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Research Papers

A Unified Approach to Kinematic and Tolerance Analysis of Locating Fixtures

[+] Author and Article Information
Antonio Armillotta, Giovanni Moroni, Quirico Semeraro

Dipartimento di Meccanica, Politecnico di Milano, Via La Masa 1, 20156 Milano, Italy

Wilma Polini

Dipartimento di Ingegneria Industriale, Università degli Studi di Cassino, Via Di Biasio 43, 03043 Cassino (FR), Italy

J. Comput. Inf. Sci. Eng 10(2), 021009 (Jun 08, 2010) (11 pages) doi:10.1115/1.3402642 History: Received February 26, 2008; Revised March 11, 2010; Published June 08, 2010; Online June 08, 2010

A workholding fixture should ensure a stable and precise positioning of the workpiece with respect to the machine tool. This requirement is even more important when modular fixtures are used for the sake of efficiency and reconfigurability. They include standard locating elements, which set the part in a predefined spatial orientation by contacting its datum surfaces. In the computer-based design of a fixture, the layout of locators must be tested against two main sources of problems. Kinematic analysis verifies that any relative motion between the part and the worktable is constrained. Tolerance analysis evaluates the robustness of part orientation with respect to manufacturing errors on datum surfaces. We propose a method to carry out both tests through a common set of geometric parameters of the fixture configuration. These derive from the singular value decomposition of the matrix that represents positioning constraints in screw coordinates. For a poorly designed fixture, the decomposition allows us to find out either unconstrained degrees of freedom of the part or a possible violation of tolerance specifications on machined features due to geometric errors on datum surfaces. In such cases, the analysis provides suggestions to plan the needed corrections to the locating scheme. This paper describes the procedure for kinematic and tolerance analysis and demonstrates its significance on a sample case of fixture design.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

Point contacts kinematically equivalent to line and plane contacts

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Figure 3

Examples of planar locating schemes

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Figure 4

Examples of three-dimensional locating schemes

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Figure 5

Quasi-singular locating conditions

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Figure 6

Reference problem in the plane

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Figure 7

Geometric transformation between machine tool and functional gage

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Figure 8

Transformation based on locator displacement

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Figure 9

Error control regions at different position tolerances

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Figure 10

Influence of locator layout on error control region

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Figure 11

Relationship between area of error control region and quasi-singularity index

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Problem with angular secondary datum

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Problem with locators acting on different surfaces

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Figure 14

Effect of the quasi-singularity index for random fixture configurations

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Figure 15

Locating fixtures for a clutch bracket

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Tolerances on the clutch bracket

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Figure 17

Estimated positioning errors for different locating schemes on the clutch bracket

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Figure 1

Types of modular locating elements

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