Parametric kinematic tolerance analysis of general planar systems

We present an algorithm for functional kinematic tolerance analysis of general planar mechanical systems with parametric tolerances. The algorithm performs worst-case analysis of systems of curved parts with contact changes, including open and closed kinematic chains. It computes quantitative variations and helps designers detect qualitative variations, such as blocking and under-cutting. The algorithm constructs a variation model for each interacting pair of parts: a mapping from the part tolerances and configurations to the kinematic variation of the pair. These models generalize the configuration space representation of nominal kinematics to toleranced parts. They are composed via sensitivity analysis and linear programming to derive the system variation at a given configuration. The variation relative to the nominal system function is computed by sampling the system variation. We demonstrate the algorithm on detailed parametric models of a movie camera film advance and of a micro-mechanical gear discriminator.