Fundamental reconfiguration theory of chain-type modular reconfigurable mechanisms

• The geometric character of module is well described via the Clifford algebra.
• Motion sequence which is a new concept is proposed to describe the discrete motion.
• Isomorphism is identified through the Burnside's Lemma and adjacency matrix.
• Interference detection algorithm is put forward to select rational motion sequence.
• The reconfiguration theory of modular reconfigurable mechanism is proposed.

This article focuses on the study of geometry constraints, motion sequence, isomorphism and interference issues of the chain-type modular reconfigurable mechanisms. The geometry representation of module is accomplished by employing the Clifford algebra. A new expression of discrete movement—“motion sequence” which is combined with exponential formula for kinematics is proposed to calculate the position and orientation of each module. Meanwhile, isomorphism is identified by using the adjacency matrix. Furthermore, an interference detection algorithm on the basis of Clifford algebra is investigated for interference detection during the movement. Finally, the principle of reconfiguration of modular mechanisms is presented in detail. Case studies are demonstrated to verify the validity and the effectiveness of our fundamental reconfiguration theory to analyze modular reconfigurable systems.