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.