A note on enveloping curves in plane

This paper revisits the classical envelope theory in plane, which deals with two planar curves in a point contact moving in relative roll-slide motion. The well known result about the centers of curvature of the generating curve and the envelope curve behaving as coordinated centers, is shown to be valid even if the instantaneous relative angular velocity is zero. The analytical approach uses the contact kinematics equations and does not require the existence of finitely accessible velocity pole and polodes of the relative motion. An example of equivalent mechanisms demonstrates the extended applicability of the theorem on coordinated centers of enveloping curves.