Screw Motion via Matrix Algebra in Three-Dimensional Generalized Space
This paper aims to investigate the screw motion in generalized space. For this purpose, firstly, the change in the screw coordinates is analyzed according to the motion of the reference frames. Moreover, the special cases of this change, such as pure rotation and translation, are discussed. Matrix m...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/11/2235 |
| _version_ | 1797466426522468352 |
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| author | Ümit Ziya Savcı |
| author_facet | Ümit Ziya Savcı |
| author_sort | Ümit Ziya Savcı |
| collection | DOAJ |
| description | This paper aims to investigate the screw motion in generalized space. For this purpose, firstly, the change in the screw coordinates is analyzed according to the motion of the reference frames. Moreover, the special cases of this change, such as pure rotation and translation, are discussed. Matrix multiplication and the properties of dual numbers are used to obtain dual orthogonal matrices, which are used to simplify the manipulation of screw motion in generalized space. In addition, the dual angular velocity matrix is calculated and shows that the exponential of this matrix can represent the screw displacement in the generalized space. Finally, to support our results, we give two examples of screw motion, the rotation part of which is elliptical and hyperbolic. |
| first_indexed | 2024-03-09T18:36:46Z |
| format | Article |
| id | doaj.art-fe03a3a30bd44efd90949df9a3c71940 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T18:36:46Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-fe03a3a30bd44efd90949df9a3c719402023-11-24T07:07:02ZengMDPI AGSymmetry2073-89942022-10-011411223510.3390/sym14112235Screw Motion via Matrix Algebra in Three-Dimensional Generalized SpaceÜmit Ziya Savcı0Department of Mathematics and Science Education, Kütahya Dumlupınar University, Kütahya 43050, TurkeyThis paper aims to investigate the screw motion in generalized space. For this purpose, firstly, the change in the screw coordinates is analyzed according to the motion of the reference frames. Moreover, the special cases of this change, such as pure rotation and translation, are discussed. Matrix multiplication and the properties of dual numbers are used to obtain dual orthogonal matrices, which are used to simplify the manipulation of screw motion in generalized space. In addition, the dual angular velocity matrix is calculated and shows that the exponential of this matrix can represent the screw displacement in the generalized space. Finally, to support our results, we give two examples of screw motion, the rotation part of which is elliptical and hyperbolic.https://www.mdpi.com/2073-8994/14/11/2235generalized spacekinematicsscrew motionmatrix algebra |
| spellingShingle | Ümit Ziya Savcı Screw Motion via Matrix Algebra in Three-Dimensional Generalized Space Symmetry generalized space kinematics screw motion matrix algebra |
| title | Screw Motion via Matrix Algebra in Three-Dimensional Generalized Space |
| title_full | Screw Motion via Matrix Algebra in Three-Dimensional Generalized Space |
| title_fullStr | Screw Motion via Matrix Algebra in Three-Dimensional Generalized Space |
| title_full_unstemmed | Screw Motion via Matrix Algebra in Three-Dimensional Generalized Space |
| title_short | Screw Motion via Matrix Algebra in Three-Dimensional Generalized Space |
| title_sort | screw motion via matrix algebra in three dimensional generalized space |
| topic | generalized space kinematics screw motion matrix algebra |
| url | https://www.mdpi.com/2073-8994/14/11/2235 |
| work_keys_str_mv | AT umitziyasavcı screwmotionviamatrixalgebrainthreedimensionalgeneralizedspace |