Metamorphic Equation of Variable Topology Mechanisms Based on the Constraint function

Abstract

Metamorphic mechanism has variable topology and possess multiple stable configurations.In order to represent its topological constraint and configuration transformation effectively and accurately,a set of mathematic parameters and equations is studied.The constraint function is defined according to the constraint features of kinematic joints.With constraint functions as elements,the adjacent matrix of the origin kinematic chains of metamorphic mechanism is proposed.Based on the adjacent matrices,metamorphic equations are established correspond to three metamorphic ways of linkages and three metamorphic ways of joints.According to different metamorphic ways,the metamorphic matrices and metamorphic functions are defined.The application example shows that the constraint function and the adjacent matrix can represent variable topology mechanisms conveniently and completely,as well as the metamorphic equations can be used to represent and analyze the configuration transformation of metamorphic mechanisms accurately.The method proposed provides a new way for the representation and analysis of variable topology mechanisms and lays a theoretic foundation on the kinematics and dynamics of metamorphic mechanisms.