AUTOMATIC DEVELOPMENT OF CONTRACTED GRAPHS FOR KINEMATIC CHAINS WITH SIMPLE JOINTS

This paper presents an algorithm for the automatic development of acceptable contracted graphs for basic kinematic chains with simple joints. First, contracted graphs with L independent loops are synthesized from those with L - 1 independent loops by the operation of loop augmentation. Next, a single value method is proposed to identify isomorphic contracted graphs efficiently. Then, a general formula for the determination of minimum degrees-of-freedom is derived to construct catalogs of acceptable contracted graphs. Finally, an interactive graphics-based algorithm is developed for the automatic sketching of acceptable contracted graphs with minimum crossing-edges. As a result, the number of acceptable contracted graphs for basic kinematic chains with simple joints up to 6 independent loops is listed.