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Tailored Formulations of Geometric Constraints for Algebraic Analysis of Mechanism Kinematics

[+] Author Affiliations
Samuli Piipponen, Eero Hyry

University of Tampere, Tampere, Finland

Jukka Tuomela

University of Eastern Finland, Joensuu, Finland

Andreas Müller

JKU Johannes Kepler University, Linz, Austria

Paper No. DETC2015-46094, pp. V05CT08A051; 9 pages
doi:10.1115/DETC2015-46094
From:
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5C: 39th Mechanisms and Robotics Conference
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5714-4
  • Copyright © 2015 by ASME

abstract

Algebraic analysis of the kinematics of large and complicated mechanisms is complicated by the fact that the computational complexity grows very quickly as a function of the number of variables. However, for mechanisms which contain only revolute and/or cylindrical joints one can always simplify the original constraint ideal by choosing the right prime component of the ideal of revolute or cylindrical joint. By making these choices one automatically discards components which are irrelevant to the problem and hence the resulting ideal is simpler than the original. In this way one can immediately analyze some systems whose analysis in the original form is not feasible. As an example we illustrate our results using the spherical 4–bar mechanism.

Copyright © 2015 by ASME
Topics: Kinematics , Algebra

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