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TECHNICAL PAPERS

Visibility Analysis for Assembly Fixture Calibration Using Screen Space Transformation

[+] Author and Article Information
Zhenyu Kong

 Dimensional Control Systems, Inc., Troy, MI 48084jkong@3dcs.com

Wenzhen Huang

Department of Industrial Engineering,  University of Wisconsin-Madison, Madison, WI 53706huang@cae.wisc.edu

Dariusz Ceglarek

Department of Industrial Engineering,  University of Wisconsin-Madison, Madison, WI 53706darek@engr.wisc.edu

J. Manuf. Sci. Eng 127(3), 622-634 (Jun 14, 2004) (13 pages) doi:10.1115/1.1947209 History: Received July 23, 2003; Revised June 14, 2004

In a number of manufacturing processes—tooling installation, calibration, and maintenance—guarantee the precision of fixtures and play important roles toward the overall quality of products. Recently, a new type of measurement equipment called a “laser tracker” was developed and utilized for assembly fixture calibration to shorten calibration time and improve the accuracy of the currently used theodolite systems. Though calibration of the assembly fixture is critical for product quality, as such, calibration time creates a significant burden for productivity of multistation assembly processes. In order to shorten calibration lead time, the number of necessary setups, determined by visibility analysis, needs to be minimized. This paper presents a screen space transformation-based visibility analysis that allows minimizing the number of setups. The screen space transformation is applied to transform the visibility problem from three- to two-dimensional space, thus, efficiently solving the visibility problem. A case study illustrates the procedure and verifies the validity of the proposed methodology. This methodology can be applied not only for manufacturing processes, such as in-line fixture calibration, but also toward analysis and optimization of AGVs, robot navigation systems, and building security.

Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Two-head theodolite system

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Figure 2

Application of the laser tracker in large fixture measurement (API Inc.)

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Figure 3

Illustrations of visibility problem for in-line fixture calibration

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Figure 4

Process of the direct visibility algorithm

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Figure 5

Illustration of the view space

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Figure 6

View space and screen space

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Figure 7

Parameters of transformation from view space to screen space

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Figure 8

Procedures of the SST-based visibility algorithm

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Figure 9

Spherical representation of OS

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Figure 10

Setup of local view coordinate system (LVCS) for different MTs

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Figure 11

Transformation from LVCS to WCS

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Figure 12

Parameters for SST in LVCS1

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Figure 13

SST in LVCS1 and LVCS2

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Figure 14

Merged LVCS1 and LVCS2 systems into one WCS system

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Figure 15

Translation of moving the observation positions to coordinate origin

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Figure 16

Visibility map for all the OPs

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Figure 18

Perspective projection of a convex MO from an MT

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Figure 19

Boundary identification of MO

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Figure 20

Modeling of MTs, MOs, and OS

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Figure 21

Simplification of MOs regarding MT1

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Figure 22

Overall visibility map for all OPs

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Figure 23

Visibility maps corresponding to individual OP

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Figure 24

Identification of minimum gap between MOs

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Figure 26

Illustration of obtaining triangle with arbitrary shape from an equilateral triangle

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Figure 27

Logic inference of the sampling interval

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Figure 17

Process of identifying the minimum number of setups for ME

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Figure 25

Sampling interval on 2D plane

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Figure 28

Scenario of the invalid sampling interval

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Figure 29

Determination of the sampling interval

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