Study Of Common Expression And Decoupling Of3D Geometric Constraints System

The research on3D geometric constraint solving has great significance for assembly modeling, assembly process planning and concurrent engineering. Although there have been a lot of literature about solution to geometric constraint systems in the past decades, still many issues remain to be resolved, especially in the field of solution to three-dimensional geometric constraint. This paper investigated the key problems in modeling, analyzing, decomposing and solving this system, and put forward a model signifying the three-dimensional entity with an abstract ball, box and ball-box body,It also explored the highly efficient solution to decoupled property, constructed a unified theory and system of three-dimensional geometric constraint solution which provides a theory basis.In the system of geometric constraint, constraints between geometric entities are very complex. How to establish an effective system model of geometric constraint is the basis of geometric constraint system study. First, this paper studies the problem of geometric constraint system modeling. On the basis of geometric constraint Euler parameters, employing E. J. Haug's simple and unified constraint expression, it studied the common characteristics between geometric constraints and geometric entities and put forward a model signifying the three-dimensional entity with an abstract sphere, box and ball box. It constructed a geometric constraint system model and formulated a system layer.It is likely that freedom degree and constraint form of the points in a three-dimensional geometric constraint system may vary. Therefore, efficient decomposition strategy and applicable solution are needed. Because of the decoupled property of three-dimensional orientation and position constraints, a method based on spherical geometry can be used, thus a single constraint is mapped into a point of the sphere. Then by constructing a coordinate system of ball flat, spherical points on the plane can be mapped into two-dimensional point, and three-dimensional problem into a two-dimensional problem. This reduces reduce the difficulty in solving and has an obvious significance of geometric reasoning. Solution to location constraint employs analytical methods.With relevant knowledge of three-dimensional geometric and the analysis of the inherent equivalence of geometric constraint systems, by combining with graph theory, this paper put forward the equivalence analysis method of three-dimensional geometric constraint system. This method optimized the topological structure of geometric constraint graph. It removed, reduced and separated the constrained closed-loop without considering the redundant constraints in the system, as well as dealt with over-constrainted, well-constrained, and under-constrainted, realizing the maximum geometric decomposition of the three-dimensional geometric constraint system.The research in this paper can be done in the prototypical system of WhutVAS, verifying the feasibility and effectiveness with practice.