An automatic method for the connectivity calculation in planar closed kinematic chains

In the initial stage of the creative design of some specific mechanisms such as the parallel manipulator, the connectivity between the base and the end-effector must satisfy the requirement. This paper proposes a new method for the connectivity calculation between two links, based on which an automatic method to acquire the connectivity matrix for planar closed kinematic chains is developed with the aid of C++ programming language. The method has several advantageous features resulting in lower complexity relative to the methods presented in the literature. The whole process to compute connectivity matrix using Floyd-Warshall algorithm, depth-first search (DFS) algorithm and the subchain mobility superposition algorithm is presented and the planar kinematic chains with up to 6 independent loops, together with the ones found in literature, are illustrated to show the validity and efficiency of the method. This method can build a convenient bridge to automatically generate the mechanisms, whose base and end-effector have the required connectivity, from the synthesized kinematic chains.