Redundancy Analysis of 3D Assembly Geometric Constraint System

Abstract

Due to the inherent drawback of graph-based structural decomposition method which can only detect structural redundant constraints, it is pointed out that the graph-based structural decomposition method must be integrated with redundancy analysis to obtain the correct decomposition result. Firstly, the theoretical basis of redundancy analysis of the geometric constraint system is discussed with the algebraic geometry. Then, the relationship between the rank of Jacobian matrix and redundant constraints is revealed. Based on a comprehensively comparative analysis of several typical method for detecting redundant constraints, a hybrid algorithm is proposed to determine the redundant constraints in 3D assembly geometric constraint system, which can avoid the incorrect determination of redundant constraints and maximize the computational efficiency. The proposed method has been implemented in a 3D geometric constraint solver called CBA3D, and an example has been given to validate its correctness and effectiveness.