Gear were invented so that large forces could be transmitted between two rotating shafts. There are a few simple geometric relationships which govern the operation of gears. First, moving gears in mesh ast like wheels that are rolling against each other without slipping. Gear teeth are much more effective in preventing slipping than friction between smoothe wheels.

The pitch of a gear is the distance between equibvalent points on adjacent teeth. (See the diagram to the right) For two gears to mesh they must have the same pitch. The pitch circle of a gear is an imaginary circle which passes through the point where the teeth touch when one gear meshes with another. The pitch diameter is the diameter of the pitch circle.

The pitch circle is the imaginary circle that passes through the contact point between two meshing gears.

Practical gears must have whole teeth and not half teeth. As a result, there are certain combinations of pitches and pitch diameters which can be made to work together. A family of gears is a group that shares the same pitch and other geometric constraints. That is why the ratios from the previous lesson was so important. Some examples of a gear family would be a 12 :24 ratio (12 teeth to 24 teeth); 4:8; 12:36 etc.

This information came from Gears, Levers and Rotating Machines by Tom Hsu Ph.D, Copyright 1995 Cambridge Physics Outlet, Inc. (Dr. Hsu is a nationally recognized innovator in science and math education. He holds a Ph.D in applied plasma physics from MIT. See the annotated links for his web location and other activities.)