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An approach to solving the forward kinematics of the 5-RPUR (3T2R) parallel manipulator

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Abstract

This work is devoted to simplifying the formulation and solution of the closure equations associated with the forward kinematic problem (FKP) of the 5-RPUR parallel manipulator, a limited-DOF robot able to perform 3T2R motion. The analysis yields a set of eighteen nonlinear equations that are solved numerically through a combination of the homotopy continuation method and the usual Newton-Raphson technique. Unlike existing methods, the proposed approach is easy to follow and can be easily translated into computer codes. Numerical examples are provided with the aim to illustrate the potential and correctness of the proposed method.

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Acknowledgments

The authors acknowledge the support of the Consejo Nacional de Ciencia y Tecnología (National Council of Science and Technology, CONACYT), of Mexico, through SNI (National Network of Researchers) fellowships.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Tecnologico Nacional de Mexico en Celaya, Celaya, 38010, GTO, Mexico

    Jaime Gallardo-Alvarado, Luis D. Aguilera-Camacho & Luis A. Alcaraz-Caracheo

  2. Department of Mechanical Engineering, University of Guanajuato, Salamanca-Valle de Santiago km 3.5+1.8, Salamanca, 36885, GTO, Mexico

    Mario A. Garcia-Murillo

  3. CONACYT-Instituto Politécnico Nacional, Ciudad de México, 03940, Mexico

    X. Yamile Sandoval-Castro

Authors
  1. Jaime Gallardo-Alvarado
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  2. Mario A. Garcia-Murillo
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  3. Luis D. Aguilera-Camacho
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  4. Luis A. Alcaraz-Caracheo
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  5. X. Yamile Sandoval-Castro
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Corresponding author

Correspondence to Mario A. Garcia-Murillo.

Additional information

Jaime Gallardo-Alvarado (ORCID No.: 0000-0002-8208-0432) received the D.Sc. in Electrical Engineering from Tecnológico Nacional de México en La Laguna, México. His interests cover screw theory, lie algebras, kinematics, and robot manipulators. In 1993, Dr. Gallardo-Alvarado joined the Department of Mechanical Engineering of the Tecnológico Nacional de México en Celaya.

Mario A. García-Murillo (ORCID No.: 0000-0002-4487-5859) received his degree in Mechanical Engineering from Universidad Autónoma Chapingo in 2008. In 2010, he obtained his M.Sc. in Mechanical Engineering from Instituto Tecnológico de Celaya in Mexico. His Ph.D. is from National Polytechnic Institute-CICATA Querétaro in 2015. Dr. Garcia-Murillo is a Full-Time Professor in the Department of Mechanical Engineering of the Universidad de Guanajuato. His current research interests include kinematics and dynamics of manipulators, parameter identification of mechanisms and kinematical modelling of human joints.

Luis D. Aguilera-Camacho (ORCID No.: 0000-0002-7588-6171) is a Professor at the Department of Mechanical Engineering Guanajuato, Mexico. His research is focused on manufacturing processes, and on the adhesion and surface analysis of materials. He also collaborates in other areas as mechanical design, kinematics and dynamics.

Luis A. Alcaraz-Caracheo (ORCID No.: 0000-0003-1319-0299) received the B.Sc. and M.Sc. in Mechanical En-gineering from Tecnológico Nacional de México en Celaya, México, and the Ph.D. in Mechanical Engineering from Instituto Politécnico Nacional, México. His in-terests cover machine design, materials, and robot manipulators. Dr. Alcaraz-Caracheo is a current Full Time Professor in Mechatronics of Tecnológico Nacional de México en Celaya.

X. Yamile Sandoval-Castro (ORCID No.: 0000-0002-8674-0004) received her degree in Communications and Electronics Engineering from Universidad Autónoma Zacatecas in 2008. In 2011, she obtained her M.Sc. in Instrumentation and Automatic Control from Universidad Autónoma de Querétaro in México. She earned her Ph.D. from National Polytechnic Institute-CICATA Querétaro in 2015. Dr. Sandoval-Castro is currently a Professor at the “CONACYT professorships program” in the Department of Mechatronics of the Research Center for Applied Science and Advanced Technology (CICATA-IPN) and a member of the SNI of México. Her current research interests include designing and modelling of soft robots by using origami and kirigami concepts, modelling of manipulators and developing of locomotion algorithms.

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Gallardo-Alvarado, J., Garcia-Murillo, M.A., Aguilera-Camacho, L.D. et al. An approach to solving the forward kinematics of the 5-RPUR (3T2R) parallel manipulator. J Mech Sci Technol 37, 1443–1453 (2023). https://doi.org/10.1007/s12206-023-0230-2

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  • DOI: https://doi.org/10.1007/s12206-023-0230-2

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