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A robust forward kinematics analysis of 3-RPR planar platforms
Rojas Libreros, Nicolás Enrique; Thomas, Federico
Universitat Politècnica de Catalunya. Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industrial; Universitat Politècnica de Catalunya. ROBiri - Grup de Robòtica de l'IRI
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 straightforwardly obtained 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.
Àrees temàtiques de la UPC::Informàtica::Robòtica
Robots -- Kinematics
Robot kinematics
3-RPR parallel robots
Coordinate-free formulations
Cayley-Menger determinants
Numerical stability
Robots -- Cinemàtica
Attribution-NonCommercial-NoDerivs 3.0 Spain
Springer Verlag

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