Dynamics and control of actuated parallel structures as a constrained optimization problem through Gauss´ principle and Appell´s equations

This paper develops a purely deductive approach for dynamic analysis of parallel robots, based on consideration of Gauss´ principle through Appell´s approach. It follows previous works, along these lines, by the author for multibody systems and continuous media. The approach consists in formulating a constrained optimization problem that simultaneously leads to the inverse and direct dynamical models, thereby exhibiting the links between both models. The Stewart-Gough platform appears as a consequence of algebra, a specific example not limiting the generality of the method.