Resolution of the Direct Position Problem of Parallel Kinematic Platforms Using the Geometrical-Iterative Method

This paper presents the application of the procedure known as the Geometrical-Iterative Method to the resolution of the direct position problem in spatial mechanisms, and in particular parallel platforms. This procedure is based on the successive application of geometric constraints used for modelling the mechanism. The application sequence of these is defined from a search algorithm directed at satisfying two basic convergence conditions. The method is a competitive alternative for the Newton-Raphson procedure in the kinematic control of parallel platforms.