Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T15:32:57.690Z Has data issue: false hasContentIssue false
  • English
  • Français

Enumeration and instantaneous mobility analysis of a class of 3-UPU parallel manipulators with equilateral triangular platforms

Published online by Cambridge University Press:  04 October 2021

Sercan Boztaş  and
Gökhan Kiper Open the ORCID record for Gökhan Kiper [Opens in a new window]
Sercan Boztaş
Affiliation:
Department of Mechanical Engineering, İzmir Institute of Technology, 35430 İzmir, Turkey
Gökhan Kiper*
Affiliation:
Department of Mechanical Engineering, İzmir Institute of Technology, 35430 İzmir, Turkey
*
*Corresponding author. E-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

In this study, several joint axis orientations on equilateral platforms and the limbs of 3-UPU parallel manipulators (PMs) are examined. The generated joint layouts for the platforms were matched with each other to generate and enumerate manipulator architectures based on certain assumptions. The structures of thus obtained manipulators are examined and limb types were determined. These limb types were analyzed using screw theory. The instantaneous mobility of the manipulators and the motion characteristics of the moving platforms are tabulated. The finite mobility analysis of one of the manipulators is performed using a software package as an example. Among several different 3-UPU PM architectures, 118 novel 3-UPU PMs with non-parasitic 3-degrees-of-freedom are significantly important. The classified 3-UPU PMs with determined motion characteristics can be used by researchers as a design alternative for their specific design task.

Keywords

Parallel manipulatorsenumerationinstantaneous mobility analysis
Type
Research Article
Information
Robotica , Volume 40 , Issue 5 , May 2022 , pp. 1538 - 1569
Copyright
© The Author(s) 2021. 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.)

Footnotes

Mr. Sercan Boztaş is currently at Research and Development Department, Dirinler Machinery Industry Co, 35620 İzmir, Turkey

References

Gao, X. S., Lei, D., Liao, Q. and Zhang, G. F., “Generalized Stewart-Gough platforms and their direct kinematics,” IEEE Trans. Robot. 21, 141–151 (2005).Google Scholar
Toz, M. and Kucuk, S., “Dimensional optimization of 6-DOF 3-CCC type asymmetric parallel manipulator,” Adv. Robot. 28(9), 625–637 (2014).CrossRefGoogle Scholar
Toz, M. and Kucuk, S., “Dexterous workspace optimization of an asymmetric six-degree of freedom Stewart–Gough platform type manipulator,” Rob. Auton. Syst. 61, 1516–1528 (2013).CrossRefGoogle Scholar
Tsai, L.-W., “Kinematics of a Three-Dof Platform with Three Extensible Limbs,” In: Recent Advances in Robot Kinematics. (Kluwer Academic Publisher, 1996) pp. 401–410.CrossRefGoogle Scholar
Yi, L., “Computer-aided geometric machining of a 3D free surface using a 3-UPU spatial parallel machine tool,” Int. J. Adv. Manuf. Tech. 26(9–10), 1018–1025 (2005).CrossRefGoogle Scholar
Qi, Z., Wang, H., Huang, Z. and Zhang, L., “Kinematics of a Quadruped/Biped Reconfigurable Walking Robot with Parallel Leg Mechanisms,” Proceedings ASME/IFToMM Int. Conf Reconfigurable Mechanisms and Robots, London (2009) pp. 558–564.Google Scholar
Li, S., Frisoli, A., Solazzi, M. and Bergamasco, M., “Mechanical Design and Optimization of a Novel fMRI Compatible Haptic Manipulator,” Proceedings 19th Int. Symp. Robot and Human Interactive Communication, Viareggio, Italy (2010) pp. 1–6.Google Scholar
Dehkordi, M., Frisoli, A., Sotgiu, E. and Bergamasco, M., “Modelling and experimental evaluation of a static balancing technique for a new horizontally mounted 3-UPU parallel mechanism,” Int. J. Adv. Robotic Sy. 9(5), 193 (2012).Google Scholar
Han, C., J., Kim, J. Kim and F. C. Park, “Kinematic sensitivity analysis of the 3-UPU parallel mechanism,” Mech. Mach. Theory 37(8), 787–798 (2002).CrossRefGoogle Scholar
Wolf, A. and Shoham, M., “Investigation of parallel manipulators using linear complex approximation,” ASME J. Mech. Des. 125(3), 564–572 (2003).CrossRefGoogle Scholar
Liu, G., Lou, Y. and Li, Z., “Singularities of parallel manipulators: a geometric treatment,” IEEE Trans, Robot, Autom. 19(4), 579–594 (2003).Google Scholar
Walter, D. R., Husty, M. L. and Pfurner, M., “The SNU 3-UPU parallel robot from a theoretical viewpoint,” Proceedings 2nd Int. Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Montpellier, France (2008).Google Scholar
Gogu, G. (2008) “Constraint Singularities and the Structural Parameters of Parallel Robots,” Advances in Robot Kinematics: Analysis and Design (Springer, 2008) pp. 21–28.CrossRefGoogle Scholar
Qu, H., Fang, Y. and Guo, S., “Parasitic rotation evaluation and avoidance of 3-UPU parallel mechanism,” Front. Mech. Eng. 7(2), 210–218, 2012.CrossRefGoogle Scholar
Bonev, I. and Zlatanov D, D., The Mystery of the Singular SNU Translational Parallel Robot. ParalleMIC-The Parallel Mechanisms Information Center, Report no 4, 2001.Google Scholar
Wolf, A., Shoham, M. and Park, F. C., “Investigation of Singularities and Self-Motions of the 3-UPU Robot,” Advances in Robot Kinematics (Springer, 2002) pp. 165–174.CrossRefGoogle Scholar
Zlatanov, D., Bonev, I. and Gosselin, C., “Constraint Singularities of Parallel Mechanisms,” Proceedings 2002 IEEE Int. Conf. Robotics and Automation, Washington, DC (2002) pp. 496–502.Google Scholar
Li, S. and Huang, Z., “Instantaneous Kinematic Characteristics of a Special 3-UPU Parallel Manipulator,” Proceedings ASME 29th Mechanisms and Robotics Conf., Long Beach, CA (2005) pp. 691–697.Google Scholar
Chen, Z., Zhang, Y., Huang, K. and Huang, Z., “Constraint and Mobility Analysis of the SNU 3-UPU Parallel Mechanism in Mixed Mode,” Advances in Reconfigurable Mechanisms and Robots II, Springer (2016) pp. 385–394.CrossRefGoogle Scholar
Wolf, A. and Shoham, M., “Screw theory tools for the synthesis of the geometry of a parallel robot for a given instantaneous task,” Mech. Mach. Theory 41(6), 656–670 (2006).CrossRefGoogle Scholar
Chen, Z., Zhang, Y., Huang, K., Ding, H. and Huang, Z., “Mobility and Motion Analysis of a Special 3-UPU Parallel Mechanism,” Proceedings 14th IFToMM World Congress, Taipei, ROC, vol. 4 (2015) pp. 256–263.Google Scholar
Tsai, L.-W. and Joshi, S., “Kinematics and optimization of a spatial 3-UPU parallel manipulator,” ASME J. Mech. Des. 122(4), 439–446 (2000).CrossRefGoogle Scholar
Tsai, L.-W. and Joshi, S., “Comparison Study of Architectures of Four 3 Degree-of-Freedom Translational Parallel Manipulators,” Proceedings 2001 IEEE Int. Conf. Robotics and Automation, Seoul, South Korea, vol. 2 (2001) pp. 1283–1288.Google Scholar
Joshi, S. and Tsai, L.-W., “Jacobian analysis of limited-dof parallel manipulators,” ASME J. Mech. Des, 124(2), 254–258, 2002.CrossRefGoogle Scholar
Parenti-Castelli, V., Di Gregorio, R. and Bubani, F., “Workspace and optimal design of a pure translation parallel manipulator,” Meccanica 35, 203–214 (2000).CrossRefGoogle Scholar
Kanaan, D., Wenger, P. and Chablat, D., “Singularity Analysis of Limited-Dof Parallel Manipulators Using Grassmann-Cayley Algebra,” Advances in Robot Kinematics: Analysis and Design (Springer, 2008) pp. 59–68.CrossRefGoogle Scholar
Kanaan, D., Wenger, P., Caro, S. and Chablat, D., “Singularity analysis of lower mobility parallel manipulators using Grassmann–Cayley algebra,” IEEE Trans. Robot. 25(5), 995–1004 (2009).CrossRefGoogle Scholar
Yang, Y. and OʼBrien, J. F., “A Geometric Approach for the Design of Singularity-Free Parallel Robots,” Proceedings 2009 IEEE Int. Conf. Robotics and Automation, Kobe, Japan (2009) pp. 1801–1806.Google Scholar
Joshi, S. and Tsai, L.-W., “A comparison study of two 3-DOF parallel manipulators: One with three and the other with four supporting legs,” IEEE Trans. Robot. Autom. 19(2), 200–209 (2003).CrossRefGoogle Scholar
Di Gregorio, R. and Parenti-Castelli, V., “Mobility analysis of the 3-UPU parallel mechanism assembled for a pure translational motion,” ASME J. Mech. Des. 124(2), 259–264 (2002).CrossRefGoogle Scholar
Zhao, J.-S., Feng, Z.-J. and Dong, J.-X., “Computation of the configuration degree of freedom of a spatial parallel mechanism by using reciprocal screw theory,” Mech. Mach. Theory 41(12), 1486–1504 (2006).CrossRefGoogle Scholar
Di Gregorio, R. and Parenti-Castelli, V., “A New Approach for the Evaluation of Kinematic and Static Performances of a Family of 3-UPU Translational Manipulators,” Romansy 16 (Springer, 2006) pp. 47–54.CrossRefGoogle Scholar
Walter, D. R. and Husty, M., “Kinematic Analysis of the Tsai-3UPU Parallel Manipulator Using Algebraic Methods,” Proceedings 13th World Congress in Mechanism and Machine Science, Guanajuato, Mexico (2011) pp. 19–25.Google Scholar
Yang, Y. and OʼBrien, J. F., “Singularity-Free Workspace Design for the Translational 3-UPU Parallel Robot,” 2010 IEEE Int. Conf. Automation Science and Engineering, Toronto, Canada (2010) pp. 222–227.Google Scholar
Bałchanowski, J., “Some aspects of topology and kinematics of a 3DOF translational parallel mechanism,” Int. J. Appl. Mech. Eng. 19(1), 5–15 (2014).CrossRefGoogle Scholar
Guan, L.-W., Wang, J.-S. and Wang, L.-P., “Mobility Analysis of the 3-UPU Parallel Mechanism Based on Screw Theory,” Proceedings 2004 IEEE Int. Conf. Intelligent Mechatronics and Automation, Chengdu, PRC (2004) pp. 309–314.Google Scholar
Zhao, J.-S., Feng, Z.-J., Zhou, K. and Dong, J.-X., “Analysis of the singularity of spatial parallel manipulator with terminal constraints,” Mech. Mach. Theory 40(3), 275–284 (2005).CrossRefGoogle Scholar
Badescu, M. and Mavroidis, C., “Workspace optimization of 3-legged UPU and UPS parallel platforms with joint constraints,” ASME J. Mech. Des. 126(2), 291–300 (2004).CrossRefGoogle Scholar
Chebbi, A., Affi, Z. and Romdhane, L., “Prediction of the pose errors produced by joints clearance for a 3-UPU parallel robot,” Mech. Mach. Theory 44(9), 1768–1783 (2009).CrossRefGoogle Scholar
Bi, J. and Wen, R., (2010) Errors Analysis of 3-UPU Parallel Manipulator Using Screw Theory,” Proceeding Int. Conf. Measuring Technology and Mechatronics Automation, Changsha, PRC (2010) pp. 137–140.Google Scholar
Wang, N., Guo, S., Fang, Y. and Li, X., “Error Sensibility Analysis of 3-UPU Parallel Manipulator Based on Probability Distribution,” Proceedings 2nd Int. Conf. Mechanic Automation and Control Engineering, Hohhot, PRC (2011) pp. 1296–1301.Google Scholar
Sun, S. H., “Accuracy analysis of 3-UPU translational parallel robot mechanism,” Adv. Mat. Res. 694–697, 1617–1620 (2013).Google Scholar
Bhutani, G. and Dwarakanath, T., “Novel design solution to high precision 3 axes translational parallel mechanism,” Mech. Mach. Theory 75, 118–130 (2014).CrossRefGoogle Scholar
Guohua, C., Bin, W., Nan, W. and Yanwei, Z., “Stiffness, workspace analysis and optimization for 3UPU parallel robot mechanism,” Indones. J. Electrical Eng. Comput. Sci. 11(9), 5253–5261 (2013).Google Scholar
Aboulissane, B. and El Bakkali, L., “Modeling and simulation of spatial mechanism,” Proceedings Xth Int. Conf. Integrated Design and Production, Tangier, Morocco (2015).Google Scholar
Laribi, M., Mlika, A., Romdhane, L. and Zeghloul, S., “Geometric and Kinematic Performance Analysis and Comparison of Three Translational Parallel Manipulators,” Proceedings 14th IFToMM World Congress, Taipei, ROC, vol. 2 (2015) pp. 565–571.Google Scholar
Wei, Y., Fan, Y., Li, Q. and Wang, Z., “Structure optimization design of 3-UPU parallel mechanism based on the comprehensive dexterity.” Recent Adv. Electr. Electron. Eng. 8(1), 26–32 (2015).Google Scholar
Karouia, M. and Hervé, J., “A Three-Dof Tripod for Generating Spherical Rotation,” Advances in Robot Kinematics (Springer, 2000) pp. 395–402.CrossRefGoogle Scholar
Di Gregorio, R., “Kinematics of the 3-UPU wrist,” Mech. Mach. Theory 38(3), 253–263 (2003).CrossRefGoogle Scholar
Di Gregorio, R., “Statics and singularity loci of the 3-UPU wrist,” IEEE Trans. Robot. 20, 630–635 (2004).CrossRefGoogle Scholar
Paganelli, D., “Avoiding Parallel Singularities of 3UPS and 3UPU Spherical Wrists,” Proceedings 2007 IEEE Int. Conf. Robotics and Automation, Rome, Italy (2007) pp. 1201–1206.Google Scholar
Chebbi, A., Affi, Z. and Romdhane, L., “Modelling and analysis of the 3-UPU spherical manipulator,” Eur. J. Comput. Mech. 22(2–4), 157–169 (2013).CrossRefGoogle Scholar
Pramanik, S. and Ghosal, A., “Development of a sun tracking system using a 3-UPU spherical wrist manipulator,” Proceedings 2nd Int. and 17th Nati Conf. Machines and Mechanisms, Kanpur, India (2015).Google Scholar
Xiangzhou, Z., Hongzan, B. and Yougao, L., “Kinematics of 3-UPU parallel manipulator with a pure spherical motion based on quaternion transformation,” Adv. Syst. Sci. Appl. 6(2), 334–340 (2006).Google Scholar
Xiangzhou, Z., Yougao, L. and Hongzan, B., “Inverse Dynamics of 3-UPU Parallel Mechanism with Pure Rotation Based on DʼAlembert Principle,” Proceedings 2007 IEEE Int. Conf. Mechatronics and Automation, Harbin, PRC (2007) pp. 2842–2847.Google Scholar
Ashith Shyam, R. B. and Ghosal, A., “Path planning of a 3-UPU wrist manipulator for sun tracking in central receiver tower systems,” Mech. Mach. Theory 119, 130–141 (2018).CrossRefGoogle Scholar
Huang, Z. and Li, Q., “Construction and Kinematic Properties of 3-UPU Parallel Mechanisms,” Proceedings ASME 27th Biennial Mechanisms and Robotics Conf., Montreal, Canada (2002) pp. 1027–1033.Google Scholar
Kiper, G. and Söylemez E, E., “Kinematic Analysis of a 3-UPU Parallel Manipulator Using Exponential Rotation Matrices,” Machines and Mechanisms, Narosa, New Delhi, India (2012) pp. 123–131.Google Scholar
Guo, S., Wang, N., Fang, Y. and Li, X., “Study on Error Sensibility of UPU Parallel Manipulator Based on Probability Distribution,” Proceedings 2011 IEEE Int. Conf. Mechatronics and Automation, Beijing, PRC (2011) pp. 2045–2050.Google Scholar
Huang, Z., Li, S. and Zuo, R., “Feasible instantaneous motions and kinematic characteristics of a special 3-dof 3-UPU parallel manipulator,” Mech. Mach. Theory 39(9), 957–970 (2004).CrossRefGoogle Scholar
Yu, J., Dai, J., Zhao, T., Bi, S. and Zong, G., “Mobility analysis of complex joints by means of screw theory,” Robotica 27(6), 915–927 (2009).CrossRefGoogle Scholar
Binbin, P., Zengming, L., Kai, W. and Yu, S., “Kinematic characteristics of 3-UPU parallel manipulator in singularity and its application,” Int. J. Adv. Robot. Syst. 8(4), 54–64 (2011).CrossRefGoogle Scholar
Miao, Z., Yao, Y. and Kong, X., “A rolling 3-UPU parallel mechanism,” Front. Mech. Eng. 8, 340–349 (2013).CrossRefGoogle Scholar
Zhao, J.-S., Feng, Z.-J., Zhou, K. and Jin, D.-W., “Re-analysis of the degree-of-freedom configuration of the platforms in spatial parallel mechanisms with constraints spaces,” Int. J. Adv. Manuf. Technol. 28, 190–196 (2006).Google Scholar
Lu, Y. and Hu, B., “Analysis of kinematics and solution of active/constrained forces of asymmetric 2UPU+X parallel manipulators,” Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 220(12), 1819–1830 (2006).CrossRefGoogle Scholar
Lu, Y., Shi, Y. and Hu, B., “Kinematic analysis of two novel 3UPU I and 3UPU II PKMs,” Robot. Auton. Syst. 56(4), 296–305 (2008).CrossRefGoogle Scholar
Hu, B. and Lu, Y., “Solving stiffness and deformation of a 3-UPU parallel manipulator with one translation and two rotations,” Robotica 29(6), 815–822 (2011).CrossRefGoogle Scholar
Chebbi, A. and Parenti-Castelli, V., “Potential of the 3-UPU Translational Parallel Manipulator,” Proceedings ASME 34th Annual Mechanisms and Robotics Conf., Montreal, Canada (2010) pp. 1089–1099.Google Scholar
Wang, M. and Ceccarelli, M., “Design and simulation for kinematic characteristics of a tripod mechanism for biped robots,” Int. J. Mech. Control 15(1), 11–18 (2013).Google Scholar
Wang, M., Carbone, G. and Ceccarelli, M., “Stiffness analysis for a tripod leg mechanism,” Proceedings 14th IFToMM World Congress, Taipei, ROC, vol. 2 (2015).Google Scholar
Wang, M., Ceccarelli, M. and Carbone, G., “A feasibility study on the design and walking operation of a biped locomotor via dynamic simulation,” Front. Mech. Eng. 11(2), 144–158 (2016).CrossRefGoogle Scholar
Wang, M., Ceccarelli, M. and Carbone, G., “Design and development of the Cassino biped locomotor,” ASME J. Mech. Robot. 12(3), 031001 (2020).CrossRefGoogle Scholar
Sarabandi, S., Grosch, P., Porta, J. M. and Thomas, F., “A Reconfigurable Asymmetric 3-UPU Parallel Robot,” Proceedings 2018 Int. Conf. Reconfigurable Mechanisms and Robots, Delft, Netherlands (2018) pp. 404–410.Google Scholar
Zhao, C., Chen, Z., Li, Y. and Huang, Z., “Motion characteristics analysis of a novel 2R1T 3-UPU parallel mechanism,” ASM. J. Mech. Des., 142(1), 012302, 2020.CrossRefGoogle Scholar
Di Gregorio, R., “A review of the literature on the lower-mobility parallel manipulators of 3-UPU or 3-URU type,” Robotics, 9(1), 5 (2020).CrossRefGoogle Scholar
Dai, J. and Jones, J., “A linear algebraic procedure in obtaining reciprocal screw systems,” J. Robotic Syst. 20, 401–412 (2003).CrossRefGoogle Scholar
Zhao, J.-S., Feng, Z.-J., Chu, F. and Ma, N., Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms (Academic Press, 2013).Google Scholar
Gezgin, E., Biokinematic Analysis of Human Arm, İzmir Institute of Technology MSc Thesis (2006).Google Scholar