Parametric kinematic tolerance analysis of general planar systems

Abstract

We present an algorithm for functional kinematic Lolerance 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 vari<ttions, such as blocking and undercutting. The algorithm constructs a variation model for each interacting pair of parts: a mapping [rom 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.

Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces

“…Wirtz [5] introduced the vectorial parameter concept which Gaunet [6] added the TTRS [7] (Technologically and Topologically Related Surfaces) parameters of Clement. Sacks and Joskowicz [8] developed a method for mobile planar mechanisms. The Jacobian Torsor of Desrochers and Laperriere [9] is a kinematic model associated to an interval method.…”

Semantic Tolerance Modeling With Generalized Intervals

“…Tolerance zone is also represented in mean-variance (μ-σ 2 ) space for analysis [10] and synthesis [11]. In kinematic approaches, geometrical variation and displacement are modeled by unified vectors and matrices [12,13,14], kinematic links in Euclidean space [15,16] and configuration space [17]. The kinematic methods distinguish size tolerances and each type of geometric tolerances.…”

Closed-Loop Analysis in Semantic Tolerance Modeling

“…Chase et al [1,19,20] performed analysis of assemblies with tolerance vectors and small kinematic adjustments with linear approximations of implicit geometric constraints. Sacks and Joskowicz [21] analyzed 2D kinematic tolerances of assemblies with contact changes by the aid of contact constraints. Zou and Morse [22] proposed a fitting condition test method based on geometric constraints of gap closure between components.…”