Higher-order Taylor approximation of finite motions in mechanisms

de Jong, J.J.; Müller, A.; Herder, J.L.

Higher-order Taylor approximation of finite motions in mechanisms

Journal article (2018)

Authors

A. Müller Johannes Kepler University Linz

J.L. Herder Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering , Precision and Microsystems Engineering

Department

Precision and Microsystems Engineering

Screw theory 5-bar mechanism Bennet linkage Higher-order kinematics Taylor approximation

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Published Date

2018

Language

English

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Department

Precision and Microsystems Engineering

Abstract

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.

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