A robust forward kinematics analysis of 3-RPR planar platforms
Visualitza/Obre
10.1007/978-90-481-9262-5_3
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/14373
Tipus de documentText en actes de congrés
Data publicació2010
EditorSpringer Verlag
Condicions d'accésAccés obert
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continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
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.
CitacióRojas, N.; Thomas, F. A robust forward kinematics analysis of 3-RPR planar platforms. A: International Symposium on Advances in Robot Kinematics. "Advances in Robot Kinematics: motion in man and machine". Piran-Portorož: Springer Verlag, 2010, p. 23-32.
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