On Some Intrinsic Features of the Dynamics of Mechanisms

Using Lie group theory, we propose to analyse the dynamics of closed mechanisms without introducing frames or bases. After a brief presentation of the mathmatical tools, the kinematics of closed mechanisms is devolopped and the manifold of configurations described. It is then possible to obtain the dynamic equations by using the principle of virtual power. An intrinsic Lagrange’s multiplier A is introduced to take the closure equation into account. Explicit linear combinations for the elimination of A are given too. Last, some kinematic relations are given which are usefull for linearisation or for numerical integration.