A robust forward kinematics analysis of 3-RPR planar platforms

Rojas, Nicolás and Thomas, Federico (2010) A robust forward kinematics analysis of 3-RPR planar platforms. In: Lenarčič, Jadran and Stanišić, Michael M (eds.) Advances in robot kinematics: motion in man and machine. Springer, pp. 23-32. ISBN 9789048192618

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The standard forward kinematics analysis of 3-RPR planar parallel platforms boils down to computing the roots of a sextic polynomial. There are many different ways to obtain this polynomial but all of them include exceptions for which the formulation is not valid. Unfortunately, near these exceptions the corresponding polynomial exhibits numerical instabilities. In this paper, we provide a way around this inconvenience by translating the forward kinematics problem to be solved into an equivalent problem fully stated in terms of distances. Using constructive geometric arguments, an alternative sextic – which is not linked to a particular reference frame – is obtained in a straightforward manner without the need of variable eliminations nor tangent-half-angle substitutions. The presented formulation is valid, without any modification, for any planar 3-RPR parallel platform, including the special architectures and configurations – which ultimately lead to numerical instabilities – that cannot be directly handled by previous formulations.

Item Type: Book Section
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Depositing User: Nicolas Rojas
Date Deposited: 07 Mar 2016 07:51
Last Modified: 07 Mar 2016 07:51
URI: http://sro.sussex.ac.uk/id/eprint/59889
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