Parallelism in planar kinematic chains (manipulators)

Parallelism is an important characteristic of closed kinematic chains particularly for chains with degrees-of-freedom (d.o.f.) greater than one since such chains can be considered for application as robot manipulators. For specified number of links and d.o.f. there exists a large number of distinct chains and hence the designer should have a clue to select the best possible chain for the specified task. In this paper quantitative measures are proposed based on graph theory to know the parallelism present due to (i) link assortment, (ii) joints––their type and number and (iii) loops including sub-chains. Link assortment influences the type of joint and the loop formation can be viewed as the adjacency of joints. Thus, the type and number of joints and their adjacency decide the extent of parallelism and its proof is given.