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Development and verification of six-degree-of-freedom error measurement system based on geometrical optics for linear stage

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Abstract

In this paper, a six-degree-of-freedom (6DOF) error measurement system based on geometric optics is proposed for linear stages. This measurement system uses an additional linear stage that drags the sensor onto the stage so that the light spot projected on the sensor moves back and forth with the moving stage. This method achieves long-range 6DOF measurement. Compared with commercial laser interferometers, the proposed measurement system has the advantages of a lower cost, a simpler structure, and the capability of measuring 6DOF errors simultaneously. Zemax software was used to simulate the relationships between the 6DOF errors and the values of position-sensitive detectors. MATLAB software was then used to construct the forward and inverse mathematical kinematic models of the optical paths and simplify the models through curve fitting. Finally, to address installation and manufacturing errors, a reverse kinematic mathematical solution was obtained through the use of a six-axis Stewart platform. The proposed measurement system was experimentally implemented on a commercial linear stage to measure the 6DOF errors and verified against results obtained with a commercial interferometer and electronic level.

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Funding

The authors gratefully acknowledge the financial support provided to this study by the Ministry of Science and Technology of Taiwan under Grant Nos. MOST 106–2628-E-006–010-MY3 and 110–2221-E-006–126-MY3.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Cheng Kung University, No. 1, University Road, Tainan City, 70101, Taiwan

    Wei-Che Tai & Chien-Sheng Liu

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  1. Wei-Che Tai
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  2. Chien-Sheng Liu
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Contributions

Wei-Che Tai was involved in writing—original draft preparation, conceptualization, methodology, software, validation. Chien-Sheng Liu helped in writing—reviewing and editing, supervision, project administration.

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Correspondence to Chien-Sheng Liu.

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Tai, WC., Liu, CS. Development and verification of six-degree-of-freedom error measurement system based on geometrical optics for linear stage. Int J Adv Manuf Technol 119, 3903–3916 (2022). https://doi.org/10.1007/s00170-022-08650-1

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  • DOI: https://doi.org/10.1007/s00170-022-08650-1

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