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A linear relaxation technique for the position analysis of multiloop linkages

AuthorsPorta, Josep M. ; Ros, Lluís ; Thomas, Federico
KeywordsClosed chain
Forward and inverse kinematics
Geometric constraint
Loop closure
Multibody system
Multiloop linkage
Issue Date2009
PublisherInstitute of Electrical and Electronics Engineers
CitationIEEE Transactions on Robotics 25(2): 225-239 (2009)
AbstractThis paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, bilinear, and quadratic monomials, and trivial trigonometric terms for the helical pair only) whose structure is later exploited by a branch-and-prune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespective of whether the linkage is rigid or mobile.
Publisher version (URL)http://dx.doi.org/10.1109/TRO.2008.2012337
Appears in Collections:(IRII) Artículos
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