Additional Math Pages & Resources

Thursday, June 9, 2011

Degrees, Gears and Ratios, Part IV

Today we will see how math might be used with gears. Here is an illustration that shows some of the different kinds of gears you might find in your car, truck, tractor, etc. This artwork came from a gear reference website that you might want to visit.

All these gears have parts described by special names and quantified by various math concepts. I can use angles (expressed in degrees) to describe the relationships of the gears to each other, the slope of the gear teeth, etc.

Counting the teeth on gears in a pair gives you ratios, which determine the input and output speeds of the shafts.

The following diagram shows names and dimensions used on simple spur gears. Here you can see that we need units of measure to describe height, width, depth, diameter, etc.

Naturally, when the gear has helical teeth, or if there is a spiral worm gear involved, we need additional ways to describe the complex curves of the teeth, and how they mesh, the directions of rotation for each gear, etc. This requires math, math and more math.

Helical teeth slide against one another, creating side forces on the shafts. Double-helical (also called herringbone) gears are hard to manufacture but the double teeth off-set any side forces, so the gears run in a straight line .

Economical production of herringbone gears was first made possible by a special kind of cutting tool invented by Andre Citroen. One of his giant gears is shown above. The logo of the Citroen car company is shaped like a double-chevron, reminding us of Andre's gear prowess.

If you like gears and know a little math, you can be dangerously creative. Here's an example created by Benjamin Cowden ...

If you want to have endless fun making gears of your own in wood or other soft materials, you could construct something like this:

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