i r bodies over a p p r o p r i a t e landmarks at the toe, b a l l (middle of the f i f t h m e t a t a r s a l - p h a l a n g e a l j o i n t ) , h e e l , ankle ( l a t e r a l m a lleolus of the f i b u l a ) , knee ( l a t e r a l femoral epicondyle, about 2 cm s u p e r i o r to the j o i n t l i n e ) , hip (g r e a t e r t r o c h a n t e r of the femur), shoulder (on the humerus, about 2 cm i n f e r i o r to the acromi a l process of the s c a p u l a ) , elbow ( l a t e r a l epicondyle of the humerus) and w r i s t (middle of the i n f e r i o r r a d i o - u l n a r j o i n t ) . The opening of the outer ear was used as the marker f o r the head (Dempster, 1955). 6 Table 1. Sex, age, mass, height and sport of s u b j e c t s Subj ect Sex Age (years) Mass (kg) Height (cm) Sport MB M 21 84.0 188.0 B a s k e t b a l l RB M 25 77.9 185.5 B a s k e t b a l l REB M 21 80.6 193.0 B a s k e t b a l l DE M 22 64 .8 175.3 B a s k e t b a l l KG M 21 86.2 182.9 T r i p l e jump CJ F 23 65.8 179. 1 High jump PJ M 21 95 .4 190.5 B a s k e t b a l l KK M 24 95.3 193.0 B a s k e t b a l l MM M 31 65.1 171.5 B a s k e t b a l l CP M 19 81. 5 188.0 B a s k e t b a l l LS M 22 78. 0 182.9 B a s k e t b a l l NS M 21 80.2 190.5 B a s k e t b a l l Mean 22.6 79.6 185.0 S .D. 3.0 10.0 6.6 DATA COLLECTION AND ANALYSIS The jumps were performed from a K i s t l e r f o r c e p l a t f o r m which had the f o l l o w i n g c h a r a c t e r i s t i c s : l i n e a r i t y , < + 1 % f u l l s c a l e output; h y s t e r e s i s , <̂  + 0.5 % f u l l s c a l e output; c r o s s t a l k , <̂  + 3 % i n a l l d i r e c t i o n s . Ground r e a c t i o n f o r c e s were c o l l e c t e d by a Data General microNova computer (MP/200) at a r a t e of 50 Hz. Simultaneously the jumps were recorded on c i n e f i l m at 50 frames per second by a Locam camera placed orthogonal to the plane of the jumps. The 7 s h u t t e r pulse c o r r e l a t o r of the camera was c o n d i t i o n e d to t r i g g e r a n a l o g - t o - d i g i t a l (A/D) conversions of the s i x channels of the f o r c e p l a t f o r m . When a button was pressed, a r e l a y was a c t i v a t e d that turned on an LED e l e c t r o n i c pulse to the A/D converter of the computer which enabled matching of the f o r c e p l a t e and camera r e c o r d s . The raw f o r c e data and x c o o r d i n a t e of the center of pressure data were low-pass d i g i t a l l y f i l t e r e d with an upper c u t o f f frequency of 20 Hz. F a u l t y f o r c e p l a t f o r m data precluded a n a l y s i s of s i x standing broad jump t r i a l s . The f i l m was p r o j e c t e d an average of 15 percent l i f e - s i z e onto a d r a f t i n g t a b l e . Body marker coordi n a t e s were d i g i t i z e d u s i n g a Numonics G r a p h i c s C a l c u l a t o r i n t e r f a c e d w i t h the Data G e n e r a l m i n i c o m p u t e r . The r e s o l u t i o n of the d i g i t i z a t i o n system was 0.5 mm while the d i g i t i z a t i o n e r r o r was c a l c u l a t e d to have a RMS e r r o r of l e s s than 3 mm, on average. The raw c i n e f i l m data were t r a n s m i t t e d to an Amdahl 470/V8 computer where they were s c a l e d and then r e f i n e d u s i n g a f r a c t i o n a l l i n e a r t r a n s f o r m a t i o n based on the work of W o l t r i n g (1980) to remove l i n e a r d i s t o r t i o n s caused by camera or p r o j e c t o r misalignment. Next the c o o r d i n a t e i n f o r m a t i o n was f i l t e r e d u sing a low-pass f i l t e r with an upper c u t o f f frequency of 6 Hz to remove high frequency noise and then d i f f e r e n t i a t e d u s ing f i n i t e d i f f e r e n c e equations (Pezzack e_t aJL̂ . , 1977 ). A seven component l i n k segment model was used to represent s u b j e c t s f o r a n a l y s i s purposes. The seven 8 segments were the f o o t , lower l e g , t h i g h , trunk, head-neck, upper arm and f o r e a r m - h a n d . T h i s a p proach has been v a l i d a t e d by Pezzack and Norman (1981). Anthropometric constants used f o r a l l s u b j e c t s were obtained from Winter (1979) and d e r i v e d from Dempster's (1955) cadaver s t u d i e s . Using l i n k segment modelling, i n c o r p o r a t i n g anthropometric, kinematic and f o r c e p l a t e data, the v e r t i c a l and h o r i z o n t a l f o r c e s and net moments of f o r c e at the ankle, knee, h i p , elbow, shoulder and neck j o i n t s were c a l c u l a t e d by i n v e r s e dynamics (Winter, 1979) us i n g the computerized software package BIOMECH ( K i n e s i o l o g y Department, U n i v e r s i t y of Waterloo). J o i n t Power. The instantaneous power developed at each j o i n t by the net moment of f o r c e was computed using the formula: P j = M J « W J (W) 1. where, Pj = instantaneous power at j o i n t j i n watts, M j = net moment of f o r c e at j o i n t j i n N«m, w j =» r e l a t i v e angular v e l o c i t y of j o i n t j i n rad/s. The s i g n , p o s i t i v e or negat i v e , of the net j o i n t moment of f o r c e i n d i c a t e d which musculature, f l e x o r or extensor, r e s p e c t i v e l y , was dominant at a p a r t i c u l a r time. Note that a net moment of f o r c e does not t e l l whether the t i s s u e s were performing p o s i t i v e or negative work or were working i s o m e t r i c a l l y . I t simply shows the magnitude and d i r e c t i o n of the net e f f e c t of a l l the muscles and other s t r u c t u r e s that created moments of f o r c e across a p a r t i c u l a r j o i n t producing the observed kinematic p a t t e r n . In g e n e r a l , a net 9 moment of f o r c e i s caused almost wholely by s k e l e t a l muscle c o n t r a c t i o n s i f the range of j o i n t movement i s not e x c e s s i v e , but ligaments, s k i n and the j o i n t capsule can a l s o c o n t r i b u t e to the moment p r o d u c t i o n . The s i g n of the instantaneous power, p o s i t i v e or negative, i n d i c a t e d what type of c o n t r a c t i o n , e i t h e r c o n c e n t r i c or e c c e n t r i c , produced the net j o i n t moment. J o i n t Work. The net mechanical work performed at each j o i n t was c a l c u l a t e d by i n t e g r a t i o n of the power h i s t o r y of the j o i n t ( B r e s l e r and Berry, 1951; Cappozzo e_t a_l. , 1976 ; Hubley and Wells, 1983; Robertson, 1985; Robertson and Mosher, 1985; White and Winter, 1985; Winter, 1983; Zarrugh, 1981). In t h i s study t r a p e z o i d a l i n t e g r a t i o n was used. The work done was determined f o r two time p e r i o d s . F i r s t the j o i n t work was computed f o r the e n t i r e jump (e) from the beginning (beg) of downward movement through to the time when the toes l e f t the f o r c e p l a t f o r m ( t o ) . Second the work done was c a l c u l a t e d f o r the p r o p u l s i v e phase (p) of the jump, from the s t a r t of upward movement (urn) to t o e - o f f ( t o ) . The f o l l o w i n g equation was used: The s i g n of the j o i n t work i n d i c a t e s whether the muscles c r o s s i n g the j o i n t were net generators ( p o s i t i v e ) or absorbers (negative) of energy during the p a r t i c u l a r time i n t e r v a l s examined. to 2 . beg e, Wj _ mechanical work done at j o i n t j i n j o u l e s . 10 The t o t a l work done at the j o i n t s (TJW) f o r both the e n t i r e jump and the p r o p u l s i v e phase of the jump was determined by summing the work done by the i n d i v i d u a l j o i n t s : 6 T J W ( e ) - 2 W J ( e ) (J) 3. j-1 Energy C a l c u l a t i o n s . The t o t a l body gain i n energy (TBE) was a l s o c a l c u l a t e d f o r both the e n t i r e jump and the p r o p u l s i v e phase of the jump. I t was obtained by t a k i n g the d i f f e r e n c e between the sum of the energy values f o r a l l the segments (TSE) at t o e - o f f and the sum of the segment energies at the beginning of the time i n t e r v a l of i n t e r e s t . to T B E ( e ) - TSE = T S E ( t o ) - T S E ( b e g ) (J) 4. beg The t o t a l segment energy was found by summing the energies of the i n d i v i d u a l segments. The i n d i v i d u a l segment energy (SE) was the t o t a l of the segment's p o t e n t i a l , t r a n s l a t i o n a l k i n e t i c and r o t a t i o n a l k i n e t i c energy v a l u e s . 7 TSE S E g ( J ) 5. s = l 2 2 S E s = m s S h s + I m s v s + I Isw s (J) 6. 2 2 where, mg = m a s s of segment s In kg, 2 g = g r a v i t a t i o n a l a c c e l e r a t i o n (9.81 m/s ), n s - height of the center of mass of segment s i n m, v s = a b s o l u t e l i n e a r v e l o c i t y of the center of mass of segment s i n m/s, l g = moment of i n e r t i a about the center of mass of segment s i n kg»m 2, wg = absolute angular v e l o c i t y of segment s i n rad/s. 11 Work-Energy A n a l y s i s . The r a t i o of the work done at a l l the j o i n t s (TJW) to the t o t a l body energy gain (TBE) was c a l c u l a t e d f o r both the e n t i r e jump and f o r the p r o p u l s i v e phase of the jump f o r the two types of jumps. T h i s was done to check the accuracy of the a n a l y s i s techniques ( c f . , Hubley and Wells, 1983). The TBE was taken as the c r i t e r i o n measure because i t was dependent upon f i r s t d e r i v a t i v e displacement-time data that was e a s i l y obtained and a l s o because i t assumed that the segments acted independently of one another (Quanbury e_t a_l. , 1975 ; Robertson and Winter, 1980). On the other hand, the TJW r e q u i r e d j o i n t f o r c e and torque values that r e l i e d on second d e r i v a t i v e i n f o r m a t i o n (Quanbury e_t a_l. , 1975). As w e l l , the j o i n t f o r c e and torque values from the more d i s t a l j o i n t s were u t i l i z e d i n the determination of the net f o r c e and torque at the more proximal j o i n t s . Hence, any e r r o r s i n d i s t a l j o i n t f o r c e or moment of f o r c e c a l c u l a t i o n s would be passed along to subsequent proximal j o i n t s i n the kinematic c h a i n . J o i n t C o n t r i b u t i o n . The absolute c o n t r i b u t i o n of the i n d i v i d u a l j o i n t work to i n c r e a s i n g the t o t a l body energy was a r r i v e d at by c a l c u l a t i n g the r a t i o of i n d i v i d u a l j o i n t work to TBE. The r e l a t i v e c o n t r i b u t i o n of the i n d i v i d u a l j o i n t s to the TJW was found by n o r m a l i z i n g the absolute work done at each j o i n t with respect to the TJW. As w e l l , the r e l a t i v e c o n t r i b u t i o n of the work done by the l e g j o i n t s alone was determined by d i v i d i n g the absolute work values f o r each l e g j o i n t by the t o t a l work done at a l l three l e g 12 j o i n t s . T h i s was done i n order that a comparison could be made with the r e s u l t s of Hubley and Wells (1983) and Robertson and Fleming (1986). A l l of the above c a l c u l a t i o n s were made f o r both types of jumps over the e n t i r e jump and p r o p u l s i v e phase of each jump. S t a t i s t i c s . T w o - t a i l e d c o r r e l a t e d t - t e s t s , with p<..05 chosen as the l e v e l of s i g n i f i c a n c e , were used to check f o r occurrences of s i g n i f i c a n t d i f f e r e n c e s i n i n d i v i d u a l j o i n t work c o n t r i b u t i o n to the standing jumps during the two time i n t e r v a l s examined. Since r e l a t i v e percent c o n t r i b u t i o n to the t o t a l work done at the l e g j o i n t s was the measurement u t i l i z e d , only two l e g j o i n t s could be examined as there were only two degrees of freedom. The ankle and the knee j o i n t s were chosen f o r a n a l y s i s because i t was assumed that i f the accuracy of the j o i n t work r e s u l t s decreased, i t would decrease from the d i s t a l to the proximal l e g j o i n t s . This assumption was based on the f a c t that the l i n k segment a n a l y s i s s t a r t e d at the toe and moved p r o x i m a l l y to the hip j o i n t . T h e r e f o r e , any e r r o r s i n l i n k segment mod e l l i n g or i n j o i n t moment c a l c u l a t i o n s would subsequently a f f e c t the r e s u l t s at the more proximal j o i n t s . Four t e s t s were done, two each f o r the ankle and knee j o i n t s . Only the r e s u l t s of the s i x sub j e c t s which had both a v e r t i c a l jump and standing broad jump analyzed were used f o r the c o r r e l a t e d t - t e s t s . Four one-way ANOVAs with repeated measures were done to t e s t the d i f f e r e n c e s between r e l a t i v e j o i n t c o n t r i b u t i o n s f o r each type of jump. Two were u t i l i z e d f o r the standing 13 broad jump (n=6) , l o o k i n g at the p r o p u l s i v e phase and the e n t i r e jump, and two f o r the v e r t i c a l jump (n=12). Neuman-Keuls post hoc procedure was used to evaluate the m u l t i p l e p a i r w i s e comparisons. The s i g n i f i c a n c e l e v e l f o r the ANOVAs and the Neuman-Keuls comparisons was again p<^05. P r i n c i p l e E v a l u a t i o n . A d e t e r m i n a t i o n of the v a l i d i t y of the p r i n c i p l e s of summation and c o n t i n u i t y of j o i n t f o r c e s with respect to standing broad and v e r t i c a l jumps was made. It was assumed that both p r i n c i p l e s only a p p l i e d during the p r o p u l s i v e phase of jumping. The c r i t e r i o n that was e s t a b l i s h e d to t e s t the summation p r i n c i p l e f o r standing broad and v e r t i c a l jumping was that the net mechanical work done by the moments of f o r c e at the three l e g j o i n t s must be p o s i t i v e f o r a l l j o i n t s during the p r o p u l s i v e phase of jumping. For the c o n t i n u i t y p r i n c i p l e i t was f e l t that l o o k i n g at both the power and moment curves would be more i n f o r m a t i v e than simply l o o k i n g at the moment curves alone because by themselves the moment curves did not i n d i c a t e when a moment of f o r c e c o n t r i b u t e d to a jump. I t was determined that the c o n t r i b u t i o n of a j o i n t to the jump began at the time when the instantaneous power curve, became p o s i t i v e as a r e s u l t of an extensor moment at that j o i n t d u r i n g the p r o p u l s i v e phase of jumping. In the case where the instantaneous power curve was p o s i t i v e more than once during the p r o p u l s i v e phase due to an extensor moment, the beginning of the f i r s t phase that accounted f o r at l e a s t 25 percent of the p o s i t i v e work done at the j o i n t during the 14 p r o p u l s i v e phase was used to i n d i c a t e the time of the power c o n t r i b u t i o n f o r the j o i n t . The sequencing of the power c o n t r i b u t i o n s from the l e g j o i n t s had to have a proximal to d i s t a l o r d e r i n g f o r the c o n t i n u i t y p r i n c i p l e to h o l d . Simultaneous power c o n t r i b u t i o n s from two or three j o i n t s precluded the c o n t i n u i t y p r i n c i p l e from h o l d i n g as d i d a sequencing that was not from proximal to d i s t a l . Performance A n a l y s i s . F i n a l l y , a performance a n a l y s i s was done on a l l analyzed jumps to give an i n d i c a t i o n of the jumping a b i l i t y of the s u b j e c t s i n v o l v e d i n the study. Using equations of motion i n c o r p o r a t i n g kinematic data r e l a t i n g to the body center of g r a v i t y , a p r e d i c t e d d i s t a n c e that the body center of g r a v i t y would move e i t h e r v e r t i c a l l y ( v e r t i c a l jump) or h o r i z o n t a l l y (standing broad jump) was determined f o r each s u b j e c t . As w e l l , the r e l e v a n t ground r e a c t i o n f o r c e s f o r the standing broad jump and v e r t i c a l jump were normalized i n terms of each s u b j e c t ' s body weight to give an i n d i c a t i o n of the appropriateness of the f o r c e p l a t e data. 15 RESULTS (Note: The means f o r standing broad jump data i n Tables 2-7, 10 and 12 are f o r an n=6 while the v e r t i c a l jump means i n the same t a b l e s are f o r an n=12.) Tables 2 and 3 c o n t a i n the r e l a t i v e c o n t r i b u t i o n s of each l e g j o i n t to the t o t a l work done by the legs f o r the two types of jumps during the e n t i r e jump and the p r o p u l s i v e phase of jumping, r e s p e c t i v e l y . Tables 4 and 5 l i s t both the absolute and r e l a t i v e c o n t r i b u t i o n of a l l s i x j o i n t s to the gain i n t o t a l body energy f o r standing broad jumping d u r i n g the e n t i r e jump and the p r o p u l s i v e phase, r e s p e c t i v e l y . Tables 6 and 7 do the same f o r the v e r t i c a l jump. In a l l cases a p o s i t i v e value i n d i c a t e s that the j o i n t was a net generator of energy f o r the time p e r i o d examined while a negative value means that the j o i n t was a net d i s s i p a t o r of energy. In Tables 4 through 7 the mean r a t i o of work done at the j o i n t s (TJW) to the energy gained (TBE) represents the r e s u l t s of the work-energy a n a l y s i s f o r the two kinds of jumps over the two time i n t e r v a l s of i n t e r e s t . Since the TJW-TBE r a t i o i s l e s s than 1 .000 i n a l l four c o n d i t i o n s , then, on average, the TJW d i d not account f o r a l l the gain i n TBE. In Table 8 are presented the r e s u l t s of the s t a t i s t i c a l a n a l y s i s on r e l a t i v e ankle and knee j o i n t c o n t r i b u t i o n to the work done at the l e g j o i n t s f o r the two types of jumps both during the p r o p u l s i v e phase and over the e n t i r e jump. 16 The means f o r r e l a t i v e j o i n t c o n t r i b u t i o n during the p r o p u l s i v e phase of v e r t i c a l jumping f o r the s i x s u b j e c t s who had both a standing broad jump and a v e r t i c a l jump analyzed were 38.8 + 4.2 percent ( a n k l e ) , 21.5 + 18.5 percent (knee) and 39.7 + 15.5 percent ( h i p ) . Over the e n t i r e v e r t i c a l jump the ankle, knee and hip means were 32.2 + 4.7, 23.8 + 8.1 and 44.0 + 10.0 perce n t , r e s p e c t i v e l y , f o r the same s u b j e c t s . Of the four c o r r e l a t e d t - t e s t s done, the only s i g n i f i c a n t d i f f e r e n c e occurred i n the ankle j o i n t f o r the e n t i r e jump. T h i s d i f f e r e n c e favored the v e r t i c a l jump. T h e r e f o r e , over the e n t i r e jump r e l a t i v e l y more work was done at the ankle j o i n t i n v e r t i c a l ~ j u m p i n g than i n standing broad jumping. T a b l e 8 a l s o shows n o n - s i g n i f i c a n t d i f f e r e n c e s f o r the c o n t r i b u t i o n of the ankle j o i n t to the jumps during the p r o p u l s i v e phase and f o r the c o n t r i b u t i o n of the knee j o i n t to the two jumps during both time i n t e r v a l s . The r e s u l t s of a l l the p a i r w i s e comparisons r e l a t i n g to the four ANOVAs are l i s t e d i n Table 9. The work values being compared are those l i s t e d i n Tables 2 and 3. The muscles c r o s s i n g the hip j o i n t d i d s i g n i f i c a n t l y more work than those of the knee j o i n t during both standing broad (p<.01) and v e r t i c a l jumping (p<.05) when the jumps were looked at i n t h e i r e n t i r e t i e s . For the p r o p u l s i v e phase, there was s i g n i f i c a n t l y more work generated at the hip j o i n t than at e i t h e r of the other two l e g j o i n t s during both v e r t i c a l (knee: p<.01; ankle: p<.05) and standing broad 17 jumping (knee: p<.01; a n k l e : p<.01). A s i g n i f i c a n t d i f f e r e n c e (p<.05), f a v o r i n g the ankle j o i n t , a l s o occurred dur i n g the e n t i r e v e r t i c a l jump when the work done at the ankLe and knee j o i n t s was compared. During the p r o p u l s i v e phase and over the e n t i r e jump i n standing broad jumping, the d i f f e r e n c e s between r e l a t i v e ankle and knee j o i n t c o n t r i b u t i o n s were n o n - s i g n i f i c a n t . As w e l l there was a n o n - s i g n i f i c a n t d i f f e r e n c e between r e l a t i v e ankle and knee j o i n t c o n t r i b u t i o n s during the p r o p u l s i v e phase of v e r t i c a l jumping. Over the e n t i r e jump i n both standing broad and v e r t i c a l jumping there were no s i g n i f i c a n t d i f f e r e n c e s between the r e l a t i v e hip and ankle j o i n t c o n t r i b u t i o n s to the t o t a l work done at the leg j o i n t s . Table 10 presents a summary of the v a r i o u s work phases that each jumper e x h i b i t e d during v e r t i c a l and standing broad jumping. Other work episodes were a l s o present f o r some jumpers. However, the ph ases that are l i s t e d i n Table 10 are those that were c o n s i s t e n t f o r a l l s u b j e c t s . In both kinds of jumps a l l s u b j e c t s e x h i b i t e d two types of ankle muscle a c t i v i t y , l a b e l l e d Al and A2, three types of knee muscle a c t i v i t y , l a b e l l e d K l , K2 and K3, and three types of hip muscle a c t i v i t y , HI, H2 and H3. In a d d i t i o n the standing broad jump had a f o u r t h i d e n t i f i a b l e type of hip muscle a c t i v i t y l a b e l l e d H4. K3 and H4 were episodes that both s t a r t e d before t o e - o f f and continued a f t e r t o e - o f f . The means and standard d e v i a t i o n s of the work done by the v a r i o u s types of c o n t r a c t i o n s are a l s o l i s t e d i n Table 10. 18 As w e l l the footnotes at the bottom of Table 10 e x p l a i n the codes used i n the t a b l e , i d e n t i f y i n g the j o i n t i n v o l v e d , the dominant muscle group and the type of c o n t r a c t i o n r e s p o n s i b l e f o r a p a r t i c u l a r work episode. F i g u r e 1 giv e s a p i c t o r i a l account of the time sequence of muscular c o n t r a c t i o n s at the h i p , Jcnee and ankle j o i n t s f o r the standing broad and v e r t i c a l jumps. The a p p r o p r i a t e codes (Tables 10) are used to l a b e l the beginning of p a r t i c u l a r work phases. The s t a r t of the p r o p u l s i v e phase f o r each type of jump i s i n d i c a t e d by the v e r t i c a l l i n e l a b e l l e d P. F i g u r e 1 shows that the standing broad jump took longer to perform than the v e r t i c a l jump. In s p i t e of t h i s , the p r o p u l s i v e phases of each jump are almost i d e n t i c a l i n l e n g t h . F i g u r e s 2, 3 and 4 show one jumper's ankle, knee and h i p kinematics and k i n e t i c s f o r standing v e r t i c a l jumping while F i g u r e s 5, 6 and 7 show another jumper's ankle, knee and hip kinematics and k i n e t i c s f o r standing broad jumping. The top graph i n each f i g u r e r epresents the r e l a t i v e angular v e l o c i t y of the j o i n t . The middle graph i s the net moment of f o r c e h i s t o r y with l a b e l s i d e n t i f y i n g the dominant muscle group. L a s t l y , the bottom graph i s the power produced by the net moment of f o r c e with l a b e l s s p e c i f y i n g the type of c o n t r a c t i o n o c c u r r i n g i n the dominant muscle group. A l l s i x f i g u r e s have the same a b s c i s s a and o r d i n a t e s c a l i n g f o r comparative purposes. As w e l l , the a p p r o p r i a t e work phases, 19 as designated i n Table 10, are i n d i c a t e d on the power curves i n F i g u r e s 2 through 7. The degree of support f o r the p r i n c i p l e s of summation of j o i n t f o r c e s and c o n t i n u i t y of j o i n t f o r c e s d u r i n g s t a n d i n g broad and v e r t i c a l jumping i s i n d i c a t e d by the r e s u l t s i n Table 11. The numerator of the r a t i o s r e p r e s e n t s the number of t r i a l s analyzed where the p r i n c i p l e was i n evidence while the denominator i s the t o t a l number of t r i a l s analyzed. One v e r t i c a l jump f o r each of the twelve subjects was analyzed but only s i x of the s u b j e c t s had standing broad jumps that could be used. An i n d i c a t i o n of the performance c a p a b i l i t i e s of the su b j e c t s i s presented i n Table 12. V a r i a b l e dl i s the d i s t a n c e the body center of g r a v i t y moved i n the v e r t i c a l or h o r i z o n t a l d i r e c t i o n s from i n i t i a l s tanding on the f o r c e p l a t e to t o e - o f f f o r the v e r t i c a l or standing broad jumps, r e s p e c t i v e l y . The p r e d i c t e d d i s t a n c e the body center of g r a v i t y would move a f t e r t o e - o f f , i n the v e r t i c a l d i r e c t i o n f o r the v e r t i c a l jump and the h o r i z o n t a l d i r e c t i o n f o r the standing broad jump, i s given by d2. L a s t l y d3, where d3 = dl+d2, gives the p r e d i c t e d d i s t a n c e , e i t h e r v e r t i c a l l y or h o r i z o n t a l l y , that the body center of g r a v i t y would move a l t o g e t h e r f o r the v e r t i c a l jump or standing broad jump, r e s p e c t i v e l y . A check of the ground r e a c t i o n f o r c e data revealed that the peak v e r t i c a l f o r c e averaged 2. 70 + 0.30 times body weight f o r the v e r t i c a l jump. The peak v e r t i c a l and 20 h o r i z o n t a l f o r c e s f o r the broad jump were 2.21 + 0.34 and 1.05 + 0.14 times body weight, r e s p e c t i v e l y . Table 2. Average r e l a t i v e c o n t r i b u t i o n of the l e g j o i n t moments to the t o t a l work done at the l e g j o i n t s d u r i n g the e n t i r e jump J o i n t Broad Jump V e r t i c a l Jump Ankle 31.5 + 3.4 % 39.2 + 8.9 % Knee 17.0 + 15.3 22.4 + 14.9 Hip 51.5 + 13.4 38.4 + 11.3 Table 3. Average r e l a t i v e c o n t r i b u t i o n of the l e g j o i n t moments to the t o t a l work done at the l e g j o i n t s during the p r o p u l s i v e phase J o i n t Broad Jump V e r t i c a l Jump Ankle 30.2 + 7.2 % 33.0 + 6.6 % Knee 18.6 + 8.3 24.8 + 8.3 Hip 51.2 + 9.5 42.2 + 10.0 21 Table 4. Average absolute and r e l a t i v e j o i n t c o n t r i b u t i o n to the gain i n t o t a l body energy f o r the e n t i r e jump i n standing broad jumping J o i n t Absolute R e l a t i v e Ankle Knee Hip Elbow Shoulder Neck TJW/TBE 25.7 + 5.6 % 13.8 + 12.6 41.5 + 12.3 6.2 + 1.9 5.0 + 4.1 0.6 + 1.6 0.928 + 0.124 27.4 + 2.9 % 15.0 + 13.4 44.8 + 11.4 7.0 + 2.8 5.4 + 4.7 0.4 + 1.6 1.000 Table 5. Average absolute and r e l a t i v e j o i n t c o n t r i b u t i o n to the gain i n t o t a l body energy during the p r o p u l s i v e phase of standing broad j umping J o i n t Absolute R e l a t i v e Ankle 26.4 + 6.3 % 30.9 + 7.5 % Knee 16.2 + 7.1 19.0 + 8.5 Hip 45.3 +11.1 52.6 + 10.1 Elbow 3.8+ 0.7 4 - 5 ± 1-1 Shoulder -5.8 + 3.4 -6.7 + 3.8 Neck -0.2 + 0.8 -0.3 + 1.0 TJW/TBE 0.856 + 0.086 1.000 22 Table 6. Average absolute and r e l a t i v e j o i n t contribution to the gain in t o t a l body energy for the entire jump in v e r t i c a l jumping Joint Absolute Relative Ankle 28.9 + 8.1 % 35.5 + 8.2 % Knee 16.0 + 10.2 20.3 + 13.3 Hip 28.7 + 9.5 34.8 + 10.4 Elbow 6.5 + 2.7 8.0 + 3.3 Shoulder 2.1 + 4.6 2.3 + 6.1 Neck -0.7 + 1.3 -0.9 + 1.5 TJW/TBW 0.814 + 0.118 1.000 Table 7. Average absolute and r e l a t i v e j o i n t contribution to the gain in t o t a l body energy during the propulsive phase of v e r t i c a l j umping Joint Absolute Relative Ankle 26.5 + 6.1 % 33.1 + 7.1 % Knee 20.2 + 7.4 24.7 + 8.1 Hip 34.1 +8.9 42.3 + 10.3 Elbow 3.8+1.7 4.8+ 2.4 Shoulder -3.4 + 3.9 -4.4 + 4.9 Neck -0.4 +0.7 - 0 . 5 + 0 . 9 TJW/TBW 0.808 + 0.093 1.000 23 Table 8. Comparison of the r e l a t i v e percent c o n t r i b u t i o n of the ankle and knee j o i n t s i n v e r t i c a l jumping to t h e i r c o n t r i b u t i o n s i n standing broad jumping Joint- P r o p u l s i v e E n t i r e Phase Jump Ankle n.s. p<.01 Knee n.s. n.s. Table 9. Comparison of r e l a t i v e j o i n t c o n t r i b u t i o n s J o i n t Comparison BROAD JUMP P r o p u l s i v e Phase E n t i r e Jump VERTICAL JUMP P r o p u l s i v e E n t i r e Phase Jump Hip-Knee Hip-Ankle Ankle-Knee p< .01 p<.01 n.s. p<. 01 n.s. n.s. p< .01 p<.05 n.s. p< .05 n.s. p<.05 24 Table 10. Average work done by contractions of the muscles crossing the ankle, knee and hip j oints Phase Broad Jump V e r t i c a l Jump * Al -23.4 + 13.5 J -25.0 + 11.3 J A2 165.6 + 41.2 173.5 + 35.4 Kl -44.4 + 31.8 -65.3 + 39.8 K2 114.0 + 27.9 164.3 + 36.5 K3 -13.7+7.6 -29.5 +17.2 HI 25.4 + 12.5 29.8 + 16.2 H2 -156.4 + 36.1 -133.2 + 46.3 H3 357.8 + 79.3 258.6 + 86.5 H4 -17.6 + 11.9 * These codes indicate the following types of muscle contract ions: Al Plantar flexor eccentric A2 Plantar flexor concentric Kl Knee extensor eccentric K2 Knee extensor concentric K3 Knee flexor eccentric Hi Hip flexor concentric H2 Hip extensor eccentric H3 Hip extensor concentric H4 Hip flexor eccentric 25 STANDING BROAD JUMP - P H IP HI H2 H 3 1 1 1 TOE- H4 I KNEE K l 1 K2 K3 1 I ANKLE A l A2 1 HIP HI H2 H 3 1 1 1 KNEE K l 1 K2 K3 1 I ANKLE A l 1 A2 VERTICAL JUMP ] 1 cm = 100 TOE- msec OFF F i g u r e 1. Sequencing of muscular c o n t r a c t i o n s f o r s t a n d i n g broad and v e r t i c a l jumping (P = s t a r t of the p r o p u l s i v e phase) 20 . -20 . 1 400. 1 -400. 1 1750. 1 •1750 1 -3500 0 .00 0.20 0.40 0 .60 TIME (SECONDS) 0.80 1.00 Figure 2. Ankle plots for v e r t i c a l jumping 27 20. cn o a: or CD ^ - 2 0 . 400. UJ O -400 . 1 1750. 1 or o -3500 •1750 1 ECCENTRIC 0 .00 0.20 0.40 0'.60 0'.80 TIME (SECONDS) .00 F i g u r e 3. Knee p l o t s f o r v e r t i c a l jumping 28 20. -20 . 1 400. 1 -400. 1 1750 . -3500. EXTENDING FLEXORS EXTENSORS CONCENTRIC TRIAL CODE.: VJ2RB a— 1 —A 1 1 X- 1 -X X—X MUSCLE POWER H 3 1750 J . ECCENTRIC 0 .00 0.20 rf- OFF 0.40 0.60 0.80 TIME (SECONDS) 1 .00 F i g u r e 4. Hip p l o t s f o r v e r t i c a l jumping 29 20 co o CE or CD ^ -20. 400. 1 0. o -400. 1 1750 . 1 £ 0. J o -3500 PLRNTRR FLEXING DORSIFLEX0RS TRIAL CODE: BJ2REB A- 1 —A 1 1 X- 1 —X NET MOMENT OF FORCE — X MUSCLE POWER 1 H PLRNTRR FLEXORS CONCENTRIC *—X—X-+-X—X-—X X X I 750_L ECCENTRIC *—X- & ^ ^ t — - t — -t- OFF 0.00 0.20 0.40 0.60 0.80 i T 0 0 T \ 2 0 TIME (SECONDS) F i g u r e 5 . A n k l e p l o t s f o r s t a n d i n g broad jumping 30 ?0 - 2 0 . 400. 1 0. -400 . 1750 . 1 - 3 5 0 0 E X T E N D I N G ~&—A A—A- F L E X I N G EXTENSORS TRIAL CODE: BJ2REB A — A ANGULAR VELOCITY' H h NET MOMENT OF FORCE X — X MUSCLE POWER - 1 7 5 0 1 E C C E N T R I C OFF 0'. 00 0 . 2 0 o ' .40 o ' .60 •'. 80 T^OO \^20 TIME (SECONDS) gure 6. Knee p l o t s f o r s t a n d i n g broad jumping 31 ?0 . O cx or CD ^ - 2 0 . 400. 1 -400 . 1 1750. 1 £ 0 . o •1750 1 -3500 0 .00 0.20 0.40 0 .60 0.80 TIME (SECONDS) 00 1.20 Figure 7. Hip plots for standing broad j umping 32 Table 11. I n d i c a t i o n of the extent of support f o r the summation and c o n t i n u i t y p r i n c i p l e s P r i n c i p l e Broad Jump V e r t i c a l Jump Summation C o n t i n u i t y 6/6 3/6 12/12 2/12 Table 12. P r e d i c t e d performance of s u b j e c t s Di stance Broad Jump V e r t i c a l Jump dl d2 d3 0.832 + 0.053 m 2.160 + 0.159 2.992 + 0.162 0.157 + 0.024 m 0.485 + 0.068 0.642 + 0.075 33 DISCUSSION LEG JOINT WORK Standing Broad Jump. The results for the standing broad jump (Tables 2 and 3) indicate that the muscles of a l l three leg j o i n t s were net generators of energy during both the entire jump and the propulsive phase of standing broad jumping. In both cases the percentage contributions of the three leg j o i n t s were very s i m i l a r . The work done by the muscles crossing the hip j o i n t accounted for just more than half of the work done at the leg j o i n t s . The ankle j o i n t was the next largest work contributor while the knee j o i n t had the smallest work output. These results d i f f e r from those of Robertson and Fleming (1986) who limited themselves to looking at r e l a t i v e leg j o i n t contribution during the propulsive phase. They found that the contributions of the muscles crossing the hip, knee and ankle j o i n t s to the work done by the legs were 45.9, 3.9 and 50.2 percent, respectively. Subsequent analysis of their data to get leg j o i n t contributions for the entire jump yielded percentages of 44.8 for the hip, -4.2 for the knee and 59.4 for the ankle. The -4.2 percent for the knee j o i n t indicated that the muscles of the knee were net dissipators of energy during the standing broad jump. For both the entire jump and the propulsive phase, the largest contributor to the work done by the leg joints was the ankle in the Robertson and Fleming (1986) study. 34 Furthermore, the knee was the l e a s t important j o i n t as f a r as generating p o s i t i v e work was concerned. There may be s e v e r a l o v e r l a p p i n g reasons f o r the d i f f e r e n c e s i n r e s u l t s between the present study and those of Robertson and Fleming (1986). In the current study the s u b j e c t s were allowed to use t h e i r arms while s u b j e c t s i n the study by Robertson and Fleming (1986) were r e s t r i c t e d i n performing the jump by keeping the hands on the h i p s . Since that i s not the t y p i c a l way to perform the v e r t i c a l jump, i t may be that some a l t e r a t i o n i n l e g j o i n t involvement occurred to compensate f o r the unusual movement p a t t e r n . T h i s change i n movement p a t t e r n may have been s u f f i c i e n t enough cause to reduce or i n h i b i t the c o n t r i b u t i o n of the hip muscles and to i n c r e a s e or enhance the c o n t r i b u t i o n of the muscles c r o s s i n g the ankle j o i n t . Another f a c t o r that c o n c e i v a b l y accounts f o r the d i f f e r e n c e i n r e s u l t s i s that the peak h o r i z o n t a l f o r c e s i n the Robertson and Fleming (1986) study averaged only 0.65 times body weight. From Roy et a l . (1973), one would expect the peak h o r i z o n t a l f o r c e to approximate body weight. This was the case i n the present study. The underestimation of the h o r i z o n t a l ground r e a c t i o n f o r c e s i n the i n v e s t i g a t i o n by Robertson and Fleming (1986) would lead to e r r o r s i n the c a l c u l a t i o n s of r e a c t i o n f o r c e s and moments of f o r c e at a l l three l e g j o i n t s and would d i r e c t l y a f f e c t the j o i n t work v a l u e s . Another p o t e n t i a l cause f o r the c o n t r a s t i n g r e s u l t s i s that the manner i n which a t h l e t e s of v a r y i n g c a p a b i l i t i e s 35 produce work may d i f f e r . The s u b j e c t s i n v o l v e d i n the c u r r e n t study were s p e c i f i c a l l y chosen because they were b e t t e r than average jumpers. This point i s supported by t h e i r p r e d i c t e d performance (2.992 m) i n the standing broad jump when compared to the p r e d i c t e d performance (2.152 m) of the s u b j e c t s i n the R o b e r t s o n and F l e m i n g (1986) i n v e s t i g a t i o n . A confounding v a r i a b l e here i s the sex of the s u b j e c t s i n v o l v e d i n the two s t u d i e s . I t must be noted that only two of the s i x s u b j e c t s i n the r e s e a r c h of Robertson and Fleming (1986) were male while a l l s i x standing broad jump s u b j e c t s i n the present study were male. The p r e d i c t e d performance of both male s u b j e c t s (2.430 m) i n the Robertson and Fleming (1986) i n v e s t i g a t i o n was b e t t e r than that of t h e i r four female c o u n t e r p a r t s (2.013 m) , but i t was w e l l below the p r e d i c t e d performance of the subjects i n the c u r r e n t study. T h e r e f o r e , as f a r as standing broad jumping i s concerned, there was d e f i n i t e l y a d i s c r e p a n c y i n the performance c a p a b i l i t i e s of the male su b j e c t s i n v o l v e d i n the two s t u d i e s . No c o n c l u s i o n can be made about the c a p a b i l i t i e s of the four female s u b j e c t s i n the study by Robertson and Fleming (1986) because no i n f o r m a t i o n f o r comparison was found i n the l i t e r a t u r e on jumping. Regarding the low c o n t r i b u t i o n of the muscles c r o s s i n g the knee j o i n t which was found i n the two s t u d i e s , other r e s e a r c h e r s who have s t u d i e d movements that were p r i m a r i l y concerned with h o r i z o n t a l displacement of the body and which contained a double l e g support phase also n o t i c e d the lac k 36 of importance of the knee j o i n t i n doing p o s i t i v e work. B r e s l e r and Berry (1951), Cappozzo et_ al.. (1976 ) and Zarrugh (1981), i n l o o k i n g at walking, and White and Winter (1985), when examining race walking, found that f o r one s t r i d e of each a c t i v i t y the muscles c r o s s i n g the ankle and hip j o i n t s generated more energy than they r e c e i v e d while the o p p o s i t e was true f o r the muscles of the knee j o i n t . None of these s t u d i e s c a l c u l a t e d the r e l a t i v e l e g j o i n t c o n t r i b u t i o n s . V e r t i c a l Jump. From the v e r t i c a l jump r e s u l t s (Table 2 and 3 ) , i t can be seen that a l l three l e g j o i n t s c o n t r i b u t e d to v e r t i c a l jumping over the e n t i r e jump and during the p r o p u l s i v e phase. There was a s l i g h t d i f f e r e n c e between the r e l a t i v e l e g j o i n t c o n t r i b u t i o n s f o r the e n t i r e jump and f o r the p r o p u l s i v e phase. Over the e n t i r e jump both the ankle and hip j o i n t s c o n t r i b u t e d almost e q u a l l y to the work done at the l e g j o i n t s while f o r the p r o p u l s i v e phase the muscles c r o s s i n g the hip j o i n t were the major net generators of energy. For both the e n t i r e jump and the p r o p u l s i v e phase of v e r t i c a l jump the c o n t r i b u t i o n of the knee j o i n t to the p o s i t i v e work done at the l e g j o i n t s was very s i m i l a r . Robertson and Fleming (1986) have also looked at the p r o p u l s i v e phase of v e r t i c a l jumping as d i d Hubley and Wells (1983). The l e g j o i n t c o n t r i b u t i o n s of 40.0 percent f o r the h i p , 24.2 percent f o r the knee and 35.8 percent f o r the ankle that Robertson and Fleming (1986) found were very c l o s e to the r e s u l t s of the present study. On the other hand, Hubley and W e l l s (1983) o b t a i n e d s u b s t a n t i a l l y 37 d i f f e r e n t percentages of 27.5, 49.0 and 23.5 f o r the muscles of the h i p , knee and ankle j o i n t s , r e s p e c t i v e l y , during the p r o p u l s i v e phase of countermovement jumping. They a l s o looked at squat jumping and obtained c o n t r i b u t i o n s almost i d e n t i c a l to those achieved i n countermovement jumping. In t h e i r study then, the knee j o i n t was the biggest generator of energy f o r the l e g s . One cause of the discrepancy i n r e s u l t s between the r e s e a r c h of Hubley and Wells (1983) and both the current study and that of Robertson and Fleming (1986) i s the performance l e v e l of the s u b j e c t s . The p r e d i c t e d r i s e i n the body center of g r a v i t y a f t e r t o e - o f f (d2 i n the present study) f o r the s i x male s u b j e c t s i n the Hubley and Wells (1983) i n v e s t i g a t i o n averaged only 33 cm (from Hubley, 1981) which i s w e l l below the 40.3-43.4 cm range achieved by male su b j e c t s i n other s t u d i e s (Asmussen and Bonde-Petersen, 1974; Bosco and Komi, 1979; Komi and Bosco, 1978a, 1978b) and the one male v e r t i c a l jump subject (42.8 cm) i n the Robertson and Fleming (1986) i n v e s t i g a t i o n . Since a l l of t h e s e s t u d i e s r e s t r i c t e d arm movements d u r i n g countermovement jumping, the performance of the s u b j e c t s can be compared. Hence the c o n c l u s i o n that the s u b j e c t s used by Hubley and Wells (1983) were poorer jumpers than the s u b j e c t s i n the other s t u d i e s . Another area of concern i s the f o r c e p l a t e . Hubley and Wells (1983) neglect to provide i n f o r m a t i o n about the c h a r a c t e r i s t i c s of t h e i r f o r c e p l a t e 38 so i t s q u a l i t y cannot be a s c e r t a i n e d , thus l e a v i n g doubts about the accuracy of t h e i r data. The other s i d e of the c o i n sees the r e s u l t s of the present i n v e s t i g a t i o n and those of Robertson and Fleming (1986) being very s i m i l a r d e s p i t e both the f a c t that Robertson and Fleming (1986) r e s t r i c t e d the use of the arms and that the performance c a p a b i l i t i e s of the s u b j e c t s i n that study, as measured by both p r e d i c t e d performance (0.501 m) and peak v e r t i c a l f o r c e (2.28 times body weight), were lower than those of the s u b j e c t s i n v o l v e d i n the present i n v e s t i g a t i o n . However, the d i f f e r e n c e s i n performance c a p a b i l i t i e s of the s u b j e c t s i n the two s t u d i e s are not as great as they i n i t i a l l y appear f o r two reasons. F i r s t , i t was to be expected that the average peak v e r t i c a l f o r c e would be l e s s i n the Robertson and Fleming (1986) study, although probably not q u i t e to the extent that i t was. This i s due to the f a c t that when Payne et_ a_l. (1968) looked at ground r e a c t i o n f o r c e s during performance of standing v e r t i c a l jumps, they n o t i c e d that use of the arms created a greater peak on the impulse curve than v e r t i c a l jump performance where use of the arms was r e s t r i c t e d . The second apparent reason i s the sex of the s u b j e c t s . Two of the three s u b j e c t s f o r Robertson and Fleming (1986) were female while only one of the twelve s u b j e c t s i n the current i n v e s t i g a t i o n was female. The p r e d i c t e d v e r t i c a l jump performance of the male subject (62.0 cm) and the female s u b j e c t s (44.1 cm) f o r Robertson and Fleming (1986) compare 39 reasonably w e l l to the male s u b j e c t s (65.6 cm) and one female subject (49.1 cm) of the present study. Fu r t h e r a n a l y s i s of the Robertson and Fleming (1986) data r e v e a l e d l e g j o i n t c o n t r i b u t i o n s over the e n t i r e v e r t i c a l jump of 40.1 percent f o r the h i p , 18.5 percent f o r the knee and 41.3 percent f o r the ankle. These were, again, very s i m i l a r to the r e s u l t s found i n the present study. In s p i t e of the s i m i l a r i t y i n r e s u l t s between the two s t u d i e s i t i s d i f f i c u l t to s t a t e with any c o n v i c t i o n that the s i m i l a r i t y i s due to an e s t a b l i s h e d t r e n d i n b o t h i n v e s t i g a t i o n s because of the small sample s i z e (n=3) f o r the v e r t i c a l jump i n the Robertson and Fleming (1986) study. While p a t t e r n s of j o i n t c o n t r i b u t i o n emerged i n the current study f o r both standing broad and v e r t i c a l jumps, the f a i r l y l a r g e i n t e r - s u b j e c t v a r i a b i l i t y e x h i b i t e d at a l l the l e g j o i n t s , with the exceptions of the ankle j o i n t over the e n t i r e standing broad jump, i n d i c a t e that the manner i n which s u b j e c t s used the major l e g muscle groups to generate work was q u i t e v a r i a b l e . T h i s f i n d i n g i s supported by the data of Hubley and Wells (1983) and Robertson and Fleming (1986) who a l s o o b t a i n e d r e l a t i v e l y l a r g e s t a n d a r d d e v i a t i o n s f o r most of the l e g j o i n t s . The v a r i a b i l i t y i n l e g j o i n t c o n t r i b u t i o n also p o i n t s out the d i f f i c u l t y i n e s t a b l i s h i n g the importance of one group of l e g extensors as the dominant muscle group f o r jumping. S t a t i s t i c s . The r e s u l t s of the four c o r r e l a t e d t - t e s t s (Table 8) show t h a t , r e l a t i v e l y , the muscles c r o s s i n g the 40 knee j o i n t c o n t r i b u t e d the same amount of work to both the standing broad and v e r t i c a l jumps, and that over the e n t i r e jump the r e l a t i v e c o n t r i b u t i o n of the muscles of the ankle j o i n t to the work done at the l e g j o i n t s was s i g n i f i c a n t l y g r e a t e r i n the v e r t i c a l jump than f o r the st a n d i n g broad jump. K i n e s i o l o g i s t s have assumed that v a r i o u s s k i l l s i n v o l v i n g the same musculature u t i l i z e the musculature d i f f e r e n t i a l l y and p h y s i o l o g i s t s , through the p r i n c i p l e of s p e c i f i c i t y , have expressed the same o p i n i o n . The one s i g n i f i c a n t r e s u l t of t h i s p r e s e n t s t u d y p a r t i a l l y r e i n f o r c e s that i d e a f o r two d i f f e r e n t jumping movements. From Tables 2, 3 and 9, i t can be seen that f o r a l l four c o n d i t i o n s the r e l a t i v e c o n t r i b u t i o n of the muscles c r o s s i n g the hip j o i n t to the work done at a l l three l e g j o i n t s was s i g n i f i c a n t l y g r e a t e r than the c o n t r i b u t i o n s of the knee muscles. As w e l l , during the p r o p u l s i v e phase of both standing broad and v e r t i c a l jumping, the r e l a t i v e amount of work done at the hip j o i n t was s i g n i f i c a n t l y g r e a t e r than the the work done at the ankle j o i n t . However, over the e n t i r e jump there was no s i g n i f i c a n t d i f f e r e n c e between the r e l a t i v e amounts of work done at the hip and ankle j o i n t s . T h i s i s because the work phase H2 (Table 10) d i s s i p a t e s a l a r g e amount of energy p r i o r to the s t a r t of the p r o p u l s i v e phase. M o d i f i c a t i o n of the v e r t i c a l jump by r e s t r i c t i n g trunk extension to i s o l a t e l e g power, i . e . the c o n t r i b u t i o n of the muscles c r o s s i n g the knee and ankle j o i n t s , i s not an uncommon p r a c t i c e . I t i s based on the 41 a s s u m p t i o n t h a t the knee m u s c u l a t u r e i s the major c o n t r i b u t o r to the work done i n jumping. But the s i g n i f i c a n t r e s u l t s f a v o r i n g the hip j o i n t i n t h i s study i n d i c a t e that r e s t r i c t i o n i n hip j o i n t movement a c t u a l l y reduces the c o n t r i b u t i o n of a major source of power i n the l e g s . Summary. The r e s u l t s f o r i n d i v i d u a l l e g j o i n t c o n t r i b u t i o n r e v e a l t h a t , over the e n t i r e jump, standing broad jumping u t i l i z e s the muscles of the ankle j o i n t d i f f e r e n t l y than v e r t i c a l jumping. They a l s o show the importance of the hip musculature i n the p r o d u c t i o n of work i n jumping, p a r t i c u l a r y during the p r o p u l s i v e phase. This f i n d i n g c o n t r a d i c t s the assumption that the knee muscles are the major c o n t r i b u t o r to the work done i n jumping. OTHER JOINT WORK Tables 4 to 7 l i s t the absolute and r e l a t i v e c o n t r i b u t i o n s of the s i x j o i n t s during the e n t i r e jump and the p r o p u l s i v e phase of both standing broad and v e r t i c a l jumping. Beside the l e g j o i n t s , the elbow was the only other j o i n t that was a net generator of energy f o r both types of jumps over the two time i n t e r v a l s of i n t e r e s t . The shoulder j o i n t was a net generator of energy f o r both types of jumps over the e n t i r e jump but a net absorber of energy during the p r o p u l s i v e phase of jumping. The muscles of the neck j o i n t accounted f o r an i n s i g n i f i c a n t amount of the energy developed or d i s s i p a t e d i n a l l cases. For both types of jumps, the upper body j o i n t s tended to c o n t r i b u t e to the 42 work done over the e n t i r e jump but c a n c e l l e d out one another dur i n g the p r o p u l s i v e phase. WORK-ENERGY ANALYSIS The work-energy r a t i o s presented i n Tables 4 to 7 show that the work done at the i n d i v i d u a l j o i n t s d i d not account f o r a l l the ga i n i n t o t a l body energy at t o e - o f f . This r e s u l t i s s i m i l a r to that of Robertson and Fleming (1986) who reported work-energy r a t i o s of 0.953 and 0.872 f o r the p r o p u l s i v e phase of v e r t i c a l and standing broad jumping, r e s p e c t i v e l y . Subsequent a n a l y s i s of t h e i r data over the e n t i r e jump gave r a t i o s of 1.312 f o r the v e r t i c a l jump and 1.317 f o r the broad jump. The r e s u l t s of both the current i n v e s t i g a t i o n and those of Robertson and Fleming (1986) oppose those of Hubley and Wells (1983) who had very good agreement between t h e i r work and energy values f o r the p r o p u l s i v e phase of both countermovement and squat jumping. Since the work-energy r a t i o s were l e s s than 1 .000 i t must be assumed that there are other sources of work that s u b j e c t s were using and which were not measured i n t h i s a n a l y s i s . The appropriateness of the model used f o r a n a l y s i s of a l l s u b j e c t s becomes q u e s t i o n a b l e i n l i g h t of the f a c t that 9 of 12 s u b j e c t s f o r both the p r o p u l s i v e phase and the e n t i r e jump i n v e r t i c a l jumping, and 3 of 6 s u b j e c t s over the e n t i r e jump and 4 of 6 s u b j e c t s during the p r o p u l s i v e phase f o r the broad jump had work-energy r a t i o s c a l c u l a t e d to be gr e a t e r than 10 percent above or below 43 1.000. There may have a l s o been systematic e r r o r s i n the modelling of the human body or i n the data c o l l e c t e d . Pezzack and Norman (1981) i n t h e i r paper on v a l i d a t i o n of j o i n t and moment output of multi-segment l i n k a g e s mentioned s e v e r a l concerns about l i n k segment m o d e l l i n g . They noted that e r r o r s i n body segment a c c e l e r a t i o n s confounded the c a l c u l a t i o n of j o i n t moments and r e a c t i o n f o r c e s because the e r r o r s accumulated i n complex (greater than s i x segments) multi-segment l i n k a g e s . They also suspected that there were l a r g e e r r o r s at the hip and shoulder where the arms and legs attached to the trunk, although they f a i l e d to s t a t e what these e r r o r s could p o s s i b l y be. As w e l l Pezzack and Norman (1981) had t r o u b l e i n a c h i e v i n g c o n s i s t e n t trunk l e n g t h because of movement of the shoulder g i r d l e . They f e l t t h at, because of the mass of the trunk, small e r r o r s i n trunk a c c e l e r a t i o n were capable of g r e a t l y i n f l u e n c i n g f o r c e and moment data. F i x i n g trunk l e n g t h p a r t i a l l y r e c t i f i e d t h i s problem. C e r t a i n l y there was a problem i n t h i s study i n a c h i e v i n g constant trunk l e n g t h , not only because of movement of the shoulder g i r d l e but a l s o due to f l e x i o n at the h i p . Even though the o p t i o n for constant trunk length i n the kinematic a n a l y s i s program was invoked, i t i s unknown as to how much t h i s c o r r e c t e d the problem. While Pezzack and Norman (1981) v a l i d a t e d l i n k segment modelling fo r up to s i x segments, using a seventh, as i n the current study, was probably not a major problem. 44 BIOMECHANICAL PRINCIPLES Using the c r i t e r i a e s t a b l i s h e d i n t h i s study to e v a l u a t e the p r i n c i p l e of summation of j o i n t f o r c e s , Table 11 shows that the p r i n c i p l e was f u l l y supported f o r the p r o p u l s i v e phase of v e r t i c a l and standing broad jumping. Thus, the extensor moments at a l l three l e g j o i n t s produced net p o s i t i v e work f o r a l l s u b j e c t s during the p r o p u l s i v e phase of both kinds of jumps. The c o n t i n u i t y p r i n c i p l e , on the other hand, f a i l e d to gain f u l l support i n e i t h e r type of jump when sequencing of the power c o n t r i b u t i o n s was used as the e v a l u a t i n g c r i t e r i o n (Table 11). However, p a r t i a l support f o r c o n t i n u i t y was i n evidence as a l l s u b j e c t s , i n both standing broad and v e r t i c a l jumping, showed hip-knee sequencing. Because of the c r i t e r i a used i n t h i s study f o r determining support f o r both p r i n c i p l e s , i t may be more a p p r o p r i a t e to c a l l them the p r i n c i p l e s of summation and c o n t i n u i t y of j o i n t powers i n s t e a d of j o i n t f o r c e s . The u t i l i t y of the two p r i n c i p l e s i s p r e s e n t l y q u e s t i o n a b l e because of the d i f f i c u l t y i n v e r i f y i n g whether the p r i n c i p l e s are being adhered to, because there i s a lac k of consensus as to how the summation and c o n t i n u i t y p r i n c i p l e s should be i n t e r p r e t e d and a l s o because of the disagreement about what type of a c t i v i t i e s the p r i n c i p l e s apply to. The o b s e r v a t i o n a l method of movement a n a l y s i s promoted by Luttgens and Wells (1982), the N a t i o n a l Coaching C e r t i f i c a t i o n Program (1979a, 1979b, 1981) and Norman (.1 975 ) 45 does not pro v i d e i n f o r m a t i o n about the f o r c e s i n v o l v e d i n a movement. I t i s erroneous to assume that the f o r c e s that cause movement of a body segment come from c o n t r a c t i o n s of muscles i n s e r t i n g on the segment. Research by Ohman and Robertson (1981), Robertson (1982) and Robertson and Mosher (1985) have shown otherwise. Ohman and Robertson (1981) found that the elbow extensors d i d no work i n a c h i e v i n g maximal hand v e l o c i t y i n a v o l l e y b a l l s p i k e . Instead, c o n c e n t r i c c o n t r a c t i o n of the shoulder extensors followed immediately by e c c e n t r i c c o n t r a c t i o n of the shoulder f l e x o r s produced the d e s i r e d a c t i o n of the forearm and hand. Robertson (1982) and Robertson and Mosher (1985) d i s c o v e r e d that f o r h u r d l i n g and soccer k i c k i n g , r e s p e c t i v e l y , the knee extensors were not g r e a t l y i n v o l v e d i n the extension of the lower l e g . Rapid f l e x i o n of the t h i g h by the hip f l e x o r s f o l l o w e d by e c c e n t r i c c o n t r a c t i o n of the hip extensors provided the major means by which the lower l e g was extended. Information about the f o r c e s i n v o l v e d i n a movement can only be e s t a b l i s h e d through a k i n e t i c a n a l y s i s . However, the drawback to a k i n e t i c a n a l y s i s of the type done i n t h i s study i s the s u b s t a n t i a l time delay between the performance and the a v a i l a b i l i t y of the i n f o r m a t i o n . This delay c o n s i d e r a b l y reduces the us e f u l n e s s of the i n f o r m a t i o n to the a t h l e t e or coach. There i s disagreement among authors about how these two p r i n c i p l e s apply to vari o u s types of a c t i v i t i e s . The 46 N a t i o n a l Coaching C e r t i f i c a t i o n Program (1979a) says that the summation of j o i n t f o r c e s p r i n c i p l e a p p l i e s to jumping, throwing, s t r i k i n g and k i c k i n g a c t i v i t i e s . In a d d i t i o n , the N a t i o n a l Coaching C e r t i f i c a t i o n Program (1979b) a l s o s t a t e s that another p r i n c i p l e , the summation of body segment v e l o c i t i e s , i s s p e c i f i c to throwing, s t r i k i n g and k i c k i n g s k i l l s . On the other hand, Norman (1975) and Dyson (1962) s t a t e that summation of j o i n t f o r c e s and summation of f o r c e s , r e s p e c t i v e l y , are p r i m a r i l y intended to deal with s e l f - p r o p u l s i o n of the t o t a l body w h i l e a d i f f e r e n t p r i n c i p l e , c a l l e d e i t h e r the summation of body segment speeds (Norman, 1975) or summation of throwing f o r c e s (Dyson, 1962), a p p l i e s to movements where maximum hand, foot or implement speed i s r e q u i r e d . Other authors, using s l i g h t l y d i f f e r e n t terms such as the summation of v e l o c i t i e s (Kreighbaum and B a r t h e l s , 1981; N o r t h r i p et a l . , 1974 ) and the summation of segment v e l o c i t i e s (Gowitzke and M i l n e r , 1980), support the idea of a p r i n c i p l e a p p l i c a b l e only to throwing, k i c k i n g and s t r i k i n g a c t i o n s . With regard to the c o n t i n u i t y p r i n c i p l e , many authors f e e l that when the o b j e c t i v e of a movement i s to maximize the speed of the d i s t a l segment there i s a d e f i n i t e sequencing of f o r c e s or body segment v e l o c i t i e s (Broer and Ze r n i c k e , 1979; Bunn, 1972; Cooper and Glassow, 1976; Dyson, 1962; Gowitzke and M i l n e r , 1980; Kreighbaum and B a r t h e l s , 1981; Luttgens and Wells, 1982; Morehouse and Cooper, 1950; N a t i o n a l Coaching C e r t i f i c a t i o n Program, 1979a; Norman, 47 1975; N o r t h r i p e_t a l . , 1974; Plagenhoef, 1971; Simonian, 1981). For jumping a c t i v i t i e s , however, where the o b j e c t i v e i s to move the a t h l e t e ' s t o t a l body mass, there i s l e s s agreement about whether sequencing occurs. The N a t i o n a l C o a c h i n g C e r t i f i c a t i o n Program (1979a) says t h a t the c o n t i n u i t y p r i n c i p l e h o l d s f o r a l l t y p e s of power a c t i v i t i e s , i mplying that sequencing occurs i n jumping movements. Dyson (1962) t h e o r i z e s that to c r e a t e maximum impulse during jumping a l l muscles i n v o l v e d should c o n t r a c t s i m u l t a n e o u s l y . However, he b e l i e v e s that i n p r a c t i c e , due to the nature of the c o n s t r u c t i o n of the human body, there i s sequencing of muscular c o n t r a c t i o n s from proximal to d i s t a l with a l l f o r c e s ending together. T h e r e f o r e , the f o r c e s f o r jumping a c t i v i t i e s , a c c ording to Dyson (1962), would overlap one another. Broer and Zernicke (1979) f e e l that f o r heavy t a s k s , i n which jumping presumably could be i n c l u d e d , the f o r c e s are a p p l i e d together. An a l t e r n a t e view i s expressed by Kreighbaum and B a r t h e l s (1981) who s t a t e that the degree of sequencing f o r movements i s r e l a t e d to the purpose of the movement, the mass of the object to be moved and the s t r e n g t h of the a t h l e t e . T h e r e f o r e , as the mass of the object to be moved i n c r e a s e s , or the s t r e n g t h of the a t h l e t e decreases, or the d e s i r e d accuracy of the movement outcome i n c r e a s e s , or the f o r c e output requirement of the movement i n c r e a s e s , the p a t t e r n i n g of the a c t i v i t y changes from, s e q u e n t i a l to simultaneous segment involvement. 48 Summary. Before any attempt to v a l i d a t e the p r i n c i p l e s of summation and c o n t i n u i t y can have meaning, p r e c i s e d e f i n i t i o n s and c r i t e r i a f o r e v a l u a t i o n need to be e s t a b l i s h e d . Only then w i l l a p p l y i n g the p r i n c i p l e s provide u s e f u l i n f o r m a t i o n . JOINT KINETICS As a r e s u l t of the s i m i l a r i t y i n the f u n c t i o n s of the corresponding work phases (Table 10) f o r standing broad and v e r t i c a l jumping, the h i p , knee and ankle k i n e t i c s of the two s o r t s of jumps w i l l be d i s c u s s e d together. Hip K i n e t i c s . I n i t i a l l y , the hip f l e x o r s were a c t i v e c o n c e n t r i c a l l y (HI) to a small extent to lower the upper body. During approximately the l a s t two-thirds of the contact time with the f o r c e p l a t e the hip extensors were dominant. F i r s t they c o n t r a c t e d e c c e n t r i c a l l y (H2) to stop l o w e r i n g of the upper body and then they c o n t r a c t e d c o n c e n t r i c a l l y (H3) to extend the upper body. H2 and H3 were episodes which d i s s i p a t e d and generated, r e s p e c t i v e l y , the l a r g e s t amounts of energy by any of the l e g j o i n t s . From F i g u r e 1 i t can be seen that the hip i s the only l e g j o i n t , f o r both types of jumps, that had a c o n c e n t r i c c o n t r a c t i o n of the j o i n t extensors (H3) that occurred before the s t a r t of the p r o p u l s i v e phase. The timing of H3 i s such that the m a j o r i t y of the mass of the body i s a c c e l e r a t i n g i n an upward d i r e c t i o n before the knee and ankle extensors c o n t r i b u t e to the jumps. 49 The standing broad jump e x h i b i t e d an e x t r a work perio d (H4) which was very b r i e f i n d u r a t i o n . The hip f l e x o r s c o n t r a c t e d e c c e n t r i c a l l y to slow upper body extension. The r o l e of t h i s work episode may have been to a l i g n the angle of the upper body, s p e c i f i c a l l y the body center of g r a v i t y , with the angle of t h r u s t of the l e g s . T h i s would then leave g r a v i t y as the only f o r c e which would cause r o t a t i o n of the body at t o e - o f f . Knee K i n e t i c s . About the time H2 occurred the knee extensors c o n t r a c t e d e c c e n t r i c a l l y (Kl) to c o n t r o l both knee f l e x i o n and, i n d i r e c t l y , lowering of the upper body. Approximately o n e - t h i r d of the way i n t o H3, the knee extensors came on c o n c e n t r i c a l l y (K2) to extend the knee. Immediately p r i o r to t o e - o f f , c o i n c i d e n t with H4 i n the standing broad jump, there was an e c c e n t r i c c o n t r a c t i o n of the knee f l e x o r s (K3) of very short d u r a t i o n . The work d i s s i p a t e d during t h i s episode was used to reduce the rate of knee extension which prevented the knee j o i n t from hyperextending. Ankle K i n e t i c s . The f i r s t muscular a c t i v i t y c o n s i s t e n t across a l l s u b j e c t s at the ankle was a p l a n t a r f l e x i o n e c c e n t r i c c o n t r a c t i o n (Al) which c o n t r o l l e d the amount of ankle f l e x i o n during the countermovement. In the v e r t i c a l jump t h i s phase occurred at about the same time as H2 and Kl and f o r the standing broad jump the phase occurred about f o u r - f i f t h s of the way i n t o H2 and t h r e e - f i f t h s of the way i n t o K l . Al was followed by a strong c o n c e n t r i c c o n t r a c t i o n 50 of the p l a n t a r f l e x o r s (A2) as the ankle j o i n t r a p i d l y extended during the l a t t e r part of the p r o p u l s i v e phase. A.2 occurred at around the same time as K2. 51 CONCLUSIONS Over the e n t i r e jump there was a d i f f e r e n c e , f a v o r i n g the v e r t i c a l jump, i n the extent to which muscles c r o s s i n g the ankle j o i n t c o n t r i b u t e d to the r e l a t i v e work done at the l e g j o i n t s during standing broad and v e r t i c a l jumping. There was no d i f f e r e n c e i n the extent to which muscles c r o s s i n g the knee j o i n t c o n t r i b u t e d to the r e l a t i v e work done at the l e g j o i n t s d u r i n g standing broad and v e r t i c a l jumping f o r e i t h e r the p r o p u l s i v e phase or the e n t i r e jump. Over the e n t i r e jump f o r both standing broad and v e r t i c a l jumping the knee m u s c u l a t u r e was not as important as the hip musculature i n c o n t r i b u t i n g to the work done at the l e g j o i n t s . During the p r o p u l s i v e phase of standing broad and v e r t i c a l jumping, the hip extensors were more important than e i t h e r the ankle p l a n t a r f l e x o r s or the knee extensors i n generating work. Using net work during the p r o p u l s i v e phase as the c r i t e r i o n , the p r i n c i p l e of summation of muscle forces h e l d f o r standing broad and v e r t i c a l jumping. The p r i n c i p l e of c o n t i n u i t y or sequencing of muscular c o n t r a c t i o n s was not w e l l supported f o r e i t h e r standing broad or v e r t i c a l jumping when the sequencing of j o i n t power c o n t r i b u t i o n s was the e v a l u a t i n g c r i t e r i o n . 52 RECOMMENDATIONS A r e l i a b i l i t y s t u d y i s r e q u i r e d to d e t e r m i n e how c o n s i s t e n t s u b j e c t s are i n a c h i e v i n g the same r e l a t i v e l e g j o i n t c o n t r i b u t i o n s during maximal jumping. This i n f o r m a t i o n i s needed b e f o r e r e s e a r c h e r s can be con f i d e n t that a trend i n j o i n t c o n t r i b u t i o n can be e s t a b l i s h e d f o r jumping a c t i v i t i e s ; The jumps, which were analyzed i n the present study, should be subjected to another l i n k segment a n a l y s i s , i n c o r p o r a t i n g a d i f f e r e n t l i n k segment model, to determine whether the poor work-energy values were due to immeasurable work output or to an i n a p p r o p r i a t e l i n k segment model. Studies to e s t a b l i s h the r e l i a b i l i t y of both f o r c e p l a t e s and a s s o c i a t e d computer programs are needed i n order to provide i n v e s t i g a t o r s with an idea as to the accuracy of t h e i r r e s u l t s . A next step i n the a p p l i c a t i o n of j o i n t power a n a l y s i s of maximal jumping, would be i t s extension to sport r e l a t e d s k i l l s . The f i r s t type of a c t i v i t i e s to be analyzed should be movements that can be performed from a s t a t i o n a r y p o s i t i o n , such as b l o c k i n g i n v o l l e y b a l l and r e b o u n d i n g i n b a s k e t b a l l . Next would f o l l o w a n a l y s i s of jumps o f f of one leg i n c o r p o r a t i n g a run-up l i k e a b a s k e t b a l l layup and ta k e - o f f f o r high, long and t r i p l e jumps. As w e l l , j o i n t power a n a l y s i s should be 53 a p p l i e d to the t r a i n i n g a c t i v i t i e s u t i l i z e d by a t h l e t e s . T h i s w i l l p r o v i d e i n f o r m a t i o n as to whether or not the r e q u i r e m e n t s of the t r a i n i n g a c t i v i t i e s c l o s e l y match the j o i n t work and power r e q u i r m e n t s of the s p o r t s k i l l s . 54 REFERENCES Asmussen, E. and Bonde-Petersen, F. (1974). Storage of e l a s t i c energy i n s k e l e t a l muscle i n man. Acta P h y s i o l . 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A v a l i d a t i o n of j o i n t r e a c t i o n f o r c e and r e s u l t a n t moment output of an 'n' l i n k p l a n e motion model of the human. I n : Morecki, A., F i d e l u s , K. , Kedzior, K. and Wit, A. (e d s . ) , Biomechanics VII-A. Baltimore: U n i v e r s i t y Park P r e s s , pp. 260-266. Pezzack, J . C , Norman, R.W. and Winter, D.A. (1977 ). An assessment of d e r i v a t i v e determining techniques used f o r motion a n a l y s i s . J . Biomechanics. 10:377-382. Plagenhoef, S. (1971). P a t t e r n s of Human Motion. Toronto: P r e n t i c e - H a l l , Inc. (1975). . jr segments 1:59-67. Quanbury, A.O., Winter, D.A. and Reimer, G.D. Instantaneous power and power flow i n body durin g walking. J . Human Movement S t u d i e s , Robertson, D.G.E. (1982). Muscular c o n t r a c t i o n s of the lea d l e g i n s p r i n t h u r d l i n g . 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B iomechani cs, 13:845-854. 57 Roy, B. , Youm, Y. and Roberts, E.M. (1973). Kinematics and k i n e t i c s of the standing long-jump i n 7-, 10-, 13- and 16-year-old boys. In: C e r q u i g l i n i , S., Venerando, A. and W a r t e n w e i l e r , J . ( e d s . ) , B i o m e c h a n i c s I I I . Balti m o r e : U n i v e r s i t y Park Press, ppT 409-416. Simonian, C. (1981). Fundamentals of Sports Biomechanics. Englewood C l i f f s , N. J . : P r e n t i c e - H a l l , Inc. White, S.C. and Winter, D. (1985). Mechanical power a n a l y s i s of the lower limb musculature i n race walking. I n t . J . Sport Biomechanics, l ( l ) : 1 5 - 2 4 . Winter, D.A. (1979). Biomechanics of Human Movement. Toronto: Wiley and Sons. Winter, D.A. (1983). Moments of f o r c e and mechanical power i n j o g g i n g . J . Biomechanics. 16(l):91-97. W o l t r i n g , H.J. (1980). Planar c o n t r o l i n multi-camera c a l i b r a t i o n f o r 3-D s t u d i e s . J . B i o m e c h a n i c s . 13:39-48. Zarrugh, M.Y. (1981). Kinematic p r e d i c t i o n of intersegment loads and power at the j o i n t s of the l e g i n walking. J . Biomechanics. 14(10 ) :713-725. 58 APPENDIX 1 - REVIEW OF LITERATURE STANDING JUMPS In 1921, Sargent (1921) presented a v e r t i c a l jump t e s t , e v e n t u a l l y c a l l e d the Sargent jump, which he thought took i n t o account s t r e n g t h , speed, energy and d e x t e r i t y . The s c o r i n g procedure that Sargent developed was an e f f i c i e n c y index that i n c o r p o r a t e d both the height and weight of the s u b j e c t . A few years l a t e r , Sargent (1924) r e a l i z e d that the t e s t measured power (the rate of work done) and not j u s t the work done. He a l s o found that height jumped was independent of the height and weight of a s u b j e c t and t h e r e f o r e only the height jumped needed to be measured to evaluate performance. In attempts to e s t a b l i s h the t e s t ' s u s e f u l n e s s , McCloy (1932) showed that the Sargent t e s t r e s u l t s c o r r e l a t e d with a composite score from a b a t t e r y of track and f i e l d events that were thought to r e q u i r e power. Van Dalen (1940) determined that the t e s t c o r r e l a t e d with other v e r t i c a l jump t e s t s . They both concluded that the Sargent t e s t was of some value i n p r e d i c t i n g an i n d i v i d u a l ' s p o t e n t i a l a b i l i t y i n events r e q u i r i n g e x p l o s i v e muscular c o n t r a c t i o n s . Gray e_t aJ.. (1962a) f e l t that many forms of the v e r t i c a l jump could not be regarded as t e s t s that measured only l e g power because trunk extension and arm movements were allowed. They were also concerned t h a t , although the Sargent t e s t was supposed to be a test of power, the r e s u l t s were not expressed i n u n i t s of power. With these thoughts 59 i n mind, they proposed a new v e r s i o n of the Sargent jump, termed the v e r t i c a l power jump, which i n v o l v e d only the l e g s . They a l s o provided a mathematical argument and equation f o r c a l c u l a t i n g the r e s u l t s i n terms of f o r c e , time and d i s t a n c e , the components of power. However, the t e s t was time-consuming because the weight and center of g r a v i t y of each subject along with two d i f f e r e n t height measurements had to be determined before the body power could be c a l c u l a t e d . Gray et al, (1962b) e v e n t u a l l y decided that i t was simpler to put the r e s u l t s i n terms of work done i n a manner p r e v i o u s l y suggested by Sargent (1921). Glencross (1966a) b u i l t a device he c a l l e d the 'power l e v e r ' whose purpose was to measure the muscle power of s p e c i f i c j o i n t a c t i o n s i n u n i t s of power. Using t h i s d e v i c e , he d i d c o r r e l a t i o n , m u l t i p l e c o r r e l a t i o n and f a c t o r analyses on the jump and reach t e s t , the standing broad jump, body weight plus four j o i n t movements that he had determined from a previous study were important to v e r t i c a l and standing broad jump performance (Glencross, 1966b). He concluded that while the v e r t i c a l and standing broad jumps appeared to be i n d i c a t o r s of l e g power, they were l i m i t e d as measures of muscle power. Despite t h e i r l i m i t a t i o n s , the standing broad jump and the v e r t i c a l jump, i n i t s va r y i n g forms, are s t i l l used f o r p r e d i c t i n g a t h l e t i c p o t e n t i a l (Johnson and Nelson, 1974) and measuring p h y s i c a l f i t n e s s . While there has been a l a r g e amount of research devoted to the standing jumps, e s p e c i a l l y the v e r t i c a l jump, most of 60 i t has been l i m i t e d to kinematic analyses of these jumps (Hay, 1975). The few k i n e t i c s t u d i e s that have been undertaken have concentrated almost e x c l u s i v e l y on the v e r t i c a l jump. Despite t h i s f a c t the movement i t s e l f i s s t i l l not w e l l understood because i n v e s t i g a t i o n s have l a r g e l y focused upon using v e r t i c a l jumping as a t o o l f o r examining f e a t u r e s p e r i p h e r a l to the jump i t s e l f . F o r example, some i n v e s t i g a t o r s (Asmussen and Bonde-Petersen, 1974; Bosco and Komi, 1979a, 1979b, 1980, 1981; Bosco et a l . , 1981 , 1982a, 1982b, 1982c; Cavagna .et a l . . 1971a; Fukashiro et. a l . , 1983; Komi and Bosco, 1978a, 1978b; V i i t a s a l o and Bosco, 1982) have used v e r t i c a l jumping to analyze work augmentaion due to p r e s t r e t c h i n g . In a few s t u d i e s i t was found that there was a s i g n i f i c a n t d i f f e r e n c e i n the r i s e of the height of the body center of g r a v i t y (c of g) i n countermovement (CMJ) jumps (Asmussen and Bonde-Petersen, 1974; Bosco and Komi, 1979a; Komi and Bosco, 1978b) and drop (DJ) jumps (Asmussen and Bonde-Petersen, 1974; Komi and Bosco, 1978b) compared to jumps i n i t i a t e d from a squat or s t a t i c (SJ) p o s i t i o n , although there was no allowance taken f o r the lower s t a r t i n g p o s i t i o n of the SJ. I t was f e l t that the d i f f e r e n c e was a t t r i b u t a b l e to the increased a b i l i t y of a p r e s t r e t c h e d muscle to do p o s i t i v e work which occurred as a r e s u l t of both the storage and r e l e a s e of energy by the muscle and muscle a c t i v a t i o n caused by the s t r e t c h r e f l e x (Bosco and Komi, 1979b; Bosco £t a l . , 1982b). Attempts to e x p l a i n the a d d i t i o n a l work output of 61 the body i n countermovement and drop jumps have centered upon e l e c t r o m y o g r a p h i c (Bosco et a l . , 1982a, 1982b; V i i t a s a l o and Bosco, 1982) and r e f l e x p o t e n t i a t i o n (Bosco e_t a l . , 1982b) of v a r i o u s l e g muscles, knee angle amplitude during jumping (Bosco and Komi, 1981; Bosco et^ a_l. , 1981, 1982a, 1982c), the v e l o c i t y of s t r e t c h of the knee extensors (Bosco and Komi, 1979b, 1981; Bosco e_t a l . , 1981 , 1982b), f i b e r typing of the vastus l a t e r a l i s muscle (Bosco and Komi, 1978a; Bosco e_t a l . , 1982c, 1983b; Komi and Bosco, 1979a; V i i t a s a l o and Bosco, 1982) and the coupling time between the e c c e n t r i c and c o n c e n t r i c work phases of the knee extensors (Bosco e_t a l . , 1981 , 1982b, 1982c). Bosco e_t a_l. (1982a), using the vastus l a t e r a l i s , vastus m e d i a l i s and rectus femoris muscles, and Bosco e_t a l . (1982b), o m i t t i n g rectus f e m oris, found that the averaged i n t e g r a t e d m y o e l e c t r i c a l a c t i v i t y (IEMG) during both the e c c e n t r i c and c o n c e n t r i c phases of a CMJ (Bosco e_t a l . , 1982b) and continuous countermovement rebound jumping (Bosco et a l . , 1982a) were lower than the IEMG of the c o n c e n t r i c phase of a SJ. From t h i s they concluded that the gre a t e r work output during countermovement jumping was due to the u t i l i z a t i o n of energy s t o r e d i n the muscles during the e c c e n t r i c phase and not due to increased muscle a c t i v i t y . On the other hand, V i i t a s a l o and Bosco (1982) found no d i f f e r e n c e i n IEMG during e i t h e r phase of a CMJ compared to a SJ, but t h e i r r e s u l t s i n c l u d e d the m y o e l e c t r i c a l a c t i v i t y 62 of two a d d i t i o n a l muscles, namely gluteus maximus and gastrocnemius. Two s t u d i e s (Bosco e_t a l . , 1982b; V i i t a s a l o and Bosco, 1982) also looked at IEMG f o r drop jumps and found that the IEMG durin g the e c c e n t r i c phase of a DJ was gr e a t e r than IEMG during a SJ, while f o r the c o n c e n t r i c phase of DJ the opposite was t r u e . These i n v e s t i g a t o r s f e l t that the incr e a s e d n e u r a l a c t i v i t y during the e c c e n t r i c phase of a DJ pointed out the p o s s i b i l i t y of increased muscle a c t i v i t a t i o n due to s p i n a l or c o r t i c a l r e f l e x e s (Bosco et_ a_l. , 1982b). Bosco et a_l. (1982b) examined the r a t i o of IEMG to the average f o r c e during the e c c e n t r i c and c o n c e n t r i c work phases. For the e c c e n t r i c phase the IEMG-force r a t i o was lower i n the DJ than the CMJ, while for the c o n c e n t r i c phase the r a t i o ascended from the DJ to the CMJ to the SJ. To these r e s e a r c h e r s t h i s i m p l i e d that the lower the IEMG-force r a t i o the grea t e r the u t i l i z a t i o n of energy s t o r e d i n the muscles during the e c c e n t r i c phase because a smaller amount of EMG a c t i v i t y was needed per u n i t of f o r c e i n both the e c c e n t r i c and c o n c e n t r i c phases. Bosco et al.. (1982a) looked at IEMG a c t i v i t y and knee amplitude i n continuous countermovement rebound jumping. For small amplitude jumps, the IEMG was bigger during the e c c e n t r i c phase and smaller during the c o n c e n t r i c phase than the IEMG f o r the corresponding phases of the l a r g e amplitude jumps. In each type of jump the IEMG a c t i v i t y during both phases was smaller than the a c t i v i t y during the c o n c e n t r i c 63 phase of a SJ. T h e r e f o r e , they concluded that f o r the same amount of IEMG a c t i v i t y during the c o n c e n t r i c phase there was more p o s i t i v e work done i n small knee amplitude jumps than i n l a r g e amplitude jumps. The parameters of v e l o c i t y of s t r e t c h , c o u p l i n g time and knee angle amplitude have i n t e r a c t e d to i n f l u e n c e performance i n v e r t i c a l jumping. Bosco and Komi (1981) showed that small amplitude movement at the knee j o i n t enhanced the f o r c e and power output of the body when sub j e c t s performed v e r t i c a l jumps with and without a countermovement. The same study showed a s i g n i f i c a n t n egative c o r r e l a t i o n between knee angle amplitude and knee j o i n t angular v e l o c i t y during p r e s t r e t c h , meaning that s m a l l e r amplitudes were a s s o c i a t e d with higher angular v e l o c i t i e s . The knee j o i n t angular v e l o c i t y was assumed to r e f l e c t the v e l o c i t y of s t r e t c h of the knee extensor muscles. In countermovement jumps, a s i g n i f i c a n t p o s i t i v e c o r r e l a t i o n e x i s t e d between l e n g t h of c o u p l i n g time, which was the t r a n s i t i o n p e r i o d between the e c c e n t r i c and c o n c e n t r i c work phases where the knee angle remained constant, and knee movement amplitude (Bosco ejt a_l. , 1981). It has been t h e o r i z e d that c o u p l i n g time may be an important f a c t o r i n the u t i l i z a t i o n of stored p o t e n t i a l energy at the c r o s s - b r i d g e l e v e l of muscle t i s s u e (Bosco e_t a_l. , 1981, 1982c). Taken together, the v a r i o u s s t u d i e s appear to i n d i c a t e t h a t to maximize the u t i l i z a t i o n of energy a v a i l a b l e because of p r e s t r e t c h i n g , movements should be made 64 w i t h s m a l l a m p l i t u d e p r e p a r a t o r y a c t i o n s to d e c r e a s e c o u p l i n g time and to i n c r e a s e the v e l o c i t y of s t r e t c h of the i n v o l v e d muscles. Performance i n v e r t i c a l jumping, as measured by power output (Bosco and Komi, 1979a; Bosco et a l . , 1983b), r i s e i n height of body c of g (Bosco and Komi, 1979a; Komi and Bosco, 1978a; V i i t a s a l o and Bosco, 1982) and percent use of energy store d during p r e s t r e t c h (Bosco e_t a_l. , 1982c), has been c o r r e l a t e d with muscle f i b e r composition of the vastus l a t e r a l i s muscle, whose a c t i o n was assumed to r e f l e c t the c o n t r i b u t i o n of the l e g extensors to the jump. For squat jumps (Bosco and Komi, 1979a) and during the f i r s t t h i r t y seconds of continuous rebound jumping (Bosco e_t a_l. , 1983b) the percent of f a s t t w i t c h f i b e r s c o r r e l a t e d s i g n i f i c a n t l y i n a p o s i t i v e manner with power output of the body. In countermovements jumps (Bosco e_t aj.. , 1979a; Komi and Bosco, 1978a) and squat jumps (Bosco and Komi, 1979a) the percent of f a s t t w i t c h f i b e r s showed a s i g n i f i c a n t p o s i t i v e r e l a t i o n s h i p with the height of r i s e of the body c of g. The performance d i f f e r e n c e between DJ and CMJ as measured by the height of r i s e of the body c of g produced a s i g n i f i c a n t p o s i t i v e c o r r e l a t i o n with percent of slow t w i t c h f i b e r s (Komi and Bosco, 1978a). V i i t a s a l o and Bosco (1982) d i v i d e d t h e i r s ubjects i n t o 'slow' and ' f a s t ' groups according to the percent of f a s t twitch f i b e r s . They found a s i g n i f i c a n t performance d i f f e r e n c e i n favor of the ' f a s t ' group i n the height of r i s e of the body c of g while performing a SJ and 65 a s i g n i f i c a n t d i f f e r e n c e f a v o r i n g the 'slow' group when performance d i f f e r e n c e s between DJ and CMJ were compared. Komi and Bosco (1978b) attempted to measure the percent u t i l i z a t i o n of e l a s t i c energy during a CMJ and DJ. They compared the maximum k i n e t i c energy l e v e l d u r i n g the e c c e n t r i c phase of jumping to- the change i n maximum k i n e t i c energy between a CMJ and a SJ and between a DJ and a SJ during the c o n c e n t r i c phase. T h e i r f i n d i n g s were that the percent u t i l i z a t i o n of e l a s t i c energy was gr e a t e r i n a CMJ than a DJ and that females when compared to males used a gre a t e r p o r t i o n of the a v a i l a b l e e l a s t i c energy i n both the CMJ and DJ c o n d i t i o n s . Many res e a r c h e r s have used v e r t i c a l jumping to examine the power output of the human body during a b a s i c movement (Bosco and Komi, 1979a, 1979b, 1980, 1981; Bosco ejt a l . , 1981 , 1982b, 1983a, 1983b, 1983c; Cavagna e_t a l . , 1971a; Davies, 1971; Davies and Rennie, 1968; D e s i p r e s , 1976). V e r t i c a l jumping has also been employed i n s t u d i e s comparing the values f o r t a k e - o f f v e l o c i t y of the body c of g found by f o r c e p l a t f o r m and cinematographic techniques (Komi and Bosco, 1978b; Lamb and S t o t h a r t , 1978; Luhtanen and Komi, 1978b). Hay _et a l . ( 1976 , 1978 , 1981 ) attempted to develop a model f o r i d e n t i f y i n g f a c t o r s that l i m i t performance i n s p e c i f i c tasks while Komor e_t a_l. (1981) used a c o n t r o l systems a n a l y s i s to study technique o p t i m i z a t i o n . In both 66 cases the v e r t i c a l jump was the movement chosen f o r a n a l y s i s « Hunebelle and Damoiseau (1973) examined the f o r c e - t i m e (impulse) curve of s u b j e c t s performing v e r t i c a l jumps on a f o r c e p l a t e and n o t i c e d that poorer jumpers produced curves that were t r i a n g u l a r i n shape and that they took a longer time to jump than the b e t t e r jumpers, who were c h a r a c t e r i z e d by t r a p e z o i d a l shaped curves. T v e i t (1976) l o o k i n g at the h o r i z o n t a l f o r c e s and h o r i z o n t a l impulses i n v e r t i c a l jumping showed that both were smaller i n jumps performed with a preparatory countermovement than without. In an attempt to provide s p e c i f i c i n f o r m a t i o n about what f a c t o r s c o n t r i b u t e to v e r t i c a l jump performance, r e s e a r c h e r s have used s e v e r a l approaches. The segmental approach (Luhtanen and Komi, 1978b; M i l l e r and E a s t , 1976) found that the segmental c o n t r i b u t i o n to the impulse generated and to the t o t a l l i n e a r momentum developed was i n f l u e n c e d by the mass of the body segments. Luhtanen and Komi (1978b) a l s o looked at the s p e c i f i c c o n t r i b u t i o n s of v a r i o u s j o i n t a c t i o n s to t a k e - o f f v e l o c i t y and determined that 56 percent of t a k e - o f f v e l o c i t y was caused by knee extension, 22 percent by p l a n t a r f l e x i o n , 10 percent by trunk extension, 10 percent by arm swing and 2 percent by head swing. The j o i n t moment technique (Hay e_t al_. , 1978 , 1981 ) found that some j o i n t moments during p a r t i c u l a r time i n t e r v a l s of the jump c o r r e l a t e d s i g n i f i c a n t l y with jump 67 performance. A problem with t h i s technique, as pointed out by Hubley and W e l l s (1983), i s t h a t i t does not d i f f e r e n t i a t e between j o i n t s u n d e r g o i n g i s o m e t r i c c o n t r a c t i o n , and t h e r e f o r e not c o n t r i b u t i n g toward height jumped, and those j o i n t s a c t i v e l y i n v o l v e d i n jump performance. Both Bangerter (1968) and Berger (1963) examined the e f f e c t s of s t r e n g t h t r a i n i n g programs on v e r t i c a l jump pe r f o r m a n c e . B a n g e r t e r (1968), u s i n g i s o l a t e d j o i n t e x e r c i s e s , concluded that the hip and knee extensors were important i n v e r t i c a l jumping but not so f o r the ankle p l a n t a r f l e x o r s . In the study by Berger (1963), s u b j e c t s e i t h e r t r a i n e d dynamically by doing one of squats, jump squats and v e r t i c a l jumps or i s o m e t r i c a l l y at two d i f f e r e n t p o s i t i o n s of knee f l e x i o n . He found that the groups that t r a i n e d by d o i n g s q u a t s and jump s q u a t s improved s i g n i f i c a n t l y more i n v e r t i c a l jump performance than the groups that t r a i n e d i s o m e t r i c a l l y or by simply jumping. A study by Roy je_t al. (1973 ) examined some kinematic and k i n e t i c f e a t u r e s of the standing broad jump as performed by groups of boys aged 7, 10, 13 and 16 y e a r s . They o b s e r v e d t h a t the maximum h o r i z o n t a l and r e s u l t a n t v e l o c i t i e s at t a k e - o f f i n c r e a s e d with age while maximum v e r t i c a l v e l o c i t y was b a s i c a l l y the same across age groups. They a l s o n o t i c e d t h a t both the maximum v e r t i c a l a c c e l e r a t i o n and the angle of t a k e - o f f were s i m i l a r for a l l age groups. Due to the f a i r l y c o n s i s t e n t r e s u l t s i n s e v e r a l 68 measures f o r a l l age groups they concluded that the b a s i c neuromuscular p a t t e r n s f o r the standing broad jump were w e l l e s t a b l i s h e d by 7 years of age. While the standing broad jump has also been used as an a c t i v i t y to v a l i d a t e l i n k segment modelling of a human (Pezzack and Norman, 1981), to date, the standing broad jump has not been i n v e s t i g a t e d as e x t e n s i v e l y as the standing v e r t i c a l jump. WORK AND POWER IN HUMAN LOCOMOTION Since the c l a s s i c works of Fenn (1930a, 1930b) and Elftman (1939a, 1939b) both work and power have been used as measures to q u a n t i f y p h y s i c a l a c t i v i t y . Much resea r c h has focused upon the mechanical energy and power aspects of the t o t a l body during walking (Cappozzo e_t al_. , 1976; Cavagna, 1975; Cavagna and Kaneko, 1977; Cavagna and Margaria, 1966; Cavagna et a l . , 1963 , 1976; Fenn, 1930a, 1930b; Gersten et a l . , 1969; Luhtanen and Komi, 1980; Pierryno w s k i e_t a l . , 1980; Ra l s t o n and Luk i n , 1969; Winter e_t al. , 1976a; Zarrugh, 1981a), running (Cavagna, 1975; Cavagna and Kaneko, 1977 ; Cavagna e_t a l . , 1964 , 197 1b; Fukunaga e_t a l . , 1978; Luhtanen and Komi, 1978a, 1980; Williams and Cavanagh, 1983) and jumping (Bosco and Komi, 1979a, 1979b, 1980, 1981; Bosco et a l . . 1981 , 1982b, 1983a, 1983b, 1983c; Cavagna _et a l . , 1971a; Davies, 1971; Davies and Rennie, 1968; D e s i p r e s , 1976; Luhtanen and Komi, 1980). However, c o n s i d e r a b l y l e s s r e s e a r c h has centered upon j o i n t and muscle e n e r g e t i c s . 69 Elftman (1939a, 1939b), while lo o k i n g at walking, was the f i r s t to combine j o i n t r e a c t i o n f o r c e s and net j o i n t moments with segmental and j o i n t kinematics to c a l c u l a t e the rat e of change of energy f o r the l e g segments, the ra t e of energy t r a n s f e r through the l e g j o i n t s due to j o i n t f o r c e s ( j o i n t f o r c e power) and the r a t e of work done by muscles c r o s s i n g the j o i n t s (muscle power). He l a t e r extended t h i s work to running (Elftman, 1940). Since then the work on j o i n t e n e r g e t i c s has focused on two complementary types of a n a l y s i s . A segmental power a n a l y s i s has been used to analyze the energy and power changes i n lower limb segments during running (Chapman and C a l d w e l l , 1983) and walking (Quanbury et a l . , 1975; Robertson and Winter, 1980; Winter and Robertson, 1978; Winter ^ t a l . , 1976b). This type of a n a l y s i s provides i n f o r m a t i o n about where energy generated by muscles c r o s s i n g a j o i n t goes, where energy absorbed at a j o i n t comes from and where energy t r a n s f e r r e d through a j o i n t between segments goes. When a segmental power a n a l y s i s i s combined with a segmental energy a n a l y s i s , a work-energy comparison can be made to check the accuracy and v a l i d i t y of the a n a l y s i s techniques (Quanbury e_t a_l. , 1975; Robertson and Winter, 1980; Winter et a l . , 1976b). A j o i n t power a n a l y s i s allows the work done by muscles c r o s s i n g a j o i n t to be c a l c u l a t e d , which then enables the r o l e and importance of the muscles i n an a c t i v i t y to be determined. This type of a n a l y s i s has been used to examine 70 the c o n t r i b u t i o n of the muscles c r o s s i n g the l e g j o i n t s i n walking ( B r e s l e r and Berry, 1951; Cappozzo e_t a l . , 1976 ; M o r r i s o n , 1970; Zarrugh, 1981b), race walking (White and Winter, 1985), j o g g i n g (Winter, 1983), running (Robertson, 1985), jumping (Hubley and W e l l s , 1983; Robertson and Fleming, 1986) and soccer k i c k i n g (Robertson and Mosher, 1985). B r e s l e r and Berry (1951), Cappozzo et a l . (1976) and Zarrugh (1981b), l o o k i n g at walking, and White and Winter (1985), examining race walking, found that f o r one s t r i d e of each a c t i v i t y the muscles c r o s s i n g the ankle and hip j o i n t s generated more energy than they r e c e i v e d while the opposite was true f o r the muscles of the knee j o i n t . While the o v e r a l l trend f o r energy g e n e r a t i o n and a b s o r p t i o n at the v a r i o u s l e g j o i n t s was s i m i l a r i n both walking and race walking, the s p e c i f i c p a t t e r n i n g of energy c o n t r i b u t i o n was q u i t e d i f f e r e n t . In walking, the ankle and hip j o i n t s together provided the m a j o r i t y of the power r e q u i r e d by the body during the stance phase (Cappozzo e_t al_. , 1976; Zarrugh, 1981b) but f o r race walking the main c o n t r i b u t o r to forward p r o p u l s i o n during the stance phase was the ankle j o i n t with the hip j o i n t c o n t r i b u t i n g to forward motion only somewhat during l a t e stance phase but mainly during e a r l y swing phase. In both forms of locomotion, the knee j o i n t had periods of energy a b s o r p t i o n p r i o r to t o e - o f f and h e e l - c o n t a c t (Cappozzo e_t a_l. , 1976 ; White and Winter, 1985; Zarrugh, 1981b). 71 For one s t r i d e of j o g g i n g (Winter, 1983) and during the stance phase of running (Robertson, 1985) i t was d i s c o v e r e d that the r o l e s of the muscles c r o s s i n g the knee and ankle j o i n t s were s i m i l a r to t h e i r r o l e s i n walking and race walking, but the r o l e of the hip j o i n t was very d i f f e r e n t . During the stance phase of running the muscles of the hip j o i n t were net absorbers of energy while no c o n c l u s i v e r o l e was evident at the hip f o r one s t r i d e of j o g g i n g . Hubley and Wells (1983), using the work-energy approach, attempted to q u a n t i f y the amount of p o s i t i v e work c o n t r i b u t e d by the muscles c r o s s i n g the h i p , knee and ankle j o i n t s during v e r t i c a l jumping. They found that f o r the p r o p u l s i v e phase of a CMJ the h i p , knee and ankle muscles c o n t r i b u t e d 27.5, 49.0 and 23.5 percent, r e s p e c t i v e l y , to the work done by the l e g s . For jumps i n i t i a t e d from a squat p o s i t i o n the j o i n t c o n t r i b u t i o n s were almost i d e n t i c a l to those i n countermovement jumping. Work done by Robertson and Fleming (1986) examined the p r o p u l s i v e phase of both v e r t i c a l and standing broad jumping. They found that f o r v e r t i c a l jumping the muscles c r o s s i n g the h i p , knee and ankle j o i n t s were r e s p o n s i b l e , r e s p e c t i v e l y , f o r 40.0 , 24.2 and 35.8 percent of the t o t a l work done at the leg j o i n t s . In standing broad jumping the r e s p e c t i v e c o n t r i b u t i o n s of the h i p , knee and a n k l e musculatures were 45.9, 3.9 and 50.2 percent. These r e s u l t s i n d i c a t e d that the muscles c r o s s i n g the knee j o i n t were not as important i n c o n t r i b u t i n g to the net work done during 72 jumping as the muscles of the ankle and hip j o i n t s . Furthermore they showed that the muscles of the legs c o n t r i b u t e d d i f f e r e n t i a l l y to the two types of jumps. The s t u d i e s on j o i n t power i n d i c a t e that f o r movements p r i m a r i l y concerned with h o r i z o n t a l displacement of the body the knee j o i n t was a net absorber of energy. They also i n d i c a t e that the r o l e of the muscles c r o s s i n g the hip j o i n t was d i f f e r e n t i n double l e g support a c t i v i t i e s , such as walking, race walking and standing broad jumping, than i n s i n g l e l e g support movements l i k e j ogging and running. In double l e g support a c t i v i t i e s the muscles of the hip j o i n t were important i n c o n t r i b u t i n g to forward motion but that was not the case i n s i n g l e l eg support movements. BIOMECHANICAL PRINCIPLES To make b i o m e c h a n i c a l i n f o r m a t i o n more e a s i l y understood and a p p l i c a b l e , the i n f o r m a t i o n i s sometimes summarized i n t o a p r i n c i p l e . Two examples of t h i s are the biomechanical p r i n c i p l e s of summation of j o i n t f o r c e s and c o n t i n u i t y of j o i n t f o r c e s . Simply s t a t e d , the p r i n c i p l e of summation of j o i n t f o r c e s says that to produce the f a s t e s t , most powerful movement p o s s i b l e , a l l the j o i n t s that can c o n t r i b u t e to the movement must be used and used to t h e i r f u l l e s t extent. This p r i n c i p l e has been d e s c r i b e d by Broer and Z e r n i c k e (1979), Bunn (1972), Cooper and Glassow (1976), Luttgens and Wells (1982), Morehouse and Cooper (1950), Norman (1975) and the L e v e l I Coaching Theory manual of the N a t i o n a l Coaching 73 C e r t i f i c a t i o n Program (1979a). Other a u t h o r s , when d i s c u s s i n g summation of f o r c e s , i n t e r p r e t the p r i n c i p l e as r e f e r r i n g to the sequencing and timing of i n t e r n a l f o r c e s c o n t r i b u t i n g to a movement (Broer and Ze r n i c k e , 1979; Bunn, 1972; Cooper and Glassow, 1976; Dyson, 1962; Jensen and S c h u l t z , 1977; N o r t h r i p et a l . , 1974; Plagenhoef, 1971; Simonian, 1981). The sequencing of muscular c o n t r a c t i o n s f o r a movement i s explained by the p r i n c i p l e of c o n t i n u i t y of j o i n t f o r c e s which s t a t e s that the order of the muscle groups or segments used should be from the l a r g e s t to the smallest (Bunn, 1972; Kreighbaum and B a r t h e l s , 1981; N a t i o n a l C o a c h i n g C e r t i f i c a t i o n Program, 1979a; Norman, 1975; Simonian, 1981), from the stro n g e s t to the weakest (Bunn, 1972; Dyson, 1962; Simonian, 1981), from the proximal to the d i s t a l (Broer and Ze r n i c k e , 1979; Dyson, 1962; Gowitzke and M i l n e r , 1980; Luttgens and Wells, 1982; N a t i o n a l Coaching C e r f i f i c a t i o n Program, 1979a; Norman, 1975; Plagenhoef, 1971), from the slowest to the f a s t e s t (Dyson, 1962; Luttgens and Wells, 1982 ; Simonian, 1981) or from the heaviest to the l i g h t e s t (Dyson, 1962; Gowitzke and M i l n e r , 1980; Kreighbaum and B a r t h e l s , 1981; Luttgens and Wells, 1982; Morehouse and Cooper, 1950). There i s some discrepancy among authors as to how the above two p r i n c i p l e s apply to various types of a c t i v i t i e s . The N a t i o n a l Coaching C e r i t i f i c a t ion Program (1979a) says that the summation of j o i n t f o r c e s p r i n c i p l e a p p l i e s to 74 jumping, throwing, s t r i k i n g and k i c k i n g a c t i v i t i e s . In a d d i t i o n , the N a t i o n a l Coaching C e r t i f i c a t i o n Program (1979b) a l s o s t a t e s that another p r i n c i p l e , the summation of body segment v e l o c i t i e s , i s a p p l i c a b l e only to throwing, s t r i k i n g and k i c k i n g s k i l l s . On the other hand, Norman (1975) s t a t e s that summation of j o i n t f o r c e s i s p r i m a r i l y intended to deal with s e l f - p r o p u l s i o n of the body while a d i f f e r e n t p r i n c i p l e , the summation of body segment speeds, a p p l i e s to movements where maximum hand, foot or implement speed i s r e q u i r e d . Dyson (1962) concurs with t h i s o p i n i o n when he mentions that summation of forces i s p a r t i c u l a r l y important i n jumping while summation of throwing f o r c e s i s a p p l i c a b l e to throwing movements. Other authors using s l i g h t l y d i f f e r e n t terms, the summation of v e l o c i t i e s (Kreighbaum and B a r t h e l s , 1981; N o r t h r i p eJL a_l. , 1974 ) and the summation of segment v e l o c i t i e s (Gowitzke and M i l n e r , 1980), support the idea of a p r i n c i p l e s p e c i f i c to throwing, k i c k i n g and s t r i k i n g a c t i o n s . Concerning the c o n t i n u i t y p r i n c i p l e , the m a j o r i t y o p i n i o n i s t h a t f o r t h r o w i n g , k i c k i n g and s t r i k i n g a c t i v i t i e s , where the o b j e c t i v e i s to maximize the speed of the d i s t a l segment i n v o l v e d i n the movement, there i s a d e f i n i t e sequencing of f o r c e s or body segment v e l o c i t i e s (Broer and Z e r n i c k e , 1979; Bunn, 1972; Cooper and Glassow, 1976; Dyson, 1962; Gowitzke and M i l n e r , 1980; Kreighbaum and B a r t h e l s , 1981; Luttgens and We l l s , 1982; Morehouse and Cooper, 1950; N a t i o n a l Coaching C e r t i f i c a t i o n Program, 75 1979a; Norman, 1975; N o r t h r i p ejt a l . , 1974; Plagenhoef, 1971; Simonian, 1981). The sequencing of f o r c e s occurs i n such a manner that each s u c c e s s i v e f o r c e i s a p p l i e d when the preceding f o r c e has made i t s maximum c o n t r i b u t i o n toward i n c r e a s i n g the v e l o c i t y of the more d i s t a l segment or segments (Broer and Z e r n i c k e , 1979; Bunn, 1972; Cooper and Glassow, 1976; Morehouse and Cooper, 1950; Plagenhoef, 1971; Simonian, 1981). For jumping a c t i v i t i e s , however, where the o b j e c t i v e i s to move the a t h l e t e ' s t o t a l body mass, there i s l e s s agreement about whether sequencing occurs. Again the N a t i o n a l Coaching C e r t i f i c a t i o n Program (1979a) says that the c o n t i n u i t y p r i n c i p l e holds f o r jumping as w e l l as f o r throwing, s t r i k i n g and k i c k i n g a c t i v i t i e s . This i m p l i e s that sequencing occurs i n jumping movements. Dyson (1962) t h e o r i z e s that to create maximum impulse during jumping a l l muscles i n v o l v e d should c o n t r a c t simultaneously. However, he says t h a t i n p r a c t i c e , due to the n a t u r e of the c o n s t r u c t i o n of the human body where the stronger body parts are a l s o the h e a v i e s t and thus have the g r e a t e s t i n e r t i a , there i s sequencing of muscular c o n t r a c t i o n s from proximal to d i s t a l with f o r c e s ending together. T h e r e f o r e , the f o r c e s f o r jumping a c t i v i t i e s , according to Dyson (1962), would overlap one another as opposed to throwing, k i c k i n g and s t r i k i n g movements where the forces would be generated s u c c e s s i v e l y . Other i n v e s t i g a t o r s are of the o p i n i o n that the f o r c e s are a p p l i e d simultaneously. Broer and Zernicke 76 (1979) b e l i e v e t h i s to be the case i n heavy tasks, i n which jumping presumably could be i n c l u d e d , while f o r the v e r t i c a l jump, Morehouse and Cooper (1950) s t a t e that the two j o i n t muscles of the th i g h a c t i n g at both the knee and hip j o i n t s cause the knees and hips to extend simult a n e o u s l y . An a l t e r n a t e view i s expressed by Kreighbaum and B a r t h e l s (1981) who s t a t e that the degree of sequencing f o r movements i s r e l a t e d to the purpose of the movement, the mass of the o b j e c t to be moved and the s t r e n g t h of the a t h l e t e . They e n v i s i o n a continuum. At one end are movements whose primary o b j e c t i v e i s the development of high speed. This i s achieved through s e q u e n t i a l movement of body segments. At the other end of the continuum are movements whose primary emphasis i s on f o r c e generation or accuracy. This i s accomplished through the simultaneous movement of body segments. T h e r e f o r e , as the mass of the object to be moved i n c r e a s e s , or the st r e n g t h of the a t h l e t e decreases, or the d e s i r e d accuracy of the movement outcome i n c r e a s e s , or the f o r c e ouput requirement of the movement i n c r e a s e s , the p a t t e r n i n g of the a c t i v i t y changes from s e q u e n t i a l to simultaneous segment involvement. Two other i n v e s t i g a t o r s have put f o r t h p r i n c i p l e s which are a p p l i c a b l e to jumping. The p r i n c i p l e of s u p e r p o s i t i o n of angular speeds i n j o i n t s (Koniar , 1973 ) says that the optimal performance by an a t h l e t e w i l l occur when the angular v e l o c i t i e s of the j o i n t s i n v o l v e d i n a movement peak simu l t a n e o u s l y . Koniar (1973) found that f o r a v e r t i c a l 77 jump, the best performance occurred when the maximum h i p , knee and ankle angular v e l o c i t i e s were achieved at the same time. Hochmuth and Marhold (1978) gave a t h e o r e t i c a l e x p l a n a t i o n of the p r i n c i p l e of the optimal p o s i t i o n of the f o r c e maximum. By observing a t h l e t i c performances they d i s c o v e r e d that humans can develop maximum a c c e l e r a t i o n for only a short p e r i o d of time. From a t h e o r e t i c a l a n a l y s i s of a c c e l e r a t i o n - t i m e dynamics they c o n c l u d e d t h a t the p o s i t i o n i n g of the maximum f o r c e depends upon the aim of the a c t i v i t y . Given the c o n s t r a i n t that an object must move a set d i s t a n c e , then to cover that d i s t a n c e i n a minimum of time the maximum f o r c e must occur at the beginning of the movement. If the aim i s to impart maximum v e l o c i t y to the o b j e c t , such as i n jumping, the maximum fo r c e must occur at the end of the a c c e l e r a t i o n phase. Recently there have been s e v e r a l s t u d i e s which have endeavoured to e s t a b l i s h the u s e f u l n e s s of v a r i o u s p r i n c i p l e s i n d i f f e r e n t a c t i v i t i e s . Robertson and Fleming (1983) looked at the a p p l i c a b i l i t y of the p r i n c i p l e s of summation and c o n t i n u i t y of j o i n t f o r c e s to the v e r t i c a l jump and standing broad jump. From the r e s u l t s of a j o i n t power a n a l y s i s f o r the l e g s they c o n c l u d e d t h a t the summation p r i n c i p l e held f o r the v e r t i c a l jump but not the standing broad jump because i n the broad jump the muscles c r o s s i n g the knee j o i n t were net absorbers of energy. They a l s o concluded that the c o n t i n u i t y p r i n c i p l e did not hold 78 f o r e i t h e r jump as a l l three extensor muscle groups of the l e g s c o n t r a c t e d n e a r l y s i m u l t a n e o u s l y i n s t e a d of s e q u e n t i a l l y as expected. Three s t u d i e s have looked s p e c i f i c a l l y at the p r i n c i p l e of summation of segmental v e l o c i t i e s . For the s t u d i e s to support the p r i n c i p l e , the rese a r c h e r s needed to f i n d an a c c e l e r a t i o n - d e c e l e r a t i o n sequence at a l l the j o i n t s i n v o l v e d i n the motion except the most d i s t a l one. The a c c e l e r a t i o n - d e c e l e r a t i o n sequence at a j o i n t was to be e x h i b i t e d by a c o n c e n t r i c c o n t r a c t i o n of the agonist muscles across the j o i n t f o l l o wed by an e c c e n t r i c c o n t r a c t i o n of the antagonist muscles ( J o r i s e_t aJL. , 1985; Robertson and Mosher, 1985). This sequencing of muscular c o n t r a c t i o n s was assumed to help a c c e l e r a t e , i n a w h i p - l i k e f a s h i o n , the segments d i s t a l to the j o i n t . Both Ohman and Robertson (1981) and Robertson and Mosher (1985) i n t h e i r s t u d i e s concluded that t h i s p r i n c i p l e d i d not completely hold. Ohman and Robertson (1981) showed that the elbow j o i n t did not e x h i b i t an a c c e l e r a t i o n - d e c e l e r a t i o n sequence and that i n f a c t the elbow extensors d i d no work i n a c h i e v i n g maximal hand v e l o c i t y i n a v o l l e y b a l l s p i k e . Instead, c o n c e n t r i c c o n t r a c t i o n of the shoulder extensors followed immediately by e c c e n t r i c c o n t r a c t i o n of the shoulder f l e x o r s produced the d e s i r e d a c t i o n of the forearm and hand. Robertson and Mosher (1985) found that f o r soccer k i c k i n g p r a c t i c a l l y no work was done by the knee extensors to extend the lower l e g . Again, the expected a c c e l e r a t i o n - d e c e l e r a t i o n sequence was 79 not evident at the knee j o i n t . The t h i r d study, by J o r i s e_t a_l. (1985), found support f o r the p r i n c i p l e and concluded that development of high segmental v e l o c i t i e s i n the overarm throw by female h a n d b a l l p l a y e r s was a p r e r e q u i s i t e f o r a c h i e v i n g f a s t b a l l v e l o c i t y . They based t h e i r c o n c l u s i o n n o t on a s e g m e n t a l a n a l y s i s and not on an a c c e l e r a t i o n - d e c e l e r a t i o n p a t t e r n i n g a n a l y s i s of the i n v o l v e d j o i n t s but on the f i n d i n g that the maximum l i n e a r v e l o c i t i e s f o r the h i p , elbow, w r i s t and b a l l a l l occurred and i n c r e a s e d s e q u e n t i a l l y , from proximal to d i s t a l . Another study by Robertson (1982), while not l o o k i n g s p e c i f i c a l l y at the u s e f u l n e s s of the summation of segmental v e l o c i t i e s p r i n c i p l e , found that the knee extensors were not i n v o l v e d i n the e x t e n s i o n of the lower l e g i n h u r d l i n g . Here, s i m i l a r to the soccer study, r a p i d f l e x i o n of the t h i g h by the hip f l e x o r s followed by e c c e n t r i c c o n t r a c t i o n of the hip extensors provided the means by which the lower l e g was extended. 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