Non-circular gears—graphic generation of involutes and base outlines

Abstract Base and involute contours associated with non-circular pitch outlines were generated by graphic construction and implemented by computer algorithms. The singular unambiguous definitions of a base circle and involute for circular gears lead to multiple interpretations when applied to non-circular pitch outlines. Four different base outlines were generated for each pitch outline presented here. These were arrived at by combining two means of fixing the pressure angle and two means of terminating the conjugate line. Involutes were then generated by applying the principle of unrolling a hypothetical cord from the base outlines and by tracing a point moving along the conjugate lines. Because of the difficulties associated with dealing analytically with generalized non-circular pitch outlines, the approach taken was the numerical equivalent of geometric constructions, reflecting the application of the principles of gearing. The outlines used were ellipses of the first three orders.