装配位置约束建模及求解

Modeling and Solving of Assembly Position Constraints

以基本几何约束组合统一表达装配约束,为提高求解效率,研究了姿态约束和位置约束的可解耦情况下位置约束的解析求解.将基本位置约束映射为移动空间并以参数方程表达,通过移动空间的增量解析求交,满足约束;在姿态约束和位置约束的不可解耦情况,联立基本约束进行整体数值法求解.文中方法保持了基本约束表达的独立性,适合于欠约束系统和完整约束系统.

Assembly constraints can generally be represented with combinations of basic geometric constraints. In order to improve solving efficiency, analytical solutions to position constraints are investigated for those cases that orientation and position constraints can be decoupled. The basic position constraints are mapped to the translation spaces that are denoted by parametric equations. The incremental translation space intersection method is employed to obtain the solutions satisfying design intention. When orientation and position constraints are coupled, numerical iteration methods are employed to solve simultaneously all the equations. This approach keeps the independency of the basic constraint expressions, and is beneficial to modeling and management of constraints of geometric constraint systems. The approach has been implemented in a prototype system named CBA and is shown suitable for under-constrained and well-constrained systems.