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The forward kinematics of 3-RPR planar robots: a review and a distance-based formulation
Rojas Libreros, Nicolás Enrique; Thomas, Federico
Universitat Politècnica de Catalunya. Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industrial
The standard forward kinematics analysis of 3-RPR planar parallel robots boils down to computing 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 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 robot, 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
3-RPR parallel robots
Cayley–Menger determinants
Coordinate-free formulations
Forward kinematics
Position analysis
Robots -- Cinemàtica
Attribution-NonCommercial-NoDerivs 3.0 Spain

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