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.

A Newton-Euler formalism is derived for geometrically exact Cosserat beam theory in a purely deductive manner, thanks to an analogy with optimal control theory. The method relies upon a joint use of Gauss least constraint principle, Appell's equations and optimal control theory, that was used in a previous work for the classical case of discrete Newton-Euler backward and forward recursions for multibody systems. Motivating applications are hyper-redundant manipulators or biomimetic robots such as eel-robots, undergoing large displacements

In this work we consider the problem of joint trajectory control with oscillations cancelling for planar multilink flexible manipulators. We extend a method due to Benosman et al. (2001) for the rest to rest motion problem. The scheme based on backward integration of the elastic dynamics, starting from a rest position of the flexible arms, is used here to solve the joint trajectory tracking problem. For slow joint motion, the obtained nominal elastic trajectory is used to compute a causal nominal feedforward torque permitting, together with a simple joint feedback term, to track the desired motion and damp out any residual tip-vibrations. For fast joint motion, the causal controller fails to solve the tracking problem: a noncausal feedforward torque is then designed to preset the elastic coordinates of the system, so that the causal control is able to drive the arm along the desired trajectory. The final position is then reached without end-effector residual oscillations. These results hold without considering any internal elastic damping effect. The scheme is validated through numerical and experimental results obtained on a two-links flexible planar arm.