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On the Maximization of Joint Velocities and Generalized Reactions in the Workspace and Singularity Analysis of Parallel Mechanisms

Published online by Cambridge University Press:  14 December 2018

Pavel Laryushkin Open the ORCID record for Pavel Laryushkin [Opens in a new window] ,
Victor Glazunov  and
Ksenia Erastova
Pavel Laryushkin
Affiliation:
Fundamentals of Machine Design Department, Bauman Moscow State Technical University, 2-ya Baumanskaya st. 5, Moscow 105005, Russia. E-mail: pav.and.lar@gmail.com
Victor Glazunov
Affiliation:
Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), Maly Kharitonyevsky Pereulok 4, Moscow 101990, Russia. E-mail: vaglznv@mail.ru
Ksenia Erastova*
Affiliation:
Fundamentals of Machine Design Department, Bauman Moscow State Technical University, 2-ya Baumanskaya st. 5, Moscow 105005, Russia. E-mail: pav.and.lar@gmail.com
*
*Corresponding author. E-mail: erastovakg@gmail.com
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Summary

An approach for calculating the maximum possible absolute values of joint velocities or generalized reactions in a leg of a parallel mechanism has been considered in this paper. The Jacobian analysis and the Screw theory-based methods have been used to acquire the result. These values are calculated for the “worst” directions of the external load or end-effector’s velocity for each leg. The feasibility of using these parameters as the measures of closeness to different types of parallel mechanism singularity is discussed. Further, how this approach is related to the state-of-the-art methods has been illustrated. The key aspect of the discussed approach is that the normalization of vectors or screws is carried out separately for angular and linear components. One possible advantage of such an approach is that it deals only with the kinematic and statics of the mechanism while still providing physically meaningful and practically applicable measures. Case studies of a 3-Degrees Of Freedom translational parallel mechanism and a planar parallel mechanism are presented for illustration and comparison.

Keywords

Parallel mechanismWorkspaceCloseness to singularitySingularity analysisScrew theoryJacobian
Type
Articles
Information
Robotica , Volume 37 , Issue 4 , April 2019 , pp. 675 - 690
Copyright
Copyright © Cambridge University Press 2018 

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References

Merlet, J.-P., Parallel Robots, 2nd edition (Springer, Dordrecht, Netherlands, 2006), 402 pp.Google Scholar
Gosselin, C. M. and Schreiber, L., “Kinematically redundant spatial parallel mechanisms for singularity avoidance and large orientational workspace,” IEEE Trans. Robot. 32(2), 286–300 (2016).10.1109/TRO.2016.2516025CrossRefGoogle Scholar
Di Gregorio, R., “Kinematics analysis and singularities of novel decoupled parallel manipulators with simplified architecture,” Robotica 35(4), 961–979 (2017).10.1017/S0263574715000910CrossRefGoogle Scholar
Mayer, St-Onge B. and Gosselin, C. M., “Singularity analysis and representation of the General Gough–Stewart platform,” Int. J. Robot. Res. 19(3), 271–288 (2000).Google Scholar
Merlet, J.-P., “Singular configurations of parallel manipulators and Grassmann geometry,” Int. J. Robot. Res. 8(5), 45–56 (1989).10.1177/027836498900800504CrossRefGoogle Scholar
Chablat, D., Wenger, Ph. and Angeles, J., “The Isoconditioning Loci of a Class of Closed-Chain Manipulators,” Proceedings of the IEEE International Conference on Robotics and Automation, Anchorage, AK, USA (2010) pp. 1970–1976.Google Scholar
O’Brien, J. F. and Wen, J. T., “Kinematic Control of Parallel Robots in the Presence of Unstable Singularities,” Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, South Korea (2001) pp. 3154–3159.Google Scholar
Sen, S., Dasgupta, B. and Mallik, A. K., “Variational approach for singularity-path planning of parallel manipulators,” Mech. Mach. Theory 38(11), 1165–1183 (2003).10.1016/S0094-114X(03)00065-XCrossRefGoogle Scholar
Bhattacharya, S., Hatwal, H. and Ghosh, A., “Comparison of an exact and an approximate method of singularity avoidance in platform type parallel manipulators,” Mech. Mach. Theory 33(7), 965–974 (1998).10.1016/S0094-114X(97)00066-9CrossRefGoogle 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).10.1115/1.2912772CrossRefGoogle Scholar
Merlet, J.-P., “Jacobian, manipulability, condition number, and accuracy of parallel robots,” J. Mech. Des. 128(1), 199–205 (2006).10.1115/1.2121740CrossRefGoogle Scholar
Chen, C. and Angeles, J., “A Generalized Transmission Index for Spatial Linkages,” 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).10.1016/S0094-114X(01)00067-2CrossRefGoogle Scholar
Alba-Gomez, O., Wenger, P. and Pamanes, A., “Consistent Kinetostatic Indices for Planar 3-DOF Parallel Manipulators, Application to the Optimal Kinematic Inversion,” 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 High-speed Machining Applications,” Proceedings of the 2010 IEEE International Conference on Robotics and Automation (ICRA 2010), Anchorage, AK, USA (2010) pp. 1155–1161.10.1109/ROBOT.2010.5509543CrossRefGoogle Scholar
Sutherland, G. and Roth, B., “A transmission index for spatial mechanisms,” J. Manuf. Sci. Eng. 95(2), 589–597 (1973).Google Scholar
Gosselin, C. M. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Rob. Autom. 6(3), 281–290 (1990).10.1109/70.56660CrossRefGoogle Scholar
Zlatanov, D., Fenton, R. G. and Benhabib, B., “A unifying framework for classification and interpretation of mechanism singularities,” J. Mech. Design 117(4), 566–572 (1995).10.1115/1.2826720CrossRefGoogle Scholar
Hubert, J. and Merlet, J.-P., “Static of parallel manipulators and closeness to singularity,” J. Mech. Robot. 1(1), 011011 (2008).10.1115/1.2961335CrossRefGoogle Scholar
Voglewede, P. A. and Ebert-Uphoff, I., “Measuring “Closeness” to Singularities for Parallel Manipulators,” 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).10.1109/TRO.2005.855993CrossRefGoogle Scholar
Pierrot, F., “Parallel Mechanisms and Redundancy,” Proceedings of the 1st International Colloquium, Collaborative Research Centre 562, Braunschweig, Germany (2002) pp. 261–277.Google Scholar
Dimentberg, F. M., The Screw Calculus and Its Applications in Mechanics (Foreign Technology Division, Springfield, VA, USA, 1968) 155 pp.Google Scholar
Mohamed, M. G. and Duffy, J., “A direct determination of the instantaneous kinematics of fully parallel robot manipulators,” ASME J. Mech. Transm. Autom. Des. 107(2), 226–229 (1985).10.1115/1.3258713CrossRefGoogle Scholar
Zlatanov, D., Bonev, I. A. and Gosselin, C. M., “Constraint Singularities of Parallel Mechanisms,” Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC, USA (2002) pp. 496–502.Google Scholar
Laryushkin, P., Glazunov, V. and Demidov, S., “Singularity Analysis of 3-DOF Translational Parallel Manipulator,” Advances on Theory and Practice of Robots and Manipulators. Proceedings of ROMANSY 2014 XX CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, Moscow, Russia (2014) pp. 47–54.Google Scholar
Bonev, I. and Gosselin, C., “Singularity Loci of Planar Parallel Manipulators with Revolute Joints,” Proceedings of the 2nd Workshop on Computational Kinematics, Seoul, South Korea (2001) pp. 1–11.Google Scholar