INTRODUCTION

Consider that two solids (1 and 2) are provided with interacting surfaces Σ1 and Σ2, and perform the prescribed transformation of motion. Surfaces Σ1 and Σ2 are in continuous tangency. These conditions are typical for the case of generation of surfaces by a tool, and for transformation of motion by gear tooth surfaces.

Henceforth, we differentiate two cases of tangency: (i) the interacting surfaces Σ1 and Σ2 are in line contact at every instant, and Σ2 is the envelope to the family of surfaces that is generated by Σ1 in coordinate system S2; and (ii) surfaces Σ1 and Σ2 are in point contact at every instant (the contact of Σ1 and Σ2 is localized).

We consider as given surface Σ1 and the location of point P of surface tangency (P is the point of the characteristic on Σ1 in the case in which Σ2 is the envelope, or the single point of tangency of Σ1 and Σ2); given as well are the value of transmission function ϕ2(ϕ1) at point P and the derivative ∂/∂ϕ1(ϕ2(ϕ1)) at P. (The characteristic is the instantaneous line of contact of enveloping surfaces). Our goals are to determine (i) direct relations between the principal curvatures and directions of contacting surfaces at P, (ii) relations between the normal curvatures of surfaces Σ1 and Σ2, and (iii) the relative normal curvatures.

The solution to these problems is important for computerized simulation of bearing contact of interacting surfaces.