Multiple-Mode Closed 7-Link Chains Based on Overconstrained 4-Link Mechanisms

This article completes the algebraic analysis of multiple-mode 7-link chains based on the concatenation of two overconstrained 4-link mechanisms with only revolute and prismatic joints, i.e. the Bennett or the overconstrained RPRP mechanisms. Both initial mechanisms are locked in one pose of their one parameter motion. Then they are transformed to a position where one joint coincides and all the links of the basic 4-link mechanisms are deleted. New links that can be arbitrarily inserted between the seven joints. The only possible types of mechanisms in this manner are the 7R, the 5R2P and the 4R3P mechanisms. Those chains have the property, that they can fulfill an arbitrary one parameter motion of the 7-link chain and, additionally, both sub-motions of the basic 4-link chains. In special configurations it is possible to switch between the modes without the need of disconnecting and reassembling. Here an algebraic approach to those mechanisms is presented that gives the opportunity to identify the motion and the transitional configurations exactly. In all of the analyzed types of mechanisms such transition configurations exist.