Geometry and kinematics of the Mecanum wheel

Mecanum wheels are used when omnidirectional movability of a vehicle is desired. That means that the vehicle can move along a prescribed path and at the same time rotate arbitrarily around its center. A Mecanum wheel consists of a set of rolls arranged around the wheel axis. In this paper we describe in detail the geometry of these rolls. We derive simple canonical parameterizations of the roll generating curve and the roll surface itself. These parametric representations reveal the geometry of the roll. With their help we can easily find an approximation of the roll surface by a torus for manufacture purposes. Based on the roll parametrization we study the kinematics of a vehicle featured with Mecanum wheels.