This paper introduces a new, visualized approach for including all the geometric feature variations in the tolerance analysis of mechanical assemblies. It focuses on how to characterize geometric feature variations in vector-loop-based assembly tolerance models. The characterization will be used to help combine the effects of all variations within an assembly in order to perform tolerance analysis of mechanical assemblies by employing commercial 3D kinematic software (e.g. ADAMS). Equivalent variational modeling, based on TAKS method, has been developed for modeling variations in 3D mechanical assemblies. Create a library of Equivalent Variational Joints (EVJs) to allow inclusion all kinds of variations in analysis, and allow the kinematic model to include both geometric and dimensional variation in a velocity analysis. EVJ, for use in tolerance analysis, was developed for commonly used 3D kinematic joint types, and was implemented with examples to explain their use to form Equivalent Variational Mechanisms (EVMs).