Assembly Constraint Solving with Spherical Geometry and Spherical Linkage Mechanism

The decoupling feasibility of orientation and position constraints is analyzed and a new algorithm based on spherical geometry and spherical linkage mechanism to solve orientation constraints is presented.The approach maps orientation constraints in 3D Euclidean space onto 2D sphere plane and manipulates the geometric entities with translation,rotation and rigid transformation in the sphere plane space. Various combinations of orientation constraints can be separated into operable and non-operable cases,making the m to be solvable by employing the sphere plane space reasoning and spherical linkage mechanism,respectively.It is easy and efficient to determine whether the case is solvable or not,and whether the re are inconsistent and consistent redundant constraints or not.Finally,the rotation transformation matrix of the rigid body can be obtained from the translation,rotation and rigid transformation of sphere plane.In comparison to numerical and symbolic methods,this new approach not only has obvious geometric clearness and operability,but also improves the solving efficiency remarkably.This method can be applied to under-constrained and wel-l constrained system;in addition,it can detect redundant constraints for over-constrained system. The method has been implemented in our prototype system InteVue-a CAD browsing system.