The structure of kinematic chains which contain links of maximum degree

Abstract This paper is concerned with the structure of planar kinematic chains which have total freedom, and which at the same time contain at least one link carrying the maximum possible number, p, of joints consistent with the requirements of total freedom. Using elementary concepts of graph theory this paper shows that a kinematic chain may contain up to two links of degree p; when one such link is present the kinematic chain can have total freedom only if M ⩽ 2, whereas when two such links are present it can have total freedom if M ⩽ 3.