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A Geometrical Procedure for the Comprehensive Position Analysis in Parallel Manipulators

Dr. Alfonso Hernandez < >
Faculty of Engineering
Bilbao Spain

May 2, 2003 at  11:30 AM

Position analysis constitutes not only a fundamental step in the design of mechanisms, but an essential tool for the operation of manipulators. Here the Iterative-Geometric Method, a general approach to calculate positions and characterize them, is introduced. The resolution of the finite displacement problem leads to the determination of the linkage motion field. In this method, a mechanism is modellized as a series of nodes and geometric constraints. The position problem being nonlinear, a sequence for the application of the geometric constraints is defined by means of hierarchical rules and criteria. These rules and criteria are derived both theoretically and experimentally. When all the geometric constraints have been applied, the first iteration is completed. Repeated application of this sequence leads to the convergence of the nodes to their actual position.

Furthermore, the mechanism may reach particular postures, whereby local or global changes of the linkage degrees of freedom occur. In these circumstances the procedure calculates the geometric matrix, whose nullspace contains the feasible motions of the mechanism. Using eigenvalue calculations, a method for the detection of the singular postures has been developed, including their categorization, following well-known classifications such as the one introduced by Gosselin and Angeles. The procedure has been implemented so far in planar manipulators, and shows promising features for its application their spatial counterparts.