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The forward kinematics of 3-RPR planar robots: A review and a distance-based formulation

AuthorsRojas, Nicolás ; Thomas, Federico
Issue Date2011
PublisherInstitute of Electrical and Electronics Engineers
CitationIEEE Transactions on Robotics 27(1): 143-150 (2011)
AbstractThe 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.
Publisher version (URL)http://dx.doi.org/10.1109/TRO.2010.2092251
Identifiersdoi: 10.1109/TRO.2010.2092251
issn: 1552-3098
e-issn: 1941-0468
Appears in Collections:(IRII) Artículos
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