Virtual Chain Approach for Mobility Analysis of Multiloop Deployable Mechanisms

Abstract

In this paper, we present a virtual chain approach for the mobility analysis of multiloop deployable mechanisms. First, the relative motion of the links of singleloop units in multiloop mechanisms are analyzed using the equivalent motion of certain types of openloop virtual kinematic chains; these kinematic chains comprise some types of joints connected in series by flexible links. This reveals that the links in these virtual chains are not rigid when the mechanism is moving. The parameters of these virtual kinematic chains (such as the link length, the twist angle of two adjacent revolute joint axes, and so on) are variable. By using this approach that involves equivalent kinematic chains, the multiloop mechanisms can be considered equivalent to singleloop mechanisms with flexible links; the closure equations of such multiloop mechanisms can also be derived. The analytical procedures are explained using examples of multiloop mechanisms in which Myard mechanisms as used as the basic singleloop units. A prototype is also fabricated to demonstrate the feasibility of the proposed multiloop mechanism. The proposed method yields a more intuitive and straightforward insight into the mobility of complicated multiloop mechanisms.