Consistent modeling resolves asymmetry in stiffness matrices

Journal article (2016)

Authors

A.G.L. Hoevenaars Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering
Clément Gosselin Laval University
P. Lambert Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering
J.L. Herder Mechatronic Systems Design - Mechanical, Maritime and Materials Engineering
Research Group
Mechatronic Systems Design (Mechanical, Maritime and Materials Engineering) (TU Delft)
Loading Asymmetry Screw theory Parallel manipulators Jacobian-derivative Stiffness analysis
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Published Date

2016

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Precision and Microsystems Engineering

Research Group

Mechatronic Systems Design

Abstract

The Cartesian stiffness analysis of mechanisms and robotic manipulators is often performed using Jacobian-based stiffness analysis methods. In general it is necessary to consider the effect of loading, which introduces a Jacobian-derivative term. However, early examples of stiffness analyses of parallel manipulators in which the effect of loading was considered resulted in asymmetric stiffness matrices, which go against the definition of stiffness. By replicating those first analyses using an alternative formulation of the stiffness analysis, this paper finds that the earlier observed asymmetry can be explained as a modeling inconsistency. If that inconsistency is corrected, symmetric matrices are obtained, which supports the notion that the Jacobian-derivative term is an integral part of the stiffness analysis of parallel manipulators and mechanisms.