Geometric Theorems and Application of the DOF Analysis of the Workpiece Based on the Constraint Normal Line

Aiming at the problem of judging the degree of freedom (DOF) of the workpiece in the fixture by experience, it is difficult to adapt to the analysis of the DOF of some singular workpieces. The workpiece and the fixture are used as rigid bodies, and the workpiece is allowed to move in the plane or sp...

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Main Authors: Guojun Luo, Xiaohui Wang, Xianguo Yan
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:Advances in Materials Science and Engineering
Online Access:http://dx.doi.org/10.1155/2021/1014708
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author Guojun Luo
Xiaohui Wang
Xianguo Yan
author_facet Guojun Luo
Xiaohui Wang
Xianguo Yan
author_sort Guojun Luo
collection DOAJ
description Aiming at the problem of judging the degree of freedom (DOF) of the workpiece in the fixture by experience, it is difficult to adapt to the analysis of the DOF of some singular workpieces. The workpiece and the fixture are used as rigid bodies, and the workpiece is allowed to move in the plane or space under the constraints of the fixture positioning point, and a set of geometric theorems for judging the DOF and overconstraint of the workpiece can be derived according to the difference in the position of the instantaneous center of the workpiece speed. The judgment of the DOF and overconstraint of the workpiece is abstracted into rules with universal meaning, which effectively overcomes the limitations of existing methods. The research results show that (1) the DOF and overconstraint of the workpiece in the fixture depend entirely on the number of positioning normal lines of the workpiece and their geometric relationship; (2) the necessary and sufficient condition for limiting the DOF of rotation of the workpiece around a certain axis is that the workpiece has a pair of parallel normal lines in the vertical plane of the axis. Using geometric theorems to judge the DOF of the workpiece is more rigorous, simple, and intuitive, which is convenient for computer-aided judgment and the reasonable layout of the positioning points of the workpiece, which can effectively avoid the misjudgment of the DOF and unnecessary overpositioning when the complex workpiece is combined and positioned on different surfaces. Several examples are used to verify the accuracy of the method and correct unreasonable positioning schemes.
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spelling doaj-art-48bd89754fba4e69a6e2a0d7df1aced62025-08-20T03:36:01ZengWileyAdvances in Materials Science and Engineering1687-84341687-84422021-01-01202110.1155/2021/10147081014708Geometric Theorems and Application of the DOF Analysis of the Workpiece Based on the Constraint Normal LineGuojun Luo0Xiaohui Wang1Xianguo Yan2School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, ChinaSchool of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, ChinaSchool of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, ChinaAiming at the problem of judging the degree of freedom (DOF) of the workpiece in the fixture by experience, it is difficult to adapt to the analysis of the DOF of some singular workpieces. The workpiece and the fixture are used as rigid bodies, and the workpiece is allowed to move in the plane or space under the constraints of the fixture positioning point, and a set of geometric theorems for judging the DOF and overconstraint of the workpiece can be derived according to the difference in the position of the instantaneous center of the workpiece speed. The judgment of the DOF and overconstraint of the workpiece is abstracted into rules with universal meaning, which effectively overcomes the limitations of existing methods. The research results show that (1) the DOF and overconstraint of the workpiece in the fixture depend entirely on the number of positioning normal lines of the workpiece and their geometric relationship; (2) the necessary and sufficient condition for limiting the DOF of rotation of the workpiece around a certain axis is that the workpiece has a pair of parallel normal lines in the vertical plane of the axis. Using geometric theorems to judge the DOF of the workpiece is more rigorous, simple, and intuitive, which is convenient for computer-aided judgment and the reasonable layout of the positioning points of the workpiece, which can effectively avoid the misjudgment of the DOF and unnecessary overpositioning when the complex workpiece is combined and positioned on different surfaces. Several examples are used to verify the accuracy of the method and correct unreasonable positioning schemes.http://dx.doi.org/10.1155/2021/1014708
spellingShingle Guojun Luo
Xiaohui Wang
Xianguo Yan
Geometric Theorems and Application of the DOF Analysis of the Workpiece Based on the Constraint Normal Line
Advances in Materials Science and Engineering
title Geometric Theorems and Application of the DOF Analysis of the Workpiece Based on the Constraint Normal Line
title_full Geometric Theorems and Application of the DOF Analysis of the Workpiece Based on the Constraint Normal Line
title_fullStr Geometric Theorems and Application of the DOF Analysis of the Workpiece Based on the Constraint Normal Line
title_full_unstemmed Geometric Theorems and Application of the DOF Analysis of the Workpiece Based on the Constraint Normal Line
title_short Geometric Theorems and Application of the DOF Analysis of the Workpiece Based on the Constraint Normal Line
title_sort geometric theorems and application of the dof analysis of the workpiece based on the constraint normal line
url http://dx.doi.org/10.1155/2021/1014708
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AT xiaohuiwang geometrictheoremsandapplicationofthedofanalysisoftheworkpiecebasedontheconstraintnormalline
AT xianguoyan geometrictheoremsandapplicationofthedofanalysisoftheworkpiecebasedontheconstraintnormalline