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Harmonograph

19 18 TWo harmonograPhs lateral and rotary Two harmonographs and some of the simple patterns they draw. On the left the simple lateral version and its patterns open and closed phase on the right the three pendulum, rotary harmonograph and its drawings concurrent and countercurrent. In the simplest version of the instrument two pendulums are suspended through holes in a table, swinging at rightangles to each other. Projected above the table, the shaft of one pendulum carries a small platform with a piece of paper clipped to it, while the shaft of the other pendulum carries an arm with a pen. As the pendulums swing the pen makes a drawing that is the result of their combined motion left side opposite. Both pendulums begin with the same length, further drawings can be obtained as one is then shortened by sliding the weight upwards and securing it with a clamp at various points. The harmonic ratios can be displayed in turn. By using three pendulums however, two circular, or rotary, movements can be combined, with fascinating results right side opposite. Two of the pendulums swing at rightangles as before, but are now both connected by arms to the pen, which in all rotary designs describes a simple circle. Situated under the circling pen, the third and variable pendulum is mounted on gimbals, a device familiar to anyone who has had to use a compass or cooking stove at sea. Here it acts as a rotary bearing, enabling the pendulum carrying the table to swing in a second circle under the pen. As the pen is lowered the two circles are combined on the paper. A further source of variation is also introduced here, for the two circular motions can swing in the same concurrent or opposite countercurrent directions, producing astonishing drawings with very different characteristics see appendices on pages 5455.
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