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Title

A robust forward kinematics analysis of 3-RPR planar platforms

AuthorsRojas, Nicolás ; Thomas, Federico
Keywords3RPR parallel robots
Coordinate-free formulations
Bilateration
Issue Date2010
PublisherSpringer
CitationAdvances in Robot Kinematics: Motion in Man and Machine: 23-32 (2010)
AbstractThe 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.
DescriptionTrabajo presentado al 12th International Symposium on Advances in Robot Kinematics (ARK-2010) celebrado en Eslovenia.
Publisher version (URL)http://dx.doi.org/10.1007/978-90-481-9262-5_3
URIhttp://hdl.handle.net/10261/30171
DOI10.1007/978-90-481-9262-5_3
ISBN978-90-481-9261-8
Appears in Collections:(IRII) Libros y partes de libros
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