Symbolic derivation of bicycle kinematics with toroidal wheels
No. 100 Waihuan Xi Road, Guangdong University of Technology, Guangzhou HEMC, Panyu District, Guangzhou, Guangdong Province, China, 510006
a Everett X. Wang: firstname.lastname@example.org
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.
© Owned by the authors, published by EDP Sciences, 2015
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.