A geometric constraint solver for 3-D assembly modeling

In this paper, we propose a geometric constraint solver for 3-D assembly applications. First, we give a new geometry and constraint expression based on Euler parameters, which can avoid singular points during the solving process and simplify constraint types. Then we present a directed graph based constructive method to geometric constraint system solving that can handle well-, over- and under-constrained systems efficiently. The basic idea of this method is that it first simplifies the constraint graph by pruning those vertices which have only in-arcs from the graph and then reduces the size of strongly connected components (SCCs) left in the graph by DOF-based analysis. The method can solve all kinds of configurations including closed-loops. After that, we apply a hybrid numerical method of Newton-Raphson and Homotopy to solve under-constrained systems. The hybrid method makes use of the high efficiency of the Newton-Raphson method as well as the outstanding convergence of the Homotopy method. Finally, we give a practical example and conclusion.