Contribution to the Optimization of Closed-Loop Multibody Systems : Application to Parallel Manipulators

This paper describes an original and robust method to optimize the design of closed-loop mechanisms, especially parallel manipulators. In other words, these mechanisms include assembling constraints we solved using a Newton-Raphson algorithm which may fail when the Jacobian matrix of the constraints is ill-conditioned. Therefore, the technique we propose takes advantage of that conditioning to penalize properly the objective function. Applications are shown: on the one hand, a simple example about the design of a planar ejector and, on the other hand, more realistic examples about the kinematical properties of parallel robots, in particular Delta-type and HexaSlide-type manipulators