The kinematics of curved profiles mating with a caged idle roller - higher-path curvature analysis

Abstract

This investigation focuses on the relative motion of a force-closure higher pair mechanism, herein termed caged-roller joint and composed of a cylindrical roller meshing with two slot profiles, carved on different bodies. A distinctive feature of such a mechanism is the pure rolling velocity constraint imposed between its components to limit friction losses. This makes the caged-roller joint an ideal candidate to control the kinematics of high-speed operating devices, such as centrifugal pendulum vibration absorbers.In this paper, a theoretical framework for the motion of caged-roller joint is proposed, employing intrinsic geometry, higher-path curvature and envelope theory. For design-analysis purposes, the correlations between instantaneous invariants, slots profiles curvature properties and pure rolling conditions within the higher pairs have been established. Eventually, the obtained results have been verified for three particular curves profiles, to test their consistency and offer an immediate application.