Research Papers

Error Modeling of a Parallel Wedge Precision Positioning Stage

[+] Author and Article Information
Qiang Zeng

e-mail: qiangzengnu@gmail.com

Kornel F. Ehmann

Department of Mechanical Engineering,
Northwestern University,
2145 Sheridan Road,
Evanston, IL 60208-3111

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received May 31, 2012; final manuscript received August 29, 2012; published online November 1, 2012. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 134(6), 061005 (Nov 01, 2012) (14 pages) doi:10.1115/1.4007640 History: Received May 31, 2011; Revised August 29, 2012

The parallel wedge precision positioning stage (PW-PPS) presents a novel configuration of a parallel mechanism for precision positioning applications. Based on its specific parallel configuration, the corresponding inverse and forward kinematic models were developed and used to formulate the volumetric error model of the mechanism. The error model that considers the influence of manufacturing errors is built in two steps. In the first, the structural parameter-induced errors associated with the PW-PPS's structural parameters and input variables were considered, while in the second, the joint clearance-induced errors produced by joint clearances were taken into account. The structural parameter-induced errors were modeled based on complete differential-coefficient theory, while the joint clearance-induced errors due to joint clearances were modeled based on the virtual work and deterministic method. In the latter case, the kinetostatic model and joint error contact modes were analyzed to build a joint clearance-induced error model. The relationship between the different error sources and the output pose error of the mechanism's moving platform was obtained. Finally, considering practical values for the mechanism's parameters and errors, the error distribution in the PW-PPS's workspace was evaluated to determine the distributive rules of the various error components.

Copyright © 2012 by ASME
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Fig. 2

Structural parameters of the PW-PPS

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Fig. 1

Structure of the PW-PPS

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Fig. 3

Forces and moments applied on the moving platform

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Fig. 4

Contact modes of a prismatic joint with nominal clearance (ηxij = ηyij = 1)

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Fig. 5

Contact modes of a planar joint with nominal clearance (ηij = 1)

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Fig. 10

Error distribution of the error components in section z = 130 mm

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Fig. 6

Flow chart of error modeling

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Fig. 7

Workspace of the PW-PPS

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Fig. 9

Error distribution in section (a) z = 130 mm and (b) z = 180 mm

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Fig. 8

Equi-error distribution of ‖ΔE‖




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