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Algebraic methods in mechanism analysis and synthesis

Published online by Cambridge University Press:  01 November 2007

Manfred L. Husty ,
Martin Pfurner ,
Hans-Peter Schröcker  and
Katrin Brunnthaler
Manfred L. Husty*
Affiliation:
University Innsbruck, Institute of Basic Sciences in Engineering, Unit Geometry and CAD, Technikerstraße 13, A6020 Innsbruck, Austria.
Martin Pfurner
Affiliation:
University Innsbruck, Institute of Basic Sciences in Engineering, Unit Geometry and CAD, Technikerstraße 13, A6020 Innsbruck, Austria.
Hans-Peter Schröcker
Affiliation:
University Innsbruck, Institute of Basic Sciences in Engineering, Unit Geometry and CAD, Technikerstraße 13, A6020 Innsbruck, Austria.
Katrin Brunnthaler
Affiliation:
University Innsbruck, Institute of Basic Sciences in Engineering, Unit Geometry and CAD, Technikerstraße 13, A6020 Innsbruck, Austria.
*
*Corresponding author. E-mail: manfred.husty@uibk.ac.at
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Summary

Algebraic methods in connection with classical multidimensional geometry have proven to be very efficient in the computation of direct and inverse kinematics of mechanisms as well as the explanation of strange, pathological behavior. In this paper, we give an overview of the results achieved within the last few years using the algebraic geometric method, geometric preprocessing, and numerical analysis. We provide the mathematical and geometrical background, like Study's parametrization of the Euclidean motion group, the ideals belonging to mechanism constraints, and methods to solve polynomial equations. The methods are explained with different examples from mechanism analysis and synthesis.

Keywords

Kinematic mappingConstraint manifoldMechanism analysisMechanism synthesisBennett mechanism6R inverse kinematicsOverconstrained mechanism
Type
Article
Information
Robotica , Volume 25 , Issue 6 , November 2007 , pp. 661 - 675
Copyright
Copyright © Cambridge University Press 2007

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