Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T18:20:39.826Z Has data issue: false hasContentIssue false
  • English
  • Français

Effective workspaces of parallel robots

Published online by Cambridge University Press:  27 June 2022

Ksenia Erastova Open the ORCID record for Ksenia Erastova [Opens in a new window]
Ksenia Erastova*
Affiliation:
Fundamentals of Machine Design Department, Bauman Moscow State Technical University, 2-ya Baumanskaya st. 5, Moscow 105005, Russia
*
E-mail: erastovakg@bmstu.ru
Get access Rights & Permissions [Opens in a new window]

Abstract

An approach for calculating the effective workspaces of parallel mechanisms has been considered in this paper. The effective workspace is a set of reachable by the end-effector points, where an important parameter (or parameters) from the point of view of operation is not higher than critical. In this article, the speed and torque in the drive and the stiffness of the mechanism are considered as such parameters. An approach to determining the appropriate effective workspace is presented for each parameter. The optimization process, which is based on presented methods, allows one to choose basic technical solutions of the designed robot: the links (lengths and cross-sections), the drives, and types of hinges, which guarantee its operability at the specified operational characteristics. Case studies of a delta robot with four degrees of freedom and a planar five-bar mechanism are presented for testing these approaches. The presented methods are of great practical importance because it uses movement parameters or operational characteristics that are decisive for this mechanism and have clear physical meaning.

Keywords

parallel mechanismrobotics designworkspacestiffnesscloseness to singularityJacobiandelta robotfive-bar mechanism
Type
Research Article
Information
Robotica , Volume 40 , Issue 12 , December 2022 , pp. 4308 - 4325
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Merlet, J.-P., Parallel Robots. Springer, (2006).Google Scholar
Kumar, V., “Characterization of workspaces of parallel manipulators,” ASME J. Mech. Des. 114(3), 368–375 (1992).CrossRefGoogle Scholar
Gosselin, C. M. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” J. Mech. Des 113(3), 220–226 (1991).CrossRefGoogle Scholar
Merlet, J.-P., “Jacobian, manipulability, condition number, and accuracy of parallel robots,” J. Mech. Des. 128(1), 199–205 (2006).CrossRefGoogle Scholar
Chen, C. and Angeles, J., “A Generalized Transmission Index for Spatial Linkages,” In: Proceedings of the ASME, 2005 IDETC/CIE Conference, Long Beach, CA, USA (2005) pp. 749–756.Google Scholar
Balli, S. and Chand, S., “Transmission angle in mechanisms,” Mech. Mach. Theory 37(2), 175–195 (2002).CrossRefGoogle Scholar
Alba-Gomez, O., Wenger, P. and Pamanes, A., “Consistent Kinetostatic Indices for Planar 3-DOF Parallel Manipulators, Application to the Optimal Kinematic Inversion,” In: Proceedings of the ASME, 2005 IDETC/CIE Conference, Long Beach, CA, USA (2005) pp. 765–774.Google Scholar
Briot, S., Pashkevich, A. and Chablat, D., “Optimal Technology-oriented Design of Parallel Robots for Highspeed Machining Applications,” In: Proceedings of the 2010 IEEE International Conference on Robotics and Automation (ICRA 2010), Anchorage, AK, USA (2010) pp. 1155–1161.Google Scholar
Sutherland, G. and Roth, B., “A transmission index for spatial mechanisms,” J. Manuf. Sci. Eng. 95(2), 589–597 (1973).Google Scholar
Laryushkin, P. A., Rashoyan, G. V. and Erastova, K. G., “On the features of applying the theory of screws to the evaluation of proximity to specific positions of the mechanisms of parallel structure,” J. Mach. Manuf. Reliab. 46(4), 349–355 (2017).CrossRefGoogle Scholar
Laryushkin, P., Antonov, A., Fomin, A. and Essomba, T., “Velocity and singularity analysis of a 5-DOF (3T2R) parallel-serial (hybrid) manipulator,” Machines 10(4), 246 (2022).CrossRefGoogle Scholar
Wang, J., Wu, C. and Liu, X. J., “Performance evaluation of parallel manipulators: motion/force transmissibility and its index,” Mech. Mach. Theory 45(10), 1462–1476 (2010).CrossRefGoogle Scholar
Yang, C., Ye, W. and Li, Q., “Review of the performance optimization of parallel manipulators,” Mech. Mach. Theory 170, 104725 (2022).CrossRefGoogle Scholar
Voglewede, P. A. and Ebert-Uphoff, I., “Measuring “Closeness” to Singularities for Parallel Manipulators,” In: Proceedings of the 2004 IEEE International Conference on Robotics and Automation, New Orleans, LA, USA (2004) pp. 4539–4544.Google Scholar
Voglewede, P. A. and Ebert-Uphoff, I., “Overarching framework for measuring closeness to singularities of parallel manipulators,” IEEE Trans. Robot 21(6), 1037–1045 (2005).CrossRefGoogle Scholar
Glozman, D. and Shoham, M., “Novel 6DOF parallel manipulator with large workspace,” Robotica 27(6), 891–895 (2009).CrossRefGoogle Scholar
Carretero, J. A., Nahon, M. A. and Podhorodeski, R. P., “Workspace analysis and optimization of a novel 3-DOF parallel manipulator,” Int. J. Rob. Automat. 15(4), 178–188 (2000).Google Scholar
Pickard, J. and Carretero, J. A., “Design Optimisation of the 3-RRR Planar Parallel Manipulator Via Wrench Capability Analysis,” In: 14th World Congress in Mechanism and Machine Science, Taipei, Taiwan (2015).Google Scholar
Merlet, J.-P., “Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries,” Int. J. Rob. Res. 18(9), 902–916 (1999).CrossRefGoogle Scholar
Laryushkin, P. A., Erastova, K. G., Filippov, G. S. and Kheylo, S. V., “Calculation of delta-type mechanisms with linear actuators and different numbers of degrees of freedom,” J. Mach. Manuf. Reliab. 48(3), 204–210 (2019).CrossRefGoogle Scholar
Kiselev, S. V., Antonov, A. V. and Fomin, A. S., “Parallel robots with a circular guide: Systematic review of kinematic schemes and methods of synthesis and analysis,” J. Mach. Manuf. Reliab. 51(1), 20–29 (2022).CrossRefGoogle Scholar
Laryushkin, P. A., Glazunov, V. and Erastova, K. G., “On the maximization of joint velocities and generalized reactions in the workspace and singularity analysis of parallel mechanisms,” Robotica 37(4), 675–690 (2019).CrossRefGoogle Scholar
Hubert, J. and Merlet, J.-P., “Static of parallel manipulators and closeness to singularity,” J. Mech. Robot. 1(1), 011011 (2008).CrossRefGoogle Scholar
Ki, W., Byoung, J. and Dong-Soo, K., “A 6-DOF force-reflecting hand controller using the fivebar parallel mechanism,” Robot. Autom. IEEE Int. Conf. 2, 1597–1602 (1998).Google Scholar
Briot, S., Glazunov, V. and Arakelian, V., “On the Design Conditions of Planar Parallel Manipulators in Near-Singular Configurations,” In: 13th World Congress in Mechanism and Machine Science, Guanajuato, Mexico (June 2011) pp.Google Scholar
Gosselin, C. and Angeles, J., “Singularity analysis of closed-loop kinematic chains”,” IEEE Trans. Robot. Autom. 6(3), 281–290 (1990).CrossRefGoogle Scholar
Quennouelle, C. and Gosselin, C. M., “A general formulation for the stiffness matrix of parallel mechanisms,”arXiv: 1212.0950 [physics.class-ph], 2012.Google Scholar
Pashkevich, A., Klimchik, A. and Chablat, D., “Enhanced stiffness modeling of manipulators with passive joints,” Mech. Mach. Theory 46(5), 662–679 (2010).CrossRefGoogle Scholar
Goncalves, R. S., Carbone, G., Carvalho, J. C. M. and Ceccarelli, M., “A comparison of stiffness analysis methods for robotic systems,” Int. J. Mech. Control 17(2), 35–58 (2010).Google Scholar
Carbone, G., “Stiffness analysis and experimental validation of robotic systems,” Front. Mech. Eng. 6(2), 182–196 (2011).Google Scholar
Ceccarelli, M.. Fundamentals of Mechanics of Robotic Manipulation (Kluwer, Dordrecht, 2004).CrossRefGoogle Scholar
Taghvaeipour, A., Angeles, J. and Lessard, L., “Computation of the Stiffness Matrix in Robotic Structures Using Finite Element Analysis,” In: Department of Mechanical Engineering and Centre for Intelligent Machines (McGill University, Canada, 2010).Google Scholar
Gonçalves, R. S. and Carvalho, J. C. M., “Singularities of Parallel Robots Using Matrix Structural Analysis,” In: Proc. of the XIII Int. Symp. on Dynamic Problems of Mechanics, Angra dos Reis, RJ, Brazil (2009).Google Scholar
Kassimali, A.. Matrix Analysis of Structures (Cengage Learning“, 2012) pp. 657–p.Google Scholar
Clavel, R., Conception d’un Robot Parallèle Rapide à 4 Degrés de Liberté: PhD thesis (École Polytechnique Fédérale de Lausanne, (1991)).Google Scholar
Clavel, R., “Device for the Movement and Positioning of an Element in Space, Patent no. 4976582 US, 1990.Google Scholar
Laryushkin, P., “Experimental study of force transfer in a delta-type mechanism with four degrees of freedom,” J. Mach. Manuf. Reliabil. 50(5), 379–387 (2021).Google Scholar
Cui, G., Zhou, H., Wang, N. and Zhang, H., “Multi-objective optimization of 3-UPS-S parallel mechanism based on isight,” Nongye Jixie Xuebao/Trans. Chin. Soc. Agric. Mach. 44, 261–266 (2013).Google Scholar
Chen, Q. and Yang, C., “Hybrid algorithm for multi-objective optimization design of parallel manipulators,” Appl. Math. Model 98(3), 245–265 (2021).CrossRefGoogle Scholar
Essomba, T., Sandoval, A., Juan, S., Laribi, M. A. and Zeghloul, S., “Multi-objective optimization of a reconfigurable spherical parallel mechanism for tele-operated craniotomy” (2020).CrossRefGoogle Scholar