Authors: Xiaobo Peng Kunwoo Lee Liping Chen
Publish Date: 2005/08/10
Volume: 28, Issue: 5-6, Pages: 561-570
Abstract
In this paper we propose a geometric constraint solver for 3D 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 underconstrained systems efficiently The basic idea of this method is that it first simplifies the constraint graph by pruning those vertices which have only inarcs from the graph and then reduces the size of strongly connected components SCCs left in the graph by DOFbased analysis The method can solve all kinds of configurations including closedloops After that we apply a hybrid numerical method of Newton–Raphson and Homotopy to solve underconstrained 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
Keywords: