Geometric Constraint Solving With Trajectory Linkage

Computer Aided Design system introduces Geometric Constraint Solving in order to be intelligent, which becomes a important kind of technology. However, Geometric Constraint Solving based on graph theory need to be improved when solving complex constraints.Meanwhile, we usually solve basic constructions that contain four more rigid bodies with the method based on numerical analysis instead of graph theory. This paper improves the simplification method for Geometric Constraint Solving based on graph theory,including simplification of geometric entities, geometric constraints and parts of constraint graph, which broadens the solution scope. In addition, this paper proposes the conception of Trajectory Linkage to solve more complex problem, and describe its solution scope and how to find rigid body with it. Then, this paper proposes a way to solve all kinds of problem that contains 3 rigid body with four-bar linkage and trajectory linkage, and show some cases which that contains 4 more rigid body with that. We also take bigraph-like and eight-bar less1-degree-of freedom constraints as examples.For 4 more complex problem, we introduce Complex Trajectory Linkage to solve, such as constraints which contains four rigid body, and 5 rigid body with Trajectory Linkage and four-bar linkage. Furthermore, we analyze some problem in parameterization and intelligence,and find that Complex Trajectory Linkage solves multi-solutions problem and over-constraint or parameter problem well. Last, with linkage、Trajectory Linkage and Complex Trajectory Linkage, this paper build a system to solve Geometric Constraint that could not be solved by reduction and decomposition only, which proves that this method can be used to solve Geometric Constraint problems.