Dynamics computation of closed-link robot mechanisms with nonredundant and redundant actuators

The authors discuss a general and systematic computational scheme of the inverse dynamics of closed-link mechanisms. It is derived by using d´Alembert´s principle and obtained without computing the Lagrange Multipliers. To account for the constraints, only the Jacobian matrix of the passive joint angles in terms of actuated ones is required. Given a nonredundant actuator system, this allows a unique representation of the constraints even for complicated multiloop closed-link mechanisms. The inverse dynamics of closed-link mechanisms that contain redundant actuators and their redundancy optimization are also discussed. For a redundant actuation system that contains N_r redundant actuators, the passive joint angles are represented by N _r+1 independent ways as functions of actuated joints. Using their Jacobian matrices, the actuation redundancy of a closed-link mechanism is parameterized by an N_r-dimensional arbitrary vector in a linear equation. Numerical examples are given to show the computational efficiency of inverse dynamics computation and the potential of closed-link manipulators with actuation redundancy