Solving 3D geometric constraints for assembly modelling

A geometric constraint solving method is presented that takes well-constrained mating conditions between a base and a mating component and directly transforms them into a 4x4 matrix that determines the relative orientation and location of the mating component with respect to the base component. In the proposed procedure, the 4x4 transformation matrix is determined by directly computing a rotation matrix T-R and a translation matrix T-L that define the relative orientation and location of the mating component, respectively. Thus, first, the rotation matrix is computed by solving a set of linens constraint equations associated with the orientation of two mating components. After repositioning the mating component by applying the rotation matrix T-R, the translation matrix is calculated by solving a set of linear constraint equations associated with location. This new method is computationally very effective, since the transformation matrix for relative orientation and location of the mating component is algebraically derived directly from the linear equations associated with the mating conditions.