UBC Undergraduate Research

Harmonograph Balasubramanian, Siddharta; Lathiff, Mohamed Nabil


The objective of the project was to design and build an electro-mechanical harmonograph for the project sponsor, Mr. Andres Wanner. The sponsor is a lecturer at the School of Arts and Technology at the Simon Fraser University. A harmonograph is an artistic drawing device capable of plotting a specific set of mathematical figures known as Lissajous curves on a two dimensional drawing surface. The following set of requirements for the device was requested by the sponsor at the start of the project: I. The device should be capable of drawing Lissajous curves of 40 cm in size on a sheet of paper with a variety of pens/pencils. II. Has custom tunable x-y ratio that can be set during operation of the device so that various types of drawings may be produced. III. Produces drawings through simple harmonic motion only (as opposed to computer-controlled plotting). IV. Is precise enough that lines drawn from multiple passes of the device trace right over each other. V. Is capable of producing drawings with some imperfections through mechanical noise for artistic effect. The final version of the harmonograph was designed and built to the above specifications. The completed device uses a dual stage hypo-cycloid drive to produce simple harmonic motion in two orthogonal axes with amplitudes of 10 cm. This drive is then coupled to a 4:1 pantograph mechanism to magnify the drawings to 40 cm. The pantograph drives a universal pen holder to produce the required drawings over a sheet of paper placed at the side of the device. The hypo-cycloid motion is produced using two bipolar stepper motors, each driven at a specific speed by a “Geckodrive” stepper motor controller. The stepping pulses required by the motor controllers are provided by an Arduino Mega microcontroller. The x-y ratio of the device is controlled through a user interface via push buttons on an Arduino LCD shield. The mechanical imperfections inherent to the machining processes deliver a slightly noisy drawing as initially requested by the sponsor. The following components were handed over to the sponsor at the end of the project: I. Two-stage hypocycloid drive II. Pantograph mechanism III. Control electronics

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