Symbolic derivation of bicycle kinematics with toroidal wheels

Abstract

Bicycle kinematics with toroidal wheels is presented in this paper. Using symbolic mathematic tool Maple, we obtain two holonomic and four nonholonomic constraint equations due to front and rear wheels of a bicycle. We show that the two holonomic constraints cannot be expressed in quartic form for bicycle rear body pitch angle unless the minor (crown) radius of the torus are the same for both the front and rear wheels. In addition, we show that all the constraints can be written in differential form, from which a constraint matrix is constructed, according to standard procedure for developing dynamics in robotics.