Quadratic Sensitivity Analysis of Fixtures and Locating Schemes for Rigid Parts

Abstract

The main purpose of locating schemes are to position parts. The locating scheme utilizes tooling elements, referred to as locators, to introduce geometric constraints. A rigid part is uniquely positioned when it is brought into contact with the locators. By using kinematic analysis we derive a quadratic sensitivity equation that relates position error in locators with the resulting displacement of the part held by the locating scheme. The sensitivity equation which depends on the locator positions and the workpiece geometry around the contact points can be used for locating scheme evaluation, robust fixture design, tolerancing and diagnosis. The quadratic sensitivity equation derived in this paper is novel by adequate dealing with locator contact at nonprismatic surfaces, nonsmall errors, locator error interaction effects and locator errors in arbitrary directions. Theory for comparing the relative gain in precision by using the quadratic sensitivity equation instead of the linear is developed. The practical relevance of the quadratic sensitivity equation is tested through numerical experiments.