Abstract
The paper discusses inverse and forward kinematics of a 4-DOF parallel mechanism with a circular rail. The mechanism can perform an unlimited rotation around one of the axes and use one of its kinematic chains for reconfiguration. The inverse kinematics has a closed-form solution, while the forward kinematics implies solving coupled polynomial equations. The paper proves that there can be sixteen different assembly modes of the mechanism and verifies the result by a homotopy continuation approach.
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Notes
- 1.
R, P, U, and S designate revolute, prismatic, universal, and spherical joints, respectively.
References
Asada, H., Granito, J.: Kinematic and static characterization of wrist joints and their optimal design. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 244–250 (1985)
Bates, D.J., Hauenstein, J.D., Sommese, A.J., Wampler, C.W.: Bertini: Software for numerical algebraic geometry. bertini.nd.edu (2006)
Bates, D.J., Newell, A.J., Niemerg, M.: BertiniLab: a MATLAB interface for solving systems of polynomial equations. Numer. Algorithm. 71(1), 229–244 (2015)
Baumann, R., Maeder, W., Glauser, D., Clavel, R.: The PantoScope: a spherical remote-center-of-motion parallel manipulator for force reflection. In: Proceedings of the IEEE International Conference on Robotics and Automation, vol. 1, pp. 718–723 (1997)
Borras, J., Thomas, F., Ottaviano, E., Ceccarelli, M.: A reconfigurable 5-DoF 5-SPU parallel platform. In: Proceedings of the ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, pp. 617–623 (2009)
Fang, H.R., Chen, Z.H., Fang, Y.F.: A novel spherical parallel manipulator with circular guide. Appl. Mech. Mater. 325–326, 1014–1018 (2013)
Furlong, T.J., Vance, J.M., Larochelle, P.M.: Spherical mechanism synthesis in virtual reality. J. Mech. Des. 121, 515–520 (1999)
Garcia, C.B., Li, T.Y.: On the number of solutions to polynomial systems of equations. SIAM J. Numer. Anal. 17, 540–546 (1980)
Gosselin, C.M., Sefrioui, J., Richard, M.J.: On the direct kinematics of spherical three-degree-of-freedom parallel manipulators of general architecture. J. Mech. Des. 116, 594–598 (1994)
Kong, X., Gosselin, C.M., Richard, P.: Type synthesis of parallel mechanisms with multiple operation modes. J. Mech. Des. 129, 595–601 (2007)
Laryushkin, P., Antonov, A., Fomin, A., Glazunov, V.: Novel reconfigurable spherical parallel mechanisms with a circular rail. Robotics 11, 30 (2022)
Li, T., Payandeh, S.: Design of spherical parallel mechanisms for application to laparoscopic surgery. Robotica 20, 133–138 (2002)
Li, Q., Chen, Q., Wu, C., Hu, X.: Two novel spherical 3-DOF parallel manipulators with circular prismatic pairs. In: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 325–328 (2006)
Lynch, K.M., Park, F.C.: Modern Robotics: Mechanics, Planning, and Control. Cambridge University Press, Cambridge (2017)
Rodriguez, J., Ruggiu, M.: A novel method for the solution of the forward displacement problem of spherical parallel manipulators. ZAMM – J. Appl. Math. Mech. 93, 73–82 (2013)
Saafi, H., Laribi, M.A., Zeghloul, S.: Forward kinematic model resolution of a special spherical parallel manipulator: comparison and real-time validation. Robotics 9, 62 (2020)
Sommese, A.J., Wampler, C.W.: The Numerical Solution of Polynomials Arising in Engineering and Science. World Scientific, Singapore (2005)
Staicu, S.: Recursive modelling in dynamics of Agile Wrist spherical parallel robot. Robot. Comput. Integrat. Manuf. 25, 409–416 (2009)
Wampler, C.W.: Displacement analysis of spherical mechanisms having three or fewer loops. J. Mech. Des. 126, 93–100 (2004)
Westwood, J.D.: Spherical mechanism analysis of a surgical robot for minimally invasive surgery–analytical and experimental approaches. Stud. Health Technol. Inf. 111, 422–428 (2005)
Wu, G., Bai, S.: Design and kinematic analysis of a 3-RRR spherical parallel manipulator reconfigured with four–bar linkages. Robot. Comput. Integrat. Manuf. 56, 55–65 (2019)
Wu, G., Caro, S., Wang, J.: Design and transmission analysis of an asymmetrical spherical parallel manipulator. Mech. Mach. Theory 94, 119–131 (2015)
Xu, C.C., Xue, C., Duan, X.C.: A novel 2R parallel mechanism for alt-azimuth pedestal. IOP Conf. Ser. Mater. Sci. Eng. 428, 012053 (2018)
Zhao, J., Feng, Z., Chu, F., Ma, N.: Kinematic synthesis of spatial mechanisms. In: Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms, pp. 429–469 (2014)
Acknowledgement
This research was supported by Russian Science Foundation (RSF) under grant no. 21-79-10409, https://rscf.ru/project/21-79-10409/.
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Laryushkin, P., Antonov, A., Fomin, A., Glazunov, V. (2022). Inverse and Forward Kinematics of a Reconfigurable Spherical Parallel Mechanism with a Circular Rail. In: Kecskeméthy, A., Parenti-Castelli, V. (eds) ROMANSY 24 - Robot Design, Dynamics and Control. ROMANSY 2022. CISM International Centre for Mechanical Sciences, vol 606. Springer, Cham. https://doi.org/10.1007/978-3-031-06409-8_26
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