Metamorphic techniques and geometric reconfiguration principles

This paper proposes a geometric way to generate metamorphic configurations and investigates metamorphic principles based on geometrized displacement group. Metamorphic reconfiguration techniques are revealed as variations of kinematic joints, kinematic links and geometric orientation constraints specifically by examining invariant configuration properties of a mechanism. The nature of all these configuration changes belongs to geometric constraint category. Metamorphic configuration units are proposed as the simplest configuration modules to envelop these reconfiguration techniques. It can self-reconfigure or be combined to generate metamorphosis. Moreover, the geometrized displacement group is lent to achieve a geometric representation for configuration modelling and further reconfiguration operations. Based on kinematic group extended qualitatively according to its group structure, the geometrized displacement group modelling is proposed for these identified metamorphic configuration units. The investigated group motion-set is an integration of its displacement group properties and kinematic extensions. The defined geometric constraint relations and the proposed dependent rules lead to metamorphic principles. In this way, the metamorphic process is mapped to matrix operations under group extension' s compositions. Design examples and a metamorphic joint are given to illustrate the feasibility of these metamorphic principles.