Abstract
Abstract The information on the mechanism is in general available through the joint coordinates. Full control of the mechanism requires that the position and orientation of each solid be derivable from this information. Formally, this derivation amounts to solving a system of algebraic equations. The latter admits in general more than one solution, each corresponding to a different mechanism assembly mode. The control problem is thus to choose the right solution, i.e., the one corresponding to the mechanism posture. It is however vain to hope that a blindly launched numerical (yet converging) algorithm will end up in a correct posture. In this paper an algorithm converging globally to the right solution is proposed. This Kantorovitch theorem based algorithm is of a polynomial complexity, and is valid for an arbitrary mechanism. Its efficiency is tested on a reputed difficult example of a generalized Gough-Stewart platform.
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