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A Simple Method to Solve the Instantaneous Kinematics of the 5-R$\underbar{P}$UR Parallel Manipulator

Published online by Cambridge University Press:  11 February 2019

Jaime Gallardo-Alvarado Open the ORCID record for Jaime Gallardo-Alvarado [Opens in a new window] ,
Mohammad H. Abedinnasab  and
Md. Nazrul Islam
Jaime Gallardo-Alvarado*
Affiliation:
Department of Mechanical Engineering, Instituto Tecnológico de Celaya, TecNM, Celaya 38010, Guanajuato, Mexico
Mohammad H. Abedinnasab
Affiliation:
Department of BiomedicalEngineering, Rowan University, Glassboro, NJ 08028, USA E-mail: [email protected]
Md. Nazrul Islam
Affiliation:
College of Computer Sciences and Information Technology, King Faisal University, Al-Hassa 31982, Saudi Arabia E-mail: [email protected]
*
*Corresponding author. E-mail: [email protected]
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Summary

In this work a simple method to solve the kinematics of the 5-R$\underbar{P}$UR parallel manipulator is introduced. Dealing with the displacement analysis, the kinematic constraint equations required to address the forward–inverse displacement analysis are established according to linear combinations of two vectors attached to the moving platform. Then, besides the solution of the inverse displacement analysis two strategies are proposed in order to solve the forward position analysis. Finally, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. Numerical examples are provided with the purpose to illustrate the proposed method. Furthermore, the numerical results obtained by means of screw theory are confirmed with the aid of commercially available software.

Keywords

Parallel manipulatorsLimited mobilityKlein formScrew theoryKinematics
Type
Articles
Information
Robotica , Volume 37 , Issue 6 , June 2019 , pp. 1143 - 1157
Copyright
© Cambridge University Press 2019 

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References

Hunt, K. H., “Structural kinematics of in-parallel-actuated robot-arms,” ASME J. Mech. Transm. Autom. Des. 105, 705–712 (1983).CrossRefGoogle Scholar
Tsai, L.-W., “Systematic Enumeration of Parallel Manipulators,” In: Parallel Kinematic Machines. Advanced Manufacturing (Boër, C. R., Molinari-Tosatti, L. and Smith, K. S., eds.) (Springer, London, 1999) pp. 33–50.CrossRefGoogle Scholar
Fang, Y. and Tsai, L.-W., “Structure synthesis of a class of 4-DoF and 5-DoF parallel manipulators with identical limb structures,” Int. J. Robot. Res. 21, 799–810 (2002).CrossRefGoogle Scholar
Lu, Y. and Hu, B., “Analysis of stiffness and elastic deformation for some 35-DOF PKMs with SPR or RPS-type legs,” ASME J. Mech. Des. 130, Paper No: 102307 (2008).CrossRefGoogle Scholar
Gallardo-Alvarado, J., Arroyo-Ramírez, B. and Rojas-Garduño, H., “Kinematics of a five-degrees-of-freedom parallel manipulator using screw theory, ”Int. J. Adv. Manufact. Technol. 45, 830–840 (2009).CrossRefGoogle Scholar
Masouleh, M. T., Gosselin, C., Husty, M. and Walter, D. R., “Forward kinematic problem of 5-RPUR parallel mechanisms (3T2R) with identical limb structures,” Mech. Mach. Theory 46, 945–959 (2011).CrossRefGoogle Scholar
Cox, D. A., Little, J. B. and O’Shea, D., Using Algebraic Geometry (Springer Verlag, New York, 1990).Google Scholar
Sangveraphunsiri, V. and Chooprasird, K., “Dynamics and control of a 5-DOF manipulator based on an H-4 parallel mechanism,” Int. J. Adv. Manufact. Technol. 52, 343–364 (2011).CrossRefGoogle Scholar
Amine, S., Masouleh, M. T., Caro, S., Wenger, P. and Gosselin, C., “Singularity analysis of 3T2R parallel mechanisms using Grassmann-Cayley algebra and Grassmann geometry,” Mech. Mach. Theory 52, 326–340 (2012).CrossRefGoogle Scholar
Pisla, D., Gherman, B., Vaida, C. and Plitea, N., “Kinematic modelling of a 5-DOF hybrid parallel robot for laparoscopic surgery,” Robotica 30, 1095–1107 (2012).CrossRefGoogle Scholar
Song, Y., Lian, B., Sun, T., Dong, G., Qi, Y. and Gao, H., “A novel five-degree-of-freedom parallel manipulator and its kinematic optimization,” ASME J. Mech. Robot. 6, Paper No: 041008 (2014).CrossRefGoogle Scholar
Ding, H., Cao, W., Cai, C. and Kecskeméthy, A., “Computer-aided structural synthesis of 5-DOF parallel mechanisms and the establishment of kinematic structure databases,” Mech. Mach. Theory 83, 14–30 (2015).CrossRefGoogle Scholar
Loizaga, M., Altuzarra, O., Pinto, C. and Petuya, V., “Control distribution of partially decoupled multi-level manipulators with five DOFs,” Robotica 35, 337–353 (2017).CrossRefGoogle Scholar
Gallardo-Alvarado, J., Orozco-Mendoza, H. and Rico-Martinez, J. M., “A novel five-degrees-of-freedom decoupled robot,” Robotica 28, 909–917 (2010).CrossRefGoogle Scholar
Gallardo-Alvarado, J., García-Murillo, M. and Castillo-Castaneda, E., “A 2(3-RRPS) parallel manipulator inspired by GoughStewart platform,” Robotica 31, 381–388 (2013).CrossRefGoogle Scholar
Wang, C., Fang, Y. and Fang, H., “Novel 2R3T and 2R2T parallel mechanisms with high rotational capability,” Robotica 35, 401–418 (2017).CrossRefGoogle Scholar
Xie, F., Liu, X.-J., Wang, J. and Wabner, M., “Kinematic optimization of a five degrees-of-freedom spatial parallel mechanism with large orientational workspace,” ASME J. Mech. Robot. 9, Paper No: JMR-16-1341 (2017).CrossRefGoogle Scholar
Cao, W., Ding, H. and Yang, D., “A method for compliance modeling of five degree-of-freedom overconstrained parallel robotic mechanisms with 3T2R output motion,” ASME J. Mech. Robot. 9, Paper No: JMR-16-1184 (2016).CrossRefGoogle Scholar
Kang, L., Kim, W. and Yi, B.-J., “Modeling and applications of a family of five-degree-of-freedom parallel mechanisms with kinematic and actuation redundancy,” ASME J. Mech. Robot. 10, Paper No: JMR-18-1065 (2018).CrossRefGoogle Scholar
Shayya, S., Krut, S., Company, O., Baradat, C. and Pierrot, F., “A novel (3T-2R) parallel mechanism with large operational workspace and rotational capability,” Proceedings 2014 IEEE International Conference on Robotics & Automation (ICRA), Hong Kong (2014) pp. 5712–5719.CrossRefGoogle Scholar
Gough, V. E. and Whitehall, S. G., “Universal Tire Test Machine,” Proceedings Institution of Technical Congress FISITA, London (1961) pp. 117–137.Google Scholar
Raghavan, M., “The Stewart platform of general geometry has 40 configurations,” ASME J. Mech. Des. 115, 277–282 (1993).CrossRefGoogle Scholar
Innocenti, C., “Forward kinematics in polynomial form of the general Stewart platform,” ASME J. Mech. Des. 123, 254–260 (2001).CrossRefGoogle Scholar
Merlet, J.-P., “Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis,” Int. J. Robot. Res. 23, 221–235 (2004).CrossRefGoogle Scholar
Rolland, L., “Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator,” Adv. Robot. 19, 995–1025 (2005).CrossRefGoogle Scholar
Gallardo-Alvarado, J., “A simple method to solve the forward displacement analysis of the general six-legged parallel manipulator,” Robot. Comput.-Integr. Manuf. 30, 55–61 (2014).CrossRefGoogle Scholar
Masouleh, M. T., Gosselin, C., Saadatzi, M. H., Kong, X. and Taghirad, H. D., “Kinematic analysis of 5-RPUR (3T2R) parallel mechanisms,” Meccanica 46, 131–146 (2011).CrossRefGoogle Scholar
Tsai, L.-W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (Wiley-Interscience, New York, 1999).Google Scholar
Sommese, A.-J. and Wampler, C.-W., The Numerical Solution of System of Polynomial Arising in Engineering and Science (World Scientific Publishing, Singapore, 2006).Google Scholar
Bates, J. D., Hauenstein, A. J., Sommese, A. J. and Wampler, C. W., Bertini: Software for numerical algebraic geometry. Available at http://www.nd.edu/-sommese/bertini.Google Scholar
Liu, C. H., Huang, K.-C. and Wang, Y.-T., “Forward position analysis of 6-3 Linapod parallel manipulators,” Meccanica 47, 1271–1282 (2012).CrossRefGoogle Scholar
Müller, A., “Problems in the control of redundantly actuated parallel manipulators caused by geometric imperfections,” Meccanica 46, 41–49 (2011).CrossRefGoogle Scholar
Gallardo-Alvarado, J., Kinematic Analysis of Parallel Manipulators by Algebraic Screw Theory (Springer International Publishing, New York, 2016).CrossRefGoogle Scholar
Gallardo-Alvarado, J., García-Murillo, M. A., Rodrguez-Castro, R. and Aguilar-Najera, C. R., “Velocity analysis of 5-RPUR parallel manipulators by means of screw theory,” Proceedings XVII Mexican Congress of Robotics, Mexico (2015) pp. 1–6.Google Scholar
Gosselin, C., Parenti-Castelli, V. and Pierrot, F., “Foreword: Fundamental issues and new trends in parallel mechanisms and manipulators,” Meccanica 46, 1–5 (2011).CrossRefGoogle Scholar