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Kinematics of the 4-RUU parallel manipulator generator of the Schönflies motion by means of screw theory

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Abstract

This work deals with the inverse–forward kinematic analysis of a symmetric parallel manipulator equipped with a rotary actuator generator of three independent translations and one rotation motion. The closure equations of the displacement analysis are easily formulated based on the unknown coordinates of two points embedded in the moving platform. The input–output equations of velocity and acceleration of the robot are systematically obtained through the reciprocal-screw theory. The pseudo-kinematic pairs that connect the limbs to the fixed platform and a passive kinematic chain connected to the robot manipulator eliminate the handling of rank-deficient Jacobian matrices, which is an undisputable advantage from the computational point of view. Furthermore, this strategy allows the use of the Lie algebra se(3) without the inherent restrictions associated with the limited mobility of the robot.

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Instituto Tecnológico de Celaya, TecNM, 38010, Celaya, GTO, México

    Jaime Gallardo-Alvarado

  2. Department of Mechanical Engineering, DICIS, Universidad de Guanajuato, 36885, Salamanca, GTO, México

    Mario A. García-Murillo

  3. Faculty of Engineering, Universiti Malasya Sabah (UMS), Jalan UMS, 88400, Kota Kinabalu, Sabah, Malaysia

    Md. Nazrul Islam

  4. Department of Biomedical Engineering, Rowan University, Glassboro, New Jersey, 08028, USA

    Mohammad H. Abedinnasab

Authors
  1. Jaime Gallardo-Alvarado
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  2. Mario A. García-Murillo
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  3. Md. Nazrul Islam
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  4. Mohammad H. Abedinnasab
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Corresponding author

Correspondence to Jaime Gallardo-Alvarado.

Additional information

Recommended by Associate Editor Kyoungchul Kong

Jaime Gallardo–Alvarado received his B.Sc. and M.Sc. degrees in mechanical engineering from Instituto Tecnológico de Celaya, México in 1985 and 1988, respectively, and his Ph.D. in electrical engineering from Instituto Tecnológico de la Laguna, México in 1999. He is the author of the book “Kinematic Analysis of Parallel Manipulators by Algebraic Screw Theory”. He had authored more than 50 journal articles, and his interests cover spatial kinematics and dynamics of robot manipulators by means of screw theory. Dr. Gallardo–Alvarado is currently a Full-time Professor in the Department of Mechanical Engineering of the Instituto Tecnológico de Celaya and member of the SNI of México.

Mario A. García–Murillo 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 México. He earned his Ph.D. from IPN CICATA Querétaro in 2014. Dr. García–Murillo is currently a Full-time Professor in the Department of Mechanical Engineering of the Universidad de Guanajuato and member of the SNI of México. His current research interests include kinematics and dynamics of manipulators.

Md. Nazrul Islam received his B.Sc. and M.Sc. degrees in mathematics from the University of Dhaka, Bangladesh, in 1992 and 1994, respectively, M.Phil. in mathematics from the Bangladesh University of Engineering and Technology, Bangladesh, in 1998, and Ph.D. degree in system design engineering from the University of Fukui, Japan in 2008. He had authored more than 35 journal and conference papers, and his interests include big data, IoT, robotics, artificial intelligence, simultaneous localization and mapping, and fluid dynamics. Dr. Md. Nazrul Islam is a Full-time Associate Professor at the Computer Engineering Program, Faculty of Engineering in the University Malaysia Sabah, Malaysia.

Mohammad H. Abedinnasab received his Ph.D. from Sharif University of Technology, Iran, in 2012. He is an Assistant Professor and the Director of the Surgical Robotics Laboratory in the Department of Biomedical Engineering at Rowan University, USA. His research interests include kinematic and dynamic analyses of parallel manipulators, surgical robotics, biomechanics, and fuzzy controllers.

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Gallardo-Alvarado, J., García-Murillo, M.A., Islam, M.N. et al. Kinematics of the 4-RUU parallel manipulator generator of the Schönflies motion by means of screw theory. J Mech Sci Technol 31, 4925–4932 (2017). https://doi.org/10.1007/s12206-017-0941-3

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  • DOI: https://doi.org/10.1007/s12206-017-0941-3

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