Title: Fixturing model and analysis

Authors: Cai-Hua Xiong, Yiming Kevin Rong, Yong Tang, You-Lun Xiong

Addresses: School of Mechanical Science and Engineering, National Key Lab of Digital Manufacturing, Huazhong University of Science and Technology, Wuhan 430074, PR China. ' Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, USA. ' School of Mechanical Engineering, South China University of Technology, Guangzhou 510641, PR China. ' School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China

Abstract: It is one of the fundamental issues in fixture automation design and planning to evaluate and control the influence of the geometric tolerances of locators on the locating errors of the workpiece. In this paper, a mapping model between the error space of locators and the workpiece locating error space is built up. Given the geometrical tolerance specification of a key feature on a workpiece, the geometry design requirements can be determined for all of the locators by using the model. On the other hand, given the geometric tolerances of locators, the calculating methods of the locating errors of the workpiece are developed for the deterministic localisation, over deterministic localisation and under deterministic localisation cases by using the mapping model. In the analysis of the locator and clamp configuration characteristics, the free motion cone, which is used to judge whether the workpiece is accessible to the fixture as well as detachable from the fixture, is defined. According to the duality theory in convex analysis, the polar of the free motion cone, namely the constrained cone, is derived. By using the constrained cone, the positions of clamps and the feasible clamping domain are determined, where the workpiece is fully constrained. The fixturing analysis models discussed in this paper are verified by several examples.

Keywords: fixture design; fixture planning; fixturing tolerance; locating errors; free motion cone; constrained cone; accessibility; detachability; form closure; fixturing modelling.

DOI: 10.1504/IJCAT.2007.012329

International Journal of Computer Applications in Technology, 2007 Vol.28 No.1, pp.34 - 45

Published online: 06 Feb 2007 *

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