Geometric reasoning in the analysis of assemblies and mechanisms

This work proposes Divide-and-Conquer techniques applied to local Geometric Constraint Satisfaction or Scene Feasibility (GCS/SF) subproblems to identify strongly constrained clusters of geometric entities. Cluster identification can be related to identifying short cycles in the Spatial Constraint graph for the GCS/SF problem. Their preprocessing uses the aforementioned Algebraic Geometry and Group theoretical techniques on the local GCS/SF problems that correspond to these cycles. Besides improving the efficiency of the solution approach, the Divide-and-Conquer techniques capture the physical essence of the problem. This is illustrated by applying tbe discussed techniques to the analysis of the degrees ot freedom of mechanisms.