Solving 3D Geometric Constraints for a Class of Closed-loop Assemblies

In this paper, we study a class of closed-loop assemblies which can be converted into equivalent ones without loops. The definition of equivalence of geometric constraint graphs is presented and a method converting a closed-loop constraint graph into the equivalent open-loop one is proposed. This method firstly determines whether a closed loop exists in the graph, and utilizes DOF reduction analysis and disturbing method to identify if the closed-loop constraints can be broken from a certain edge. This method simplifies the closed-loop geometric constraint problems in CAD software introduced by the user and reduces the solving complexity. Furthermore, the dissected geometric constraint graph could better represent the assembling procedure.