Invariant Link Rotatability of N-Bar Kinematic Chains

This paper proposes and proves the concept of invariant link rotatability between any two links, adjoined or not, in planar single-loop kinematic chains. It was found that in any planar single-loop chain formed by a set of links and revolute joints, the rotatability between any two links, whether they are adjoined or not, is independent of the order of connection. Simple and general approaches were also proposed to identify the exact rotatability between any two links of a single-loop N-bar chain. When a nonrevolvable link reaches the limit orientation with respect to another nonrevolvable link, disregard whether they are adjoined or not, all other links become collinear or parallel to each other. This paper fully extends Ting’s rotatability laws to deal with the rotatability between nonadjoined links.