Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T16:49:50.220Z Has data issue: false hasContentIssue false
  • English
  • Français

Principle of Force Analysis of Overconstrained Parallel Mechanisms Considering Link Weight

Published online by Cambridge University Press:  18 February 2019

Yundou Xu ,
Ling Lu ,
Wenlan Liu ,
Jinwei Guo ,
Jiantao Yao  and
Yongsheng Zhao
Yundou Xu
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao, China
Ling Lu
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn School of Mechanical Engineering, Yanshan University, Qinhuangdao, China
Wenlan Liu
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn
Jinwei Guo
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn
Jiantao Yao
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao, China
Yongsheng Zhao*
Affiliation:
Parallel Robot and Mechatronic System Laboratory of Hebei Province, Yanshan University, Qinhuangdao, China. E-mails: ydxu@ysu.edu.cn, luling@ysu.edu.cn, 1063075717@qq.com, 1473733099@qq.com, jtyao@ysu.edu.cn Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao, China
*
*Corresponding author. E-mail: yszhao@ysu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Summary

The fundamental cause for the statically indeterminate problem in the force analysis of overconstrained parallel mechanisms (PMs) is found to be the presence of the linearly dependent overconstrained wrenches. Based on the fundamental cause, a unified expression of the solution for the magnitudes of the constraint wrenches of both the limb stiffness decoupled and limb stiffness coupled overconstrained PMs is derived. When the weight of each link is considered, depending on whether additional component forces are generated along the axes of the overconstrained wrenches, two different situations should be considered. One situation is that no additional component force is generated along the axes of the overconstrained wrenches under the weight of the links in the corresponding limb. In this case, the added constraint wrenches at the limb’s end can be calculated directly, and used as a part of the generalized external wrench. The other situation is that additional component forces are generated. In this case, the elastic deformations in the axes of the overconstrained wrenches generated by those component forces should be considered, and the deformation compatibility equations between the overconstrained wrenches are reformulated.

Keywords

OverconstrainedForce analysisConstrained wrenchesParallel mechanismStiffness matrix
Type
Articles
Information
Robotica , Volume 37 , Issue 9 , September 2019 , pp. 1533 - 1544
Copyright
© Cambridge University Press 2019 

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

Mavroidis, C. and Roth, B., “Analysis of overconstrained mechanisms,” J. Mech. Des. Trans. ASME 117, 69–74 (1995).CrossRefGoogle Scholar
Huang, Z. and Li, Q. C., “Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method,” Int. J. Rob. Res. 22, 59–79 (2003).Google Scholar
Fang, Y. F. and Tsai, L. W., “Enumeration of a class of overconstrained mechanisms using the theory of reciprocal screws,” Mech. Mach. Theory 39, 1175–1187 (2004).CrossRefGoogle Scholar
Dai, J. S., Huang, Z. and Lipkin, H., “Mobility of overconstrained parallel mechanisms,” J. Mech. Des. Trans. ASME 128, 220–229 (2006).CrossRefGoogle Scholar
Gan, D., Dai, J. S., Dias, J. and Seneviratne, L. D., “Variable motion/force transmissibility of a metamorphic parallel mechanism with reconfigurable 3T and 3R motion,” J. Mech. Rob. 8, 051001_1–9 (2016).Google Scholar
Gan, D., Dai, J. S., Dias, J. and Seneviratne, L. D., “Joint force decomposition and variation in unified inverse dynamics analysis of a metamorphic parallel mechanism,” Meccanica 51, 1583–1593 (2016).CrossRefGoogle Scholar
Bonnemains, T., Chanal, H., Bouzgarrou, B. C. and Ray, P., “Dynamic model of an overconstrained PKM with compliances: The Tripteor X7,” Rob. Comput. Integr. Manuf. 29, 180–191 (2013).CrossRefGoogle Scholar
Li, Y. M. and Staicu, S., “Inverse dynamics of a 3-PRC parallel kinematic machine,” Nonlinear Dyn. 67, 1031–1041 (2012).CrossRefGoogle Scholar
Wu, J., Chen, X. L. and Wang, L. P., “Dynamic load-carrying capacity of a novel redundantly actuated parallel conveyor,” Nonlinear Dyn. 78, 241–250 (2014).CrossRefGoogle Scholar
Müller, A., “Consequences of geometric imperfections for control of redundantly actuated parallel manipulators,” IEEE Trans. Rob. 26, 21–31 (2010).CrossRefGoogle Scholar
Liang, D., Song, Y. M., Sun, T. and Dong, G., “Optimum design of a novel redundantly actuated parallel manipulator with multiple actuation modes for high kinematic and dynamic performance,” Nonlinear Dyn. 83, 631–658 (2016).CrossRefGoogle Scholar
Cheng, C., Xu, W. L. and Shang, J. Z., “Optimal distribution of the actuating torques for a redundantly actuated masticatory robot with two higher kinematic pairs,” Nonlinear Dyn. 79, 1235–1255 (2014).CrossRefGoogle Scholar
Xu, Y. D., Yao, J. T. and Zhao, Y. S., “Internal forces analysis of the active overconstrained parallel manipulators,” Int. J. Rob. Autom. 30, 511–518 (2015).Google Scholar
Yao, J. T., Hou, Y. L., Chen, J., Lu, L. and Zhao, Y. S., “Theoretical analysis and experiment research of a statically indeterminate pre-stressed six-axis force sensor,” Sens. Actuators A. Phys. 150, 1–11 (2009).CrossRefGoogle Scholar
Kerr, D. R., Griffis, M., Sanger, D. J. and Duffy, J., “Redundant grasps, redundant manipulators, and their dual relationships,” J. Rob. Syst. 9, 973–1000 (1992).CrossRefGoogle Scholar
Vertechy, R. and Parenti-Castelli, V., “Static and stiffness analyses of a class of over-constrained parallel manipulators with legs of type US and UPS,” Proc. IEEE Int. Conf. Rob. Autom. 561–567 (2007).Google Scholar
Pashkevich, A., Chablat, D. and Wenger, P., “Stiffness analysis of overconstrained parallel manipulators,” Mech. Mach. Theory 44, 966–982 (2009).CrossRefGoogle Scholar
Bi, Z. M., “Kinetostatic modeling of Exechon parallel kinematic machine for stiffness analysis,” Int. J. Adv. Manuf. Technol. 71, 325–335 (2014).CrossRefGoogle Scholar
Alessandro, C., “Unified formulation for the stiffness analysis of spatial mechanisms,” Mech. Mach. Theory 105, 272–284 (2016).Google Scholar
Sun, T., Lian, B. and Song, Y., “Stiffness analysis of a 2-dof over-constrained RPM with an articulated traveling platform,” Mech. Mach. Theory 96, 165–178 (2016).CrossRefGoogle Scholar
Lian, B., Sun, T., Song, Y., Jin, Y. and Mark, P., “Stiffness analysis and experiment of a novel 5-DoF parallel kinematic machine considering gravitational effects,” Int. J. Mach. Tool Manu. 95, 82–96 (2015).CrossRefGoogle Scholar
Song, S. M. and Gao, X. C., “The mobility equation and the solvability of joint forces/torques in dynamic analysis,” J.Mech. Des. Trans. ASME 114, 257–262 (1992).CrossRefGoogle Scholar
Wojtyra, M., “Joint reaction forces in multibody systems with redundant constraints,” Multibody Syst. Dyn. 14, 23–46 (2005).CrossRefGoogle Scholar
Wojtyra, M. and Fraczek, J., “Solvability of reactions in rigid multibody systems with redundant nonholonomic constraints,” Multibody Syst. Dyn. 30, 153–171 (2013).CrossRefGoogle Scholar
Frączek, J. and Wojtyra, M., “On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and coulomb friction in joints,” Mech. Mach. Theory 46, 312–334 (2011).CrossRefGoogle Scholar
Wojtyra, M. and Frączek, J., “Joint reactions in rigid or flexible body mechanisms with redundant constraints,” Bull. Pol. Acad. Sci. Tech. Sci. 60, 617–626 (2012).Google Scholar
Wojtyra, M. and Fraczek, J., “Comparison of selected methods of handling redundant constraints in multibody systems simulations,” J. Comput. Nonlinear Dyn. 8, 021007-(1–9) (2013).Google Scholar
Zahariev, E. and Cuadrado, J., “Dynamics of mechanisms in over-constrained and singular configurations,” J. Theor. App. Mech-Pol. 41, 3–18 (2011).Google Scholar
Huang, Z., Zhao, Y. and Liu, J. F., “Kinetostatic analysis of 4-R(CRR) parallel manipulator with overconstraints via reciprocal-screw theory,” Adv. Mech. Eng. 2010, 1–11 (2010).Google Scholar
Xu, Y. D., Liu, W. L., Yao, J. T. and Zhao, Y. S., “A method for force analysis of the overconstrained lower mobility parallel mechanism,” Mech. Mach. Theory 88, 31–48 (2015).CrossRefGoogle Scholar
Liu, W. L., Xu, Y. D., Yao, J. T. and Zhao, Y. S., “Methods for force analysis of overconstrained parallel mechanisms: a review,” Chin. J. Mech. Eng. 30, 1460–1472 (2017).CrossRefGoogle Scholar
Liu, W. L., Xu, Y. D., Yao, J. T. and Zhao, Y. S., “The weighted Moore-Penrose generalized inverse and the force analysis of overconstrained parallel mechanisms,” Multibody Syst. Dyn. 39, 363–383 (2017).CrossRefGoogle Scholar
Xu, Y. D., Zhou, S. S., Yao, J. T. and Zhao, Y. S., “Rotational axes analysis of the 2-RPU/SPR 2R1T parallel mechanism,” Mech. Mach. Sci. 22, 113–121 (2014).CrossRefGoogle Scholar