Articles | Volume 8, issue 1
Research article
12 Apr 2017
Research article |  | 12 Apr 2017

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

Chin-Hsing Kuo, Jyun-Wei Su, and Lin-Chi Wu

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.

Short summary
This paper investigates a special cube-connected toy that can be reconfigured into several different structures by hand operation. The reconfiguration of the toy is formulated by using an exclusive mathematic modeling through which the physical reconfiguration of the toy can be expressed and manipulated in an algebraic consideration. This research is an example of how mathematics can be applied to study the reconfiguration of mechanisms and mechanical structures.