A method for the identification of the connectivity in multi-loop kinematic chains: Analysis of chains with total and partial mobility

In this paper, a new algorithm for the computation of the connectivity in kinematic chains having total and partial mobility is presented. The adopted algorithm, based on graph theory, is able, firstly, to recognize when a kinematic chain has partial mobility and, then, to find the corresponding connectivity matrix. The new strategy consists in a recursive procedure, called “circuits gradual freezing”, which detects the sets of independent loops for each grade of recursion, and assigns to each pair of vertices the weighted distance. Results have shown the feasibility of the new approach and its better performance in some difficult cases.