Kinematic Creep in a Continuously Variable Transmission: Traction Drive Mechanics for Cobots

Abstract

Two continuously variable transmissions are examined, one that relates a pair of linear speeds and another that relates a pair of angular speeds. These devices are elemental in the design of cobots, a new class of robot that creates virtual guiding surfaces to aid a human operator in assembly tasks. Both of these transmissions are traction drive mechanisms that rely on the support of either lateral or longitudinal forces across rolling contacts with spin. When a rolling contact between elastic bodies or even between rigid bodies in spin is called upon to transmit a tractive force, kinematic creep develops, expressing a departure from the intended rolling constraint. Creep in turn gives rise to nonideal properties in a cobot’s virtual guiding surfaces. This paper develops simple models of the two transmissions by expressing the relative velocity field in the contact patch between rolling bodies in terms of creep and spin. Coulomb friction laws are applied in a quasi-static analysis to produce complete force-motion models. These models may be used to evaluate a cobot’s ability to support forces against its virtual guiding surfaces.