Generation of rotation matrix for assembly models with arbitrary angle constraints

Assembly modeling, which is established by geometric constraints, plays an important role in product design. However, most constraint solving methods are only applicable for the cases in which the orientation constraints between base and mating component are either fit or against. This paper presents a modified geometric constraint solving method. It allows arbitrary angles for the orientation constraints and implements them into rotation matrix that determines the relative orientation of a mating component to a base component. The method transforms the constraints to a set of nonlinear equations firstly, and then solves it algebraically instead of using numerical methods.