Efficient dynamic simulation of a single closed chain manipulator

An efficient serial algorithm for the dynamic simulation of a single closed chain is developed. The algorithm is valid for a manipulator with any number of degrees of freedom, N, and it is still applicable when the manipulator is in a singular position. A moving base may also be incorporated into the system. Arbitrary joints are allowed, including multiple-degree-of-freedom joints, and a general contact model is used. The operational space inertia matrix of the chain is used to solve for the unknown contact force vector at the tip, which is then used in the solution for the closed chain joint accelerations. The final solution requires only an additional n_c×n_c matrix inverse for the closed chain part, where n_c is the number of degrees of constraint at the manipulator tip. The computational complexity of the algorithm is (ON³). The reduction of the order of computation complexity of O(N) is briefly discussed