An Algebraic Formulation for the Configuration Transformation of a Class of Reconfigurable Cube Mechanisms

Abstract. This paper presents an algebraic strategy for formulating the configuration transformation of a special class of reconfigurable cube mechanism (RCM) made by 2³ cyclically connected sub-cubes. The RCM studied here is kinematically equivalent to a spatial eight-bar linkage having eight transformable configurations. In this paper, the reconfiguration characteristics of the RCM are figured out first. Then, the initial configuration of the RCM is described by a joint-screw matrix, from which all the consecutive joint-screw matrices that represent the configuration transformation of the RCM can be derived. An illustrative example is provided to determine the eight joint-screw matrices of an RCM at an initial configuration. This reconfiguration formulation is further applied to enumerate all feasible topological configurations of such a special reconfigurable mechanism. The results show that, for such a special kind of reconfigurable cube mechanisms, there is only one feasible initial topological configuration for the RCM to perform a complete cycle of reconfiguration.