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Higher-order Taylor approximation of finite motions in mechanisms

Published online by Cambridge University Press:  29 June 2018

J. J. de Jong ,
A. Müller  and
J. L. Herder
J. J. de Jong*
Affiliation:
University of Twente, Enschede, The Netherlands
A. Müller
Affiliation:
Johannes Kepler University, Linz, Austria. E-mail: a.mueller@jku.at
J. L. Herder
Affiliation:
Delft University of Technology, Delft, The Netherlands. E-mail: j.l.herder@tudelft.nl
*
*Corresponding author. E-mail: j.j.dejong@utwente.nl
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Summary

Higher-order derivatives of kinematic mappings give insight into the motion characteristics of complex mechanisms. Screw theory and its associated Lie group theory have been used to find these derivatives of loop closure equations up to an arbitrary order. In this paper, this is extended to the higher-order derivatives of the solution to these loop closure equations to provide an approximation of the finite motion of serial and parallel mechanisms. This recursive algorithm, consisting solely of matrix operations, relies on a simplified representation of the higher-order derivatives of open chains. The method is applied to a serial, a multi-DOF parallel, and an overconstrained mechanism. In all cases, adequate approximation is obtained over a large portion of the workspace.

Keywords

Higher-order kinematicsTaylor approximationScrew theory5-bar mechanismBennet linkage
Type
Articles
Information
Robotica , Volume 37 , Special Issue 7: Computational Kinematics Conference, CK 2017 , July 2019 , pp. 1190 - 1201
Copyright
© Cambridge University Press 2018 

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