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Miscellaneous Mechanisms
Rack and Pinion

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Whenever you see graphics of gears on the web, they look like medieval cogs - slab-sided teeth, sometimes shown in mesh with gears that have different pitches. Worse, sometimes when the graphics designer wants a mechanical metaphor for a smoothly operating organization, he/she'll show three gears all in mesh. It's pretty jarring to someone who has learned over thirty or forty years to read gear trains at sight. Maybe it's an apt metaphor after all. Maybe the organizations ARE locked up.

As a public service to counter the prevailing mechanical illiteracy on the web, I'm publishing this animation of a basic rack and pinion. The gear teeth are straight-ahead 14-1/2 degree full-depth involute forms. To generate the proper forms for the rack and pinion teeth, I did the calculations in MathCAD 6.0 and copied the coordinates into Java polygons that then get transformed and rendered on the fly.

In the animation (drawn showing the pinion driving the rack), as the teeth mesh, their points of contact, marked here by red dots, roll down the involute form. As they roll, the contact points all fall on the pressure line, also drawn in red. The pressure line passes through the tangent point between the rack pitch line and the pinion pitch circle. In this case, the pressure line makes an angle of 14-1/2 degrees with the rack pitch line. (This is what distinguishes this as a 14-1/2 degree gear set.)

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Your comments and suggestions are welcomed.
07-09-03 3:55 PM