Complete kinematic analysis of single-loop multiple-mode 7-link mechanisms based on Bennett and overconstrained RPRP mechanisms

In this paper we analyze one degree-of-freedom (DOF) single-loop multiple-mode 7-link mechanisms based on the concatenation of two overconstrained 4-link spatial mechanisms with only revolute and prismatic joints, i.e., the Bennett and the overconstrained RPRP mechanisms. Both initial mechanisms are locked in one configuration of their one parameter motion and transformed in such a way that two joints, each from one of the initial mechanisms, coincide. Afterwards, all links are removed, and seven new links connecting these seven joints are inserted to construct a single-loop mechanism. The only mechanisms obtained in this manner are the 7R, 5R2P, and 4R3P mechanisms. These mechanisms have the property to inherit both operation modes of the initial 4-link mechanisms and fulfill a general one-parameter motion of the 7-link mechanisms. In special configurations it is possible to switch between the motion modes without disconnecting and reassembling. Unlike previous papers in which numeric approaches were used, an algebraic approach to identify the operation modes and the transitional configurations is presented in this paper. The kinematic analysis of the entire class of multiple-mode 7-link mechanisms is discussed in detail.