A Linear Relaxation Technique for the Position Analysis of Multiloop Linkages

J.M. Porta, L. Ros, F. Thomas
2009 IEEE Transactions on robotics  
This report presents a new method able to isolate all configurations that a multi-loop linkage can adopt. We tackle the problem by providing formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear and bilinear terms, and trivial trigonometric functions for the helical pair exclusively) whose special structure is later exploited by a branch-and-prune method based on linear relaxations. The
more » ... laxations. 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, irrespectively of whether the linkage is rigid or mobile.
doi:10.1109/tro.2008.2012337 fatcat:6su7f5idljb5np2fwrjxoqx7eq