Research Papers

A Method for Compliance Modeling of Five Degree-of-Freedom Overconstrained Parallel Robotic Mechanisms With 3T2R Output Motion

[+] Author and Article Information
Wen-ao Cao

School of Mechanical Engineering and
Electronic Information,
China University of Geosciences (Wuhan),
Wuhan 430074, China
e-mail: cwao1986@163.com

Huafeng Ding

School of Mechanical Engineering and
Electronic Information,
China University of Geosciences (Wuhan),
Wuhan 430074, China
e-mail: dhf@ysu.edu.cn

Donghao Yang

School of Mechanical Engineering and
Electronic Information,
China University of Geosciences (Wuhan),
Wuhan 430074, China
e-mail: yangdh9311@163.com

1Corresponding author.

Manuscript received June 24, 2016; final manuscript received November 9, 2016; published online December 22, 2016. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 9(1), 011011 (Dec 22, 2016) (11 pages) Paper No: JMR-16-1184; doi: 10.1115/1.4035270 History: Received June 24, 2016; Revised November 09, 2016

This paper presents an approach to compliance modeling of three-translation and two-rotation (3T2R) overconstrained parallel manipulators, especially for those with multilink and multijoint limbs. The expressions of applied wrenches (forces/torques) exerted on joints are solved with few static equilibrium equations based on screw theory. A systematic method is proposed for deriving the stiffness model of a limb with considering the couplings between the stiffness along the constrained wrench and the one along the actuated wrench based on strain energy analysis. The compliance model of a 3T2R overconstrained parallel mechanism is established based on stiffness models of limbs and the static equilibrium equation of the moving platform. Comparisons show that the compliance matrix obtained from the method is close to the one obtained from a finite-element analysis (FEA) model. The proposed method has the characteristics of involving low computational efforts and considering stiffness couplings of each limb.

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Gosselin, C. , 1990, “ Stiffness Mapping for Parallel Manipulators,” IEEE Trans. Rob. Autom., 6(3), pp. 377–382. [CrossRef]
Griffis, M. , and Duffy, J. , 1993, “ Global Stiffness Modeling of a Class of Simple Compliant Couplings,” Mech. Mach. Theory, 28(2), pp. 207–224. [CrossRef]
Bhattacharya, S. , Hatwal, H. , and Ghosh, A. , 1995, “ On the Optimum Design of Stewart Platform Type Parallel Manipulators,” Robotica, 13(2), pp. 133–140. [CrossRef]
El-Khasawneh, B. S. , and Ferreira, P. M. , 1999, “ Computation of Stiffness and Stiffness Bounds for Parallel Link Manipulators,” Int. J. Mach. Tools Manuf., 39(2), pp. 321–342. [CrossRef]
Ceccarelli, M. , and Carbone, G. , 2002, “ A Stiffness Analysis for CaPaMan (Cassino Parallel Manipulator),” Mech. Mach. Theory, 37(5), pp. 427–439. [CrossRef]
Huang, T. , Zhao, X. , and Whitehouse, D. J. , 2002, “ Stiffness Estimation of a Tripod-Based Parallel Kinematic Machine,” IEEE Trans. Rob. Autom., 18(1), pp. 50–58. [CrossRef]
Hu, B. , Yu, J. , Lu, Y. , Sui, C. , and Han, J. , 2012, “ Statics and Stiffness Model of Serial-Parallel Manipulator Formed by k Parallel Manipulators Connected in Series,” ASME J. Mech. Rob., 4(2), p. 0210121. [CrossRef]
Yoon, W.-K. , Suehiro, T. , Tsumaki, Y. , and Uchiyama, M. , 2004, “ Stiffness Analysis and Design of a Compact Modified Delta Parallel Mechanism,” Robotica, 22(4), pp. 463–475. [CrossRef]
Dai, J. S. , and Ding, X. , 2005, “ Compliance Analysis of a Three-Legged Rigidly-Connected Platform Device,” ASME J. Mech. Des., 128(4), pp. 755–764. [CrossRef]
Majou, F. , Gosselin, C. , Wenger, P. , and Chablat, D. , 2007, “ Parametric Stiffness Analysis of the Orthoglide,” Mech. Mach. Theory, 42(3), pp. 296–311. [CrossRef]
Xu, Q. , and Li, Y. , 2008, “ An Investigation on Mobility and Stiffness of a 3-DOF Translational Parallel Manipulator Via Screw Theory,” Rob. Comput. Integr. Manuf., 24(3), pp. 402–414. [CrossRef]
Wang, Y. , Liu, H. , Huang, T. , and Chetwynd, D. G. , 2009, “ Stiffness Modeling of the Tricept Robot Using the Overall Jacobian Matrix,” ASME J. Mech. Rob., 1(2), p. 021002. [CrossRef]
Gosselin, C. M. , and Zhang, D. , 2002, “ Stiffness Analysis of Parallel Mechanisms Using a Lumped Model,” Int. J. Rob. Autom., 17(1), pp. 17–27.
Zhang, D. , and Gosselin, C. M. , 2002, “ Kinetostatic Analysis and Design Optimization of the Tricept Machine Tool Family,” ASME J. Manuf. Sci. Eng., 124(3), pp. 725–733. [CrossRef]
Zhang, D. , and Gosselin, C. M. , 2002, “ Kinetostatic Modeling of Parallel Mechanisms With a Passive Constraining Leg and Revolute Actuators,” Mech. Mach. Theory, 37(6), pp. 599–617. [CrossRef]
Pashkevich, A. , Chablat, D. , and Wenger, P. , 2009, “ Stiffness Analysis of Overconstrained Parallel Manipulators,” Mech. Mach. Theory, 44(5), pp. 966–982. [CrossRef]
Fang, Y. , and Tsai, L. W. , 2002, “ Structure Synthesis of a Class of 4-DoF and 5-DoF Parallel Manipulators With Identical Limb Structures,” Int. J. Rob. Res., 21(9), pp. 799–810. [CrossRef]
Huang, Z. , and Li, Q. , 2003, “ Type Synthesis of Symmetrical Lowermobility Parallel Mechanisms Using the Constraint Synthesis Method,” Int. J. Rob. Res., 22(1), pp. 59–79.
Motevalli, B. , Zohoor, H. , and Sohrabpour, S. , 2010, “ Structural Synthesis of 5 DoFs 3T2R Parallel Manipulators With Prismatic Actuators on the Base,” Rob. Auton. Syst., 58(3), pp. 307–321. [CrossRef]
Ding, H. , Cao, W. , Cai, C. , and Kecskemethy, A. , 2015, “ Computer-Aided Structural Synthesis of 5-DOF Parallel Mechanisms and the Establishment of Kinematic Structure Databases,” Mech. Mach. Theory, 83, pp. 14–30. [CrossRef]
Hunt, K. H. , 1978, Kinematic Geometry of Mechanisms, Oxford University Press, Oxford, UK.
Huang, Z. , Li, Q. , and Ding, H. , 2012, Theory of Parallel Mechanisms, Springer, Dordrecht, The Netherlands.
Joshi, S. A. , and Tsai, L.-W. , 2002, “ Jacobian Analysis of Limited-DOF Parallel Manipulators,” ASME J. Mech. Des., 124(2), pp. 254–258. [CrossRef]
Enferadi, J. , and Tootoonchi, A. A. , 2011, “ Accuracy and Stiffness Analysis of a 3-RRP Spherical Parallel Manipulator,” Robotica, 29(2), pp. 193–209. [CrossRef]
Li, Y. , and Xu, Q. , 2008, “ Stiffness Analysis for a 3-PUU Parallel Kinematic Machine,” Mech. Mach. Theory, 43(2), pp. 186–200. [CrossRef]
Ferdinand, P. , Beer, E. , Russell, J., Jr. , and DeWolf, J. T. , 2009, Mechanics of Materials, McGraw-Hill Press, New York.
Waldron, K. J. , and Hunt, K. H. , 1991, “ Series-Parallel Dualities in Actively Coordinated Mechanisms,” Int. J. Rob. Res., 10(5), pp. 473–480. [CrossRef]
Li, Y. G. , Liu, H. T. , Zhao, X. M. , Huang, T. , and Chetwynd, D. G. , 2010, “ Design of a 3-DOF PKM Module for Large Structural Component Machining,” Mech. Mach. Theory, 45(6), pp. 941–954. [CrossRef]
Hu, B. , and Lu, Y. , 2011, “ Solving Stiffness and Deformation of a 3-UPU Parallel Manipulator With One Translation and Two Rotations,” Robotica, 29(6), pp. 815–822. [CrossRef]
Cheng, G. , Xu, P. , Yang, D. , and Liu, H. , 2013, “ Stiffness Analysis of a 3CPS Parallel Manipulator for Mirror Active Adjusting Platform in Segmented Telescope,” Rob. Comput. Integr. Manuf., 29(5), pp. 302–311. [CrossRef]
Wang, M. , Liu, H. , Huang, T. , and Chetwynd, D. G. , 2015, “ Compliance Analysis of a 3-SPR Parallel Mechanism With Consideration of Gravity,” Mech. Mach. Theory, 84, pp. 99–112. [CrossRef]


Grahic Jump Location
Fig. 1

Typical 3T2R overconstrained parallel mechanisms: (a) structure type, (b) 5-RRUR mechanism, (c)5-PRUR mechanism, and (d) 5-RPRRR mechanism

Grahic Jump Location
Fig. 3

Limb i of 5-RRUR parallel mechanism

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Fig. 4

Three substructures of limb i

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Fig. 5

Local frame of substructure ij

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Fig. 6

Deformations of 5-RRUR parallel mechanism under an external unit couple along x-direction: (a) x-direction linear deformation, (b) y-direction linear deformation, (c) z-direction linear deformation, (d) x-direction angular deformation, (e) y-direction angular deformation, and (f) z-direction angular deformation

Grahic Jump Location
Fig. 7

Deformations of 5-PRUR parallel mechanism under an external unit force along z-direction: (a) x-direction linear deformation, (b) y-direction linear deformation, (c) z-direction linear deformation, (d) x-direction angular deformation, (e) y-direction angular deformation, and (f) z-direction angular deformation



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