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A Polynomial Approach to Inverse Kinematics of Rolling Contact

[+] Author Affiliations
Lei Cui

Carnegie Mellon University, Pittsburgh, PA

Jian S. Dai

King’s College London, University of London, London, UK

Paper No. DETC2012-70852, pp. 1563-1570; 8 pages
doi:10.1115/DETC2012-70852
From:
  • ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B
  • Chicago, Illinois, USA, August 12–15, 2012
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4503-5
  • Copyright © 2012 by ASME

abstract

A moving object has three rotational degrees of freedom with respect to the fixed one when the two objects maintain rolling contact. Thus three kinematic inputs are considered necessary for the moving object to follow a trajectory described by its velocity profile as function of time. This paper formulates the problem as a system of three nonlinear equations and reduces it to solving a polynomial of degree six with one variable. This leads to fast and accurate numerical approximations of roots on a computer either by commercial software or open-source software. This polynomial formulation is different from previous ones that require solving a system of nonlinear ordinary differential equations.

Copyright © 2012 by ASME

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