Modeling and Solving of Assembly Position Constraints

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 wel-l constrained systems.