Abstract. In design and manufacturing applications, geometric models and multi-body dynamic models are developed independently. After a geometric model is created in a computer-aided design system, it should be translated into the dynamic model manually. This work reports on the geometric constraint confusion to unify the geometric and dynamic models. We use the Euler parameter to represent the geometric entity and constraint to unify the geometric and dynamic model representations. When the geometric model is assembled in a design system, it would be translated into the dynamic model automatically, and we also get the differential algebraic equations (DAE) automatically.