0
Research Papers

New Indices for Optimal Design of Redundantly Actuated Parallel Manipulators

[+] Author and Article Information
Qinchuan Li

Mechatronic Institute,
Zhejiang Sci-Tech University,
Hangzhou 310018, Zhejiang Province, China
e-mail: lqchuan@zstu.edu.cn

Ningbin Zhang

Mechatronic Institute,
Zhejiang Sci-Tech University,
Hangzhou 310018, Zhejiang Province, China
e-mail: zhangningbin0617@126.com

Feibo Wang

Mechatronic Institute,
Zhejiang Sci-Tech University,
Hangzhou 310018, Zhejiang Province, China
e-mail: wfbace@hotmail.com

1Corresponding author.

Manuscript received June 23, 2016; final manuscript received October 29, 2016; published online December 2, 2016. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 9(1), 011007 (Dec 02, 2016) (10 pages) Paper No: JMR-16-1183; doi: 10.1115/1.4035126 History: Received June 23, 2016; Revised October 29, 2016

Redundantly actuated parallel manipulators (PMs) receive growing interest due to their reduced singularity and enlarged workspace. This paper proposes new indices for optimal design and analysis of redundantly actuated PMs by evaluating their motion/force transmissibility. First, we proposed a method to extract a multi-DOF (degrees-of-freedom) redundantly actuated PM into several subsidiary one-DOF PMs with two or more actuators by locking some actuators in an ergodic manner. Then, a new index of output transmission performance is proposed by investigating the mean value of the instantaneous power produced by the multiple actuation wrenches and one twist of the moving platform of one-DOF PMs. A local transmission index (LTI) is defined as the minimum value of the index of output and input transmission performance. A global transmission index (GTI) is then established based on the LTI. The proposed LTI and GTI are coordinate-free and have clear physical interpretation. Finally, the validity and universality of the new indices are demonstrated by optimization and analysis of redundantly actuated lower-mobility PMs with extra articulated six-DOF or limited-DOF limbs.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Kim, J. , Park, F. C. , Ryu, S. J. , Kim, J. , Hwang, J. C. , Park, C. , and Iurascu, C. C. , 2001, “ Design and Analysis of a Redundantly Actuated Parallel Mechanism for Rapid Machining,” IEEE Trans. Rob. Autom., 17(4), pp. 423–434. [CrossRef]
Cheng, H. , Yiu, Y. , and Li, Z. , 2003, “ Dynamics and Control of Redundantly Actuated Parallel Manipulators,” IEEE-ASME Trans. Mech., 8(4), pp. 483–491. [CrossRef]
Muller, A. , 2005, “ Internal Preload Control of Redundantly Actuated Parallel Manipulators—It's Application to Backlash Avoiding Control,” IEEE Trans. Rob., 21(4), pp. 668–677. [CrossRef]
Nokleby, S. B. , Fisher, R. , Podhorodeski, R. P. , and Firmani, F. , 2005, “ Force Capabilities of Redundantly-Actuated Parallel Manipulators,” Mech. Mach. Theory, 40(40), pp. 578–599. [CrossRef]
Kim, S. H. , Jeon, D. , Shin, H. P. , In, W. , and Kim, J. , 2009, “ Design and Analysis of Decoupled Parallel Mechanism With Redundant Actuator,” Int. J. Precis. Eng. Manuf., 10(4), pp. 93–99. [CrossRef]
Shin, H. , Lee, S. , In, W. , Jeong, J. I. , and Kim, J. , 2011, “ Kinematic Optimization of a Redundantly Actuated Parallel Mechanism for Maximizing Stiffness and Workspace Using Taguchi Method,” ASME J. Comput. Nonlinear Dyn., 6(1), pp. 607–617. [CrossRef]
Shin, H. , Kim, S. , Jeong, J. , and Kim, J. , 2012, “ Stiffness Enhancement of a Redundantly Actuated Parallel Machine Tool by Dual Support Rims,” Int. J. Precis. Eng. Manuf., 13(9), pp. 1539–1547. [CrossRef]
Shin, H. , Lee, S. , Jeong, J. I. , and Kim, J. , 2013, “ Antagonistic Stiffness Optimization of Redundantly Actuated Parallel Manipulators in a Predefined Workspace,” IEEE-ASME Trans. Mech., 18(3), pp. 1161–1169. [CrossRef]
Jin, S. , Kim, J. , and Seo, T. , 2015, “ Optimization of a Redundantly Actuated 5R Symmetrical Parallel Mechanism Based on Structural Stiffness,” Robotica, 33(9), pp. 1973–1983. [CrossRef]
Lee, G. , Sul, S. K. , and Kim, J. , 2015, “ Energy-Saving Method of Parallel Mechanism by Redundant Actuation,” Int. J. Precis. Eng. Manuf. Technol., 2(4), pp. 345–351. [CrossRef]
Wu, J. , Wang, J. , Li, T. , and Wang, L. , 2007, “ Performance Analysis and Application of a Redundantly Actuated Parallel Manipulator for Milling,” J. Intell. Rob. Syst., 50(2), pp. 163–180. [CrossRef]
Wu, J. , Wang, J. , and Li, T. , 2007, “ Dexterity and Stiffness Analysis of a Three-Degree-of-Freedom Planar Parallel Manipulator With Actuation Redundancy,” Proc. Inst. Mech. Eng. Part C, 221(8), pp. 961–969. [CrossRef]
Wu, J. , Wang, J. , and Wang, L. , 2008, “ Optimal Kinematic Design and Application of a Redundantly Actuated 3DOF Planar Parallel Manipulator,” ASME J. Mech. Des., 130(5), pp. 680–682. [CrossRef]
Wu, J. , Li, T. , and Xu, B. , 2013, “ Force Optimization of Planar 2-DOF Parallel Manipulators With Actuation Redundancy Considering Deformation,” Proc. Inst. Mech. Eng. Part C, 227(6), pp. 1371–1377. [CrossRef]
Wang, C. , Fang, Y. , Guo, S. , and Chen, Y. , 2013, “ Design and Kinematical Performance Analysis of a 3-RUS/RRR Redundantly Actuated Parallel Mechanism for Ankle Rehabilitation,” ASME J. Mech. Rob., 5(4), pp. 1585–1606. [CrossRef]
Wang, C. , Fang, Y. , Guo, S. , and Zhou, C. , 2015 “ Design and Kinematic Analysis of Redundantly Actuated Parallel Mechanisms for Ankle Rehabilitation,” Robotica, 33(2), pp. 366–384. [CrossRef]
Wang, C. , Fang, Y. , and Guo, S. , 2015, “ Multi-Objective Optimization of a Parallel Ankle Rehabilitation Robot Using Modified Differential Evolution Algorithm,” Chin. J. Mech. Eng., 28(4), pp. 702–715. [CrossRef]
Qu, H. , Fang, Y. , and Guo, S. , 2015, “ Structural Synthesis of a Class of 3-DOF Wrist Mechanisms With Redundantly-Actuated Closed-Loop Units,” Proc. Inst. Mech. Eng. Part C, 230(2), pp. 276–290. [CrossRef]
Palpacelli, M. C. , Palmieri, G. , and Callegari, M. , 2012, “ A Redundantly Actuated 2-Degrees-of-Freedom Mini Pointing Device,” ASME J. Mech. Rob., 4(4), p. 031012. [CrossRef]
Xie, F. , Liu, X. J. , and Zhou, Y. , 2014, “ Optimization of a Redundantly Actuated Parallel Kinematic Mechanism for a 5-Degree-of-Freedom Hybrid Machine Tool,” Proc. Inst. Mech. Eng. Part B, 228(12), pp. 1630–1641. [CrossRef]
Saafi, H. , Laribi, M. A. , and Zeghloul, S. , 2014, “ Redundantly Actuated 3-RRR Spherical Parallel Manipulator Used as a Haptic Device: Improving Dexterity and Eliminating Singularity,” Robotica, 33(5), pp. 1–18.
Liang, D. , Song, Y. , Sun, T. , and Dong, G. , 2016, “ Optimum Design of a Novel Redundantly Actuated Parallel Manipulator With Multiple Actuation Modes for High Kinematic and Dynamic Performance,” Nonlinear Dyn., 83(1–2), pp. 631–658. [CrossRef]
Yoshikawa, T. , 1985, “ Manipulability of Robotic Mechanisms,” Int. J. Rob. Res., 4(2), pp. 3–9. [CrossRef]
Gosselin, C. , and Angeles, J. , 1991, “ A Global Performance Index for the Kinematic Optimization of Robotic Manipulators,” ASME J. Mech. Des., 113(3), pp. 220–226. [CrossRef]
Merlet, J. P. , 2006, “ Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots,” ASME J. Mech. Des., 128(1), pp. 199–206. [CrossRef]
Gosselin, C. , 1992, “ The Optimum Design of Robotic Manipulators Using Dexterity Indices,” Rob. Auton. Syst., 9(4), pp. 213–226. [CrossRef]
Angeles, J. , 1992, “ The Design of Isotropic Manipulator Architectures in the Presence of Redundancies,” Int. J. Rob. Res., 11(3), pp. 196–201. [CrossRef]
Ma, O. , and Angeles, J. , 1991, “ Optimum Architecture Design of Platform Manipulator,” International Conference on Advanced Robotics, 1991, 'robots in Unstructured Environments', 91 ICAR, June 19–22, Vol. 2, pp. 1130–1135.
Kim, S. , and Ryu, J. , 2003, “ New Dimensionally Homogeneous Jacobian Matrix Formulation by Three End-Effector Points for Optimal Design of Parallel Manipulators,” IEEE Trans. Rob. Autom., 19(4), pp. 731–736. [CrossRef]
Pond, G. , and Carretero, J. , 2006, “ Formulating Jacobian Matrices for the Dexterity Analysis of Parallel Manipulators,” Mech. Mach. Theory, 41(12), pp. 1505–1519. [CrossRef]
Ball, R. S. , 1998, A Treatise on the Theory of Screws, Vol. 1, Cambridge University Press Cambridge, UK.
Lin, C. C. , and Chang, W. T. , 2002, “ The Force Transmissivity Index of Planar Linkage Mechanisms,” Mech. Mach. Theory, 37(12), pp. 1465–1485. [CrossRef]
Chen, C. , and Angeles, J. , 2007, “ Generalized Transmission Index and Transmission Quality for Spatial Linkages,” Mech. Mach. Theory, 42(9), pp. 1225–1237. [CrossRef]
McCarthy, J. M. , 2011, “ Geometric Design of Linkages,” Interdiscip. Appl. Math., 11(4), p. 583.
Glazunov, V. A. , Arkaelyan, V. , Briot, S. , and Rashoyan, G. V. , 2012, “ Speed and Force Criteria for the Proximity to Singularities of Parallel Structure Manipulators,” J. Mach. Manuf. Reliab., 41(3), pp. 194–199. [CrossRef]
Marlow, K. , Isaksson, M. , and Nahavandi, S. , 2016, “ Motion/Force Transmission Analysis of Planar Parallel Manipulators With Closed-Loop Sub-Chains Via Screw Theory,” ASME J. Mech. Rob., 8(4).
Wang, J. , Wu, C. , and Liu, X. J. , 2010, “ Performance Evaluation of Parallel Manipulators: Motion/Force Transmissibility and Its Index,” Mech. Mach. Theory, 45(10), pp. 1462–1476. [CrossRef]
Wu, C. , Liu, X. J. , Wang, L. , and Wang, J. , 2010, “ Optimal Design of Spherical 5R Parallel Manipulators Considering the Motion/Force Transmissibility,” ASME J. Mech. Des., 132(3), p. 031002. [CrossRef]
Liu, X. J. , Wu, C. , and Wang, J. , 2012, “ A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators,” ASME J. Mech. Rob., 4(4), pp. 61–68.
Xie, F. , Liu, X. J. , Chen, X. , and Wang, J. , 2011, “ Optimum Kinematic Design of a 3-DOF Parallel Kinematic Manipulator With Actuation Redundancy,” Intelligent Robotics and Applications, Springer Berlin, pp. 250–259.
Xie, F. , Liu, X. J. , and Zhou, Y. , “ Development and Experimental Study of a Redundant Hybrid Machine With Five-Face Milling Capability in One Setup,” Int. J. Precis. Eng. Manuf., 15(1), pp. 13–21. [CrossRef]
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]
Li, Q. , and Herve, J. M. , 2014, “ Type Synthesis of 3-DOF RPR-Equivalent Parallel Mechanisms,” IEEE Trans. Rob., 30(6), pp. 1333–1343. [CrossRef]
Hunt, K. , 1983, “ Structural Kinematics of In-Parallel-Actuated Robot-Arms,” ASME J. Mech. Des., 105(4), pp. 705–712.
Bonev, I. A. , 2002, “ Geometric Analysis of Parallel Mechanisms,” Ph.D. thesis, Laval University, Quebec, QC.

Figures

Grahic Jump Location
Fig. 1

The redundantly actuated four-bar mechanism

Grahic Jump Location
Fig. 2

Procedure of evaluating a general redundantly actuated PM

Grahic Jump Location
Fig. 3

CAD model of a series of 1T2R nonredundant and redundant actuation PMs: (a) 2-UPR-RPU PM, (b) 2UPR-RPU-SPS PM, and (c) 2UPR-2RPU PM

Grahic Jump Location
Fig. 4

Procedure of transmissibility evaluation for the 2UPR-RPU-SPS PM

Grahic Jump Location
Fig. 5

LTI distributions: (a) 2-UPR-RPU PM, (b) 2UPR-RPU-SPS PM before optimization, (c) 2UPR-RPU-SPS PM after optimization, and (d) GTI atlases

Grahic Jump Location
Fig. 6

Parameter design space: (a) three-dimensional view and (b) planar view

Grahic Jump Location
Fig. 7

Optimization procedure for the 2UPR- RPU-SPS PM

Grahic Jump Location
Fig. 8

Schematic diagram of a 3-RPS PM and its variant PMs

Grahic Jump Location
Fig. 9

LTI distributions: (a) three RPS, (b) center-one, (c) middle-one, (d) middle-two, (e) middle-three PMs, and (f) GTI atlases

Grahic Jump Location
Fig. 10

CAD model of the 2URR-2RRU PM

Grahic Jump Location
Fig. 11

Generation of indices: (a) input index, (b) output index, and (c) LTI with r1 = 250 mm, r2 = 400 mm, l = 400 mm, h = 300 mm

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In