三维装配约束推理的球面几何和球面机构法

Assembly Constraint Solving with Spherical Geometry and Spherical Linkage Mechanism

分析了装配姿态约束和位置约束的可解耦性,提出求解姿态约束的球面几何和球面机构法.将姿态约束的组合分为可操作和不可操作的情形,可操作的情形利用简单的球平面中平移、旋转和刚性变换推理,快速地判定冗余约束和求解约束;不可操作的情形利用球面四杆机构求解.该方法具有很强的几何解释性和可操作性,降低求解复杂度.该方法在自主研发的CAD浏览器系统InteVue中实现.

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 them 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 there 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 underconstrained and well-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.