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Kinematics of a nine-legged in-parallel manipulator with configurable platform

Published online by Cambridge University Press:  21 July 2022

Jaime Gallardo-Alvarado Open the ORCID record for Jaime Gallardo-Alvarado [Opens in a new window] ,
Mario A. Garcia-Murillo Open the ORCID record for Mario A. Garcia-Murillo [Opens in a new window]  and
Ramon Rodriguez-Castro
Jaime Gallardo-Alvarado*
Affiliation:
Mechanical Engineering Department, National Technological Institute of Mexico/Celaya Campus, Celaya, Mexico
Mario A. Garcia-Murillo
Affiliation:
Mechanical Engineering Department, DICIS, University of Guanajuato, Guanajuato, Mexico
Ramon Rodriguez-Castro
Affiliation:
Mechanical Engineering Department, National Technological Institute of Mexico/Celaya Campus, Celaya, Mexico
*
*Corresponding author. E-mail: jaime.gallardo@itcelaya.edu.mx
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Abstract

Configurable platforms bring a research field to expand the attributes of parallel manipulators. This work is devoted to investigate the kinematics of a nine-degrees-of-freedom parallel manipulator whose active kinematic pairs are located near to the fixed platform, and it is equipped with a 6-R configurable platform. The mobility of the proposed 9-UPUR{6R} configurable parallel manipulator is such that it is possible to manipulate the kinematics of a grasping triangle associated to the configurable platform. The theory of screws is systematically applied to solve the direct and inverse infinitesimal kinematics of the manipulator. As an intermediate step, the displacement analysis is approached by means of algebraic geometry. The contribution is complemented with numerical examples to illustrate the versatility of the method of kinematic analysis.

Keywords

parallel manipulatorconfigurable platformkinematicsscrew theory
Type
Research Article
Information
Robotica , Volume 40 , Issue 12 , December 2022 , pp. 4455 - 4474
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Wang, J., Yao, Y. and Kong, X., “A reconfigurable tri-prism mobile robot with eight modes,” Robotica 36(10), 1454–1476 (2018).CrossRefGoogle Scholar
Huang, G., Guo, S., Zhang, D., Qu, H. and Tang, H., “Kinematic analysis and multi-objective optimization of a new reconfigurable parallel mechanism with high stiffness,” Robotica 36(2), 187–203 (2018).CrossRefGoogle Scholar
Han, B., Zheng, D., Xu, Y., Yao, J. and Zhao, Y., “Kinematic characteristics and dynamics analysis of an overconstrained scissors double-hoop truss deployable antenna mechanism based on screw theory,” IEEE Access 7, 104755–140768 (2019).Google Scholar
Mohamed, M. G. and Gosselin, C. M., “Design and analysis of kinematically redundant parallel manipulators with configurable platforms,” IEEE Trans. Robot. 21(3), 277–287 (2005).CrossRefGoogle Scholar
Lambert, P. and Herder, J. L., “Parallel robots with configurable platforms: fundamental aspects of a new class of robotic architectures,” Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci. 230(1), 11–47 (2016).CrossRefGoogle Scholar
Hoevenaars, A. G. L., Gosselin, C., Lambert, P. and Herder, J. L., “A systematic approach for the Jacobian analysis of parallel manipulators with two end-effectors,” Mech. Mach. Theory 109(1), 171–194 (2017).CrossRefGoogle Scholar
Tian, C., Zhang, D., Tang, H. and Chenwei, W., “Structure synthesis of reconfigurable generalized parallel mechanisms with configurable platforms,” Mech. Mach. Theory 160, 104281 (2021).CrossRefGoogle Scholar
Yi, B. J., Na, H. Y., Lee, J. H., Hong, Y. S., Oh, S. R., Suh, I. H. and Kim, W. K., “Design of a parallel-type gripper mechanism,” Int. J. Robot. Res. 21(7), 661–676 (2002).CrossRefGoogle Scholar
Pfurner, M., “Analysis of A Delta Like Parallel Mechanism with an Overconstrained Serial Chain as Platform,” In: Proceedings 14th World Congress in Mechanism and Machine Science, Taipei, Taiwan, IFToMM (2015).Google Scholar
Gallardo-Alvarado, J., “A Gough–Stewart parallel manipulator with configurable platform and multiple end-effectors,” Meccanica 55, 597–613 (2020).CrossRefGoogle Scholar
Merlet, J.-P., “Redundant parallel manipulators,” J. Lab. Robot. Automat. 8(1), 17–24 (1996).3.0.CO;2-#>CrossRefGoogle Scholar
Wang, J. and Gosselin, C. M., “Kinematic analysis and design of kinematically redundant parallel mechanisms,” ASME J. Mech. Des. 126(1), 109–118 (2004).CrossRefGoogle Scholar
Wu, T.-M., “A study of convergence on the Newton-homotopy continuation method,” Appl. Math. Comput. 168(2), 1169–1174 (2005).Google Scholar
Gallardo-Alvarado, J., “An application of the Newton-homotopy continuation method for solving the forward kinematic problem of the 3-RRS parallel manipulator,” Math. Probl. Eng. 2019(8), 1–6 (2019).Google Scholar
Gallardo-Alvarado, J.. Kinematic Analysis of Parallel Manipulators by Algebraic Screw Theory (Springer, Cham, Switzerland, 2016).CrossRefGoogle Scholar
Gallardo, J. and Rico, J. M., “Screw Theory and Helicoidal Fields,” In: Proceedings of the 25th Biennial Mechanisms Conference, Atlanta, ASME. paper DETC98/MECH-5893 (1998).Google Scholar
Rico-Martinez, J. M. and Duffy, J., “An application of screw algebra to the acceleration analysis of serial chains,” Mech. Mach. Theory 31(4), 445–457 (1996).CrossRefGoogle Scholar
Rico-Martinez, J. M. and Duffy, J., “Forward and inverse acceleration analyses of in-parallel manipulators,” ASME J. Mech. Des. 122(3), 299–303 (2000).CrossRefGoogle Scholar
Sharafian, M. E., Taghvaeipour, A. and Ghassabzadeh, S. M., “Revisiting screw theory-based approaches in the constraint wrench analysis of robotic systems,” Robotica 40(5), 1406–1430 (2022). Published on line: 1-25, 2021.CrossRefGoogle Scholar
Craig, J. J.. Introduction to Robotics: Mechanics and Control (Pearson, Hoboken, NJ, USA, 2018).Google Scholar