On the Elastokinematics of the Involute Gear Pair

Abstract

The planar motion of the spur-gear pair having unseparated teeth of involute and elastically deformable form is analyzed by reducing it to an elastically and inertially constrained five-bar chain of mobility three. Particular concern is in describing the movement of the material point of profile contact and so in establishing the displacement and velocity constraint equations that govern the four angular coordinates that describe the instantaneous state of the assemblage. An expression is developed for the elasticity-dependent sliding velocity at tooth contact. The concept of the virtual base circle is introduced to make explicit the irrelevance to deforming teeth of the pitch point and the invariance property of the common normal that are apt to rigid teeth.