Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel Robots
Quaternions are used in various applications, especially in those where it is necessary to model and represent rotational movements, both in the plane and in space, such as in the modeling of the movements of robots and mechanisms. In this article, a methodology to model the rigid rotations of coupl...
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| Format: | Article |
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MDPI AG
2025-07-01
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| Series: | Robotics |
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| Online Access: | https://www.mdpi.com/2218-6581/14/7/94 |
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| author | Francisco Cuenca Jiménez Eusebio Jiménez López Mario Acosta Flores F. Peñuñuri Ricardo Javier Peón Escalante Juan José Delfín Vázquez |
| author_facet | Francisco Cuenca Jiménez Eusebio Jiménez López Mario Acosta Flores F. Peñuñuri Ricardo Javier Peón Escalante Juan José Delfín Vázquez |
| author_sort | Francisco Cuenca Jiménez |
| collection | DOAJ |
| description | Quaternions are used in various applications, especially in those where it is necessary to model and represent rotational movements, both in the plane and in space, such as in the modeling of the movements of robots and mechanisms. In this article, a methodology to model the rigid rotations of coupled bodies by means of unit quaternions is presented. Two parallel robots were modeled: a planar RRR robot and a spatial motion PRRS robot using the proposed methodology. Inverse kinematic problems were formulated for both models. The planar RRR robot model generated a system of 21 nonlinear equations and 18 unknowns and a system of 36 nonlinear equations and 33 unknowns for the case of space robot PRRS; both systems of equations were of the polynomial algebraic type. The systems of equations were solved using the Broyden–Fletcher–Goldfarb–Shanno nonlinear programming algorithm and Mathematica V12 symbolic computation software. The modeling methodology and the algebra of unitary quaternions allowed the systematic study of the movements of both robots and the generation of mathematical models clearly and functionally. |
| format | Article |
| id | doaj-art-49ff8c6262bc486c806cfc21ad48a87e |
| institution | Kabale University |
| issn | 2218-6581 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Robotics |
| spelling | doaj-art-49ff8c6262bc486c806cfc21ad48a87e2025-08-20T03:56:46ZengMDPI AGRobotics2218-65812025-07-011479410.3390/robotics14070094Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel RobotsFrancisco Cuenca Jiménez0Eusebio Jiménez López1Mario Acosta Flores2F. Peñuñuri3Ricardo Javier Peón Escalante4Juan José Delfín Vázquez5Engineering Design Department, Universidad Nacional Autónoma de México, Ciudad de México 04510, MexicoResearch and Development Department, Universidad Tecnológica del Sur de Sonora-Universidad La Salle Noroeste-ITESCA, Cuidad Obregón 85190, Sonora, MexicoFaculty of Chemical Sciences and Engineering, Universidad Autónoma del Estado de Morelos, Cuernacava 62209, Morelos, MexicoFaculty of Engineering, Universidad Autónoma de Yucatán, Mérida 97160, Yucatán, MexicoFaculty of Engineering, Universidad Autónoma de Yucatán, Mérida 97160, Yucatán, MexicoResearch and Development Department, Tecnológico Nacional de México/ITS de Cajeme, Cuidad Obregón 85024, Sonora, MexicoQuaternions are used in various applications, especially in those where it is necessary to model and represent rotational movements, both in the plane and in space, such as in the modeling of the movements of robots and mechanisms. In this article, a methodology to model the rigid rotations of coupled bodies by means of unit quaternions is presented. Two parallel robots were modeled: a planar RRR robot and a spatial motion PRRS robot using the proposed methodology. Inverse kinematic problems were formulated for both models. The planar RRR robot model generated a system of 21 nonlinear equations and 18 unknowns and a system of 36 nonlinear equations and 33 unknowns for the case of space robot PRRS; both systems of equations were of the polynomial algebraic type. The systems of equations were solved using the Broyden–Fletcher–Goldfarb–Shanno nonlinear programming algorithm and Mathematica V12 symbolic computation software. The modeling methodology and the algebra of unitary quaternions allowed the systematic study of the movements of both robots and the generation of mathematical models clearly and functionally.https://www.mdpi.com/2218-6581/14/7/94roboticsquaternionskinematicsparallel mechanisms |
| spellingShingle | Francisco Cuenca Jiménez Eusebio Jiménez López Mario Acosta Flores F. Peñuñuri Ricardo Javier Peón Escalante Juan José Delfín Vázquez Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel Robots Robotics robotics quaternions kinematics parallel mechanisms |
| title | Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel Robots |
| title_full | Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel Robots |
| title_fullStr | Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel Robots |
| title_full_unstemmed | Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel Robots |
| title_short | Methodology for Modeling Coupled Rigid Multibody Systems Using Unitary Quaternions: The Case of Planar RRR and Spatial PRRS Parallel Robots |
| title_sort | methodology for modeling coupled rigid multibody systems using unitary quaternions the case of planar rrr and spatial prrs parallel robots |
| topic | robotics quaternions kinematics parallel mechanisms |
| url | https://www.mdpi.com/2218-6581/14/7/94 |
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