Solving 3D Geometric Constraints for Closed-Loop Assemblies

Abstract

In the design activity, part geometry is assembled together to create an assembly model. The number of parts may range from a few tens to a few millions and typically the relationship among them constructs a closed-loop with under-constrained state in a constraint graph. In this paper, we propose a 3D constraint solving method for closed-loop assemblies with under-constrained states. The proposed constraint solving process consists of two steps: 1) cut operation, 2) paste operation. In the cut operation, the closed-loop constraint graph is first converted into an open kinematic chain by removing a “cut” constraint from the closed-loop constraint graph and determining kinematic joints from the assembly constraints. Then, an initial kinematic configuration satisfying all the assembly constraints of the open chain graph is computed algebraically. In the paste operation, an assembly configuration of the closed-loop assembly is determined by numerically computing a kinematic configurati