The standard forward-kinematics analysis of 3-RPR planar parallel robots boils down to computation of the roots of a sextic polynomial. There are many different ways to obtain this polynomial, but most 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 sexticwhich is not linked to a particular reference frameis straightforwardly obtained with the need for neither variable eliminations nor tangent-half-angle substitutions. The presented formulation is valid, with no modification, for any planar 3-RPR parallel robot, including the special architectures and configurationswhich ultimately lead to numerical instabilitiesthat cannot be directly handled by previous formulations. © 2010 IEEE. ; This research has been partially supported by the Spanish Ministry of Science and Innovation under the I+D project DPI2007- 60858. The first author is supported by the Colombian Ministry of Communications and Colfuturo through the ICT National Plan of Colombia. ; Peer Reviewed
The forward kinematics of 3-RPR planar robots: A review and a distance-based formulation
2011-01-01
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
DDC: | 629 |
The forward kinematics of 3-RPR planar robots: a review and a distance-based formulation
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