A linear relaxation technique for the position analysis of multiloop linkages

This 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.This work was supported by projects: 'Reconstrucció i anàlisi del moviment de grans estructures robòtiques i bioquímiques.' (J-05265), 'Analysis and motion planning of complex robotic systems' (4802).This work was supported in part by the Spanish Ministry of Science and Innovation under Project DPI2007-60858, and by the “Comunitat de Treball dels Pirineus” under Project 2006ITT-10004.Peer Reviewe