Higher-order Taylor approximation of finite motions in mechanisms

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 high...

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Bibliographic Details
Published in:Robotica 2019-07, Vol.37 (7), p.1190-1201
Main Authors: de Jong, J. J., Müller, A., Herder, J. L.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Derivatives
Group theory
Lie groups
Mathematical analysis
Parallel degrees of freedom
Screw theory
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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.
ISSN:0263-5747
1469-8668
DOI:10.1017/S0263574718000462