Kinematic Creep in a Continuously Variable Transmission:
Traction Drive Mechanics for Cobots
R. Brent Gillespie, Carl A. Moore, Michael Peshkin, J. Edward
Colgate
ASME Journal of Mechanical Design, Vol. 124, No. 4, pp. 713-722, December
2002.
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.