Chapter 7: Gear and Sprocket Calculations

7.1 INVOLUTE FUNCTION CALCULATIONS

Involute functions are used in some of the equations required to perform involute gear design. These functional values of the involute curve are easily calculated with the aid of the pocket calculator. Refer to the following text for the procedure required to calculate the involute function.

The Involute Function: inv = tan arc . The involute function is widely used in gear calculations. The angle for which involute tables are tabulated is the slope of the involute with respect to a radius vector R (see Fig. 7.1).

Figure 7.1: Involute geometry.

Involute Geometry (See Fig. 7.1). The involute of a circle is defined as the curve traced by a point on a straight line which rolls without slipping on the circle. It is also described as the curve generated by a point on a nonstretching string as it is unwound from a circle. The circle is called the base circle of the involute. A single involute curve has two branches of opposite hand, meeting at a point on the base circle, where the radius of curvature is zero. All involutes of the same base circle are congruent and parallel, while involutes of different base circles are geometrically similar.

Figure 7.1 shows the elements of involute geometry. The generating line was originally in position G ₀, tangent to the base circle at P ₀. The line then rolled about the base circle through the...