O(N) forward dynamics computation of open kinematic chains based on the principle of virtual work

This paper describes an efficient algorithm for the forward dynamics of open kinematic chains with O(N) complexity, where N is the number of links in the chain. The method is based on the principle of virtual work and does not use any theory in linear algebra or the concept of articulated body inertia. The idea of this method is to add a link one by one from the leaflinks to the root evaluating the constraint force at each new joint. The algorithm consists of two iterative procedures: from the leaflinks to the root to compute the constraint forces, and from the root to the leaf to compute the joint accelerations. Some numerical examples show the efficiency of the proposed algorithm. Similarity and differences with other O(N) algorithms are also discussed.