Synthesis of Four-Link Initial Kinematic Chains with Spherical Pairs for Spatial Mechanisms
This research addresses the problem of the initial synthesis of kinematic chains with spherical kinematic pairs, which are essential in the design of spatial mechanisms used in robotics, aerospace, and mechanical systems. The goal is to establish the existence of solutions for defining the geometric...
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MDPI AG
2025-03-01
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| Series: | Applied Sciences |
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| author | Samal Abdreshova Algazy Zhauyt Kuanysh Alipbayev Serikbay Kosbolov Alisher Aden Aray Orazaliyeva |
| author_facet | Samal Abdreshova Algazy Zhauyt Kuanysh Alipbayev Serikbay Kosbolov Alisher Aden Aray Orazaliyeva |
| author_sort | Samal Abdreshova |
| collection | DOAJ |
| description | This research addresses the problem of the initial synthesis of kinematic chains with spherical kinematic pairs, which are essential in the design of spatial mechanisms used in robotics, aerospace, and mechanical systems. The goal is to establish the existence of solutions for defining the geometric and motion constraints of these kinematic chains, ensuring that the synthesized mechanism achieves the desired motion with precision. By formulating the synthesis problem in terms of nonlinear algebraic equations derived from the spatial positions and orientations of the links, we analyze the conditions under which a valid solution exists. We explore both analytical and numerical methods to solve these equations, highlighting the significance of parameter selection in determining feasible solutions. Specifically, our approach demonstrates the visualization of fixed points, such as <i>A</i>, <i>B</i>, and <i>C</i>, alongside their spatial differences with respect to reference points and transformation matrices. We detail methods for plotting transformation components, including rotation matrix elements (<i>e</i>, <i>m</i>, and <i>n</i>) and derived products from these matrices, as well as the representation of angular parameters (<i>θ<sub>i</sub></i>, <i>ψ<sub>i</sub></i>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi></mrow></semantics></math></inline-formula><i><sub>i</sub></i>) in a three-dimensional context. The proposed techniques not only facilitate the debugging and analysis of complex kinematic behaviors but also provide a flexible tool for researchers in robotics, computer graphics, and mechanical design. By offering a clear and interactive visualization strategy, this framework enhances the understanding of spatial relationships and transformation dynamics inherent in multi-body systems. |
| format | Article |
| id | doaj-art-a19eab59993346799dc41f2011fc0723 |
| institution | OA Journals |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-a19eab59993346799dc41f2011fc07232025-08-20T02:09:13ZengMDPI AGApplied Sciences2076-34172025-03-01157360210.3390/app15073602Synthesis of Four-Link Initial Kinematic Chains with Spherical Pairs for Spatial MechanismsSamal Abdreshova0Algazy Zhauyt1Kuanysh Alipbayev2Serikbay Kosbolov3Alisher Aden4Aray Orazaliyeva5Department of Electronic Engineering, Almaty University of Power Engineering and Telecommunications Named after Gumarbek Daukeyev, Almaty 050013, KazakhstanDepartment of Electronic Engineering, Almaty University of Power Engineering and Telecommunications Named after Gumarbek Daukeyev, Almaty 050013, KazakhstanDepartment of Electronic Engineering, Almaty University of Power Engineering and Telecommunications Named after Gumarbek Daukeyev, Almaty 050013, KazakhstanDepartment of Aerospace Engineering, Almaty University of Power Engineering and Telecommunications Named after Gumarbek Daukeyev, Almaty 050013, KazakhstanDepartment of Electronic Engineering, Almaty University of Power Engineering and Telecommunications Named after Gumarbek Daukeyev, Almaty 050013, KazakhstanDepartment of Aerospace Engineering, Almaty University of Power Engineering and Telecommunications Named after Gumarbek Daukeyev, Almaty 050013, KazakhstanThis research addresses the problem of the initial synthesis of kinematic chains with spherical kinematic pairs, which are essential in the design of spatial mechanisms used in robotics, aerospace, and mechanical systems. The goal is to establish the existence of solutions for defining the geometric and motion constraints of these kinematic chains, ensuring that the synthesized mechanism achieves the desired motion with precision. By formulating the synthesis problem in terms of nonlinear algebraic equations derived from the spatial positions and orientations of the links, we analyze the conditions under which a valid solution exists. We explore both analytical and numerical methods to solve these equations, highlighting the significance of parameter selection in determining feasible solutions. Specifically, our approach demonstrates the visualization of fixed points, such as <i>A</i>, <i>B</i>, and <i>C</i>, alongside their spatial differences with respect to reference points and transformation matrices. We detail methods for plotting transformation components, including rotation matrix elements (<i>e</i>, <i>m</i>, and <i>n</i>) and derived products from these matrices, as well as the representation of angular parameters (<i>θ<sub>i</sub></i>, <i>ψ<sub>i</sub></i>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>φ</mi></mrow></semantics></math></inline-formula><i><sub>i</sub></i>) in a three-dimensional context. The proposed techniques not only facilitate the debugging and analysis of complex kinematic behaviors but also provide a flexible tool for researchers in robotics, computer graphics, and mechanical design. By offering a clear and interactive visualization strategy, this framework enhances the understanding of spatial relationships and transformation dynamics inherent in multi-body systems.https://www.mdpi.com/2076-3417/15/7/3602visualizationtransformationspatial mechanismsynthesisapproximation |
| spellingShingle | Samal Abdreshova Algazy Zhauyt Kuanysh Alipbayev Serikbay Kosbolov Alisher Aden Aray Orazaliyeva Synthesis of Four-Link Initial Kinematic Chains with Spherical Pairs for Spatial Mechanisms Applied Sciences visualization transformation spatial mechanism synthesis approximation |
| title | Synthesis of Four-Link Initial Kinematic Chains with Spherical Pairs for Spatial Mechanisms |
| title_full | Synthesis of Four-Link Initial Kinematic Chains with Spherical Pairs for Spatial Mechanisms |
| title_fullStr | Synthesis of Four-Link Initial Kinematic Chains with Spherical Pairs for Spatial Mechanisms |
| title_full_unstemmed | Synthesis of Four-Link Initial Kinematic Chains with Spherical Pairs for Spatial Mechanisms |
| title_short | Synthesis of Four-Link Initial Kinematic Chains with Spherical Pairs for Spatial Mechanisms |
| title_sort | synthesis of four link initial kinematic chains with spherical pairs for spatial mechanisms |
| topic | visualization transformation spatial mechanism synthesis approximation |
| url | https://www.mdpi.com/2076-3417/15/7/3602 |
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