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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Wiley
2021-01-01
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| 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. |
| format | Article |
| id | doaj-art-48bd89754fba4e69a6e2a0d7df1aced6 |
| institution | Kabale University |
| issn | 1687-8434 1687-8442 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Materials Science and Engineering |
| 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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