0
Research Papers

Optimization Design of a Walkable Fixture Mechanism

[+] Author and Article Information
Xiao-Jin Wan

Hubei Key Laboratory of Advanced Technology
of Automotive Components,
Wuhan University of Technology,
Wuhan 430070, China;
Hubei Collaborative Innovation Center for
Automotive Components Technology,
Wuhan University of Technology,
Wuhan 430070, China;
State Key Laboratory of Digital Manufacturing
Equipment and Technology of China,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: wxj_2001@163.com

Hanjie Zhang

Hubei Key Laboratory of Advanced Technology
of Automotive Components,
Wuhan University of Technology,
Wuhan 430070, China;
Hubei Collaborative Innovation Center for
Automotive Components Technology,
Wuhan University of Technology,
Wuhan 430070, China

1Corresponding author.

Manuscript received November 19, 2017; final manuscript received March 21, 2018; published online May 21, 2018. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 140(8), 081002 (May 21, 2018) (12 pages) Paper No: MANU-17-1719; doi: 10.1115/1.4039856 History: Received November 19, 2017; Revised March 21, 2018

In this paper, a novel fixture mechanism with combining a mobility of the legged robot and advantages of parallel mechanism is designed to hold the different size and shape, large-scale workpiece. The proposed mobile fixture mechanism holds the workpiece as a parallel manipulator while it walks as a legged robot. This kind of robotized fixtures can possess high self-configurable ability to accommodate a wider variety of products. In order to obtain the best kinematic dexterity and accuracy characteristics, comprehensive performance optimization is performed by non-dominated-genetic algorithm (NSGA-II). In the optimization procedure, a conventional kinematic transformation matrix (Jacobian matrix) and error propagation matrix are obtained through derivation and differential motion operations. The singular values and condition number based on velocity Jacobians and error amplification factors based on error propagation matrix are derived; in addition, relative pose error range of end effector is also derived. On the basis of the above measure indices, three kinds of nonlinear optimization problems are defined to obtain the optimal architecture parameters for better kinematic accuracy and dexterity in workspace. Comparison analyses of the optimized results are performed.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Li, B. , Shiu, B. W. , and Lau, K. J. , 2003, “Robust Fixture Configuration Design for Sheet Metal Assembly With Laser Welding,” ASME J. Manuf. Sci. Eng., 125(1), pp. 120–127. [CrossRef]
Meshreki, M. , Ko¨vecses, J. , Attia, H. , and Tounsi, N. , 2008, “Dynamics Modeling and Analysis of Thin-Walled Aerospace Structures for Fixture Design in Multiaxis Milling,” ASME J. Manuf. Sci. Eng., 130(3), pp. 361–374. [CrossRef]
Luo, C. , Zhu, L. M. , and Ding, H. , 2011, “Two-Sided Quadratic Model for Workpiece Fixturing Analysis,” ASME J. Manuf. Sci. Eng., 133(3), p. 031004. [CrossRef]
Xing, Y. , 2017, “Fixture Layout Design of Sheet Metal Parts Based on Global Optimization Algorithms,” ASME J. Manuf. Sci. Eng., 139(10), p. 101004. [CrossRef]
Gameros, A. A. , Axinte, D. , Siller, H. R. , Lowth, S. , and Winton, P. , 2017, “Experimental and Numerical Study of a Fixturing System for Complex Geometry and Low Stiffness Components,” ASME J. Manuf. Sci. Eng., 139(4), p. 045001. [CrossRef]
Mohammed, A. , Schmidt, B. , and Wang, L. , 2017, “Energy-Efficient Robot Configuration for Assembly,” ASME J. Manuf. Sci. Eng., 139(5), p. 051007. [CrossRef]
Zheng, F. , Hua, L. , Han, X. , Li, B. , and Chen, D. , 2017, “Synthesis of Shaped Noncircular Gear Using a Three-Linkage Computer Numerical Control Shaping Machine,” ASME J. Manuf. Sci. Eng., 139(7), p. 071003. [CrossRef]
Zhao, Y. M. , Lin, Y. , Xi, F. , Guo, S. , and Ouyang, P. , 2017, “Switch-Based Sliding Mode Control for Position-Based Visual Servoing of Robotic Riveting System,” ASME J. Manuf. Sci. Eng., 139(4), p. 041010. [CrossRef]
Zhang, J. , Zhao, Y. Q. , and Jin, Y. , 2016, “Elastodynamic Modeling and Analysis for an Exechon Parallel Kinematic Machine,” ASME J. Manuf. Sci. Eng., 138(3), pp. 7190–7200.
Merlet, J.-P. , 2006, Parallel Robots, Springer, Dordrecht, The Netherlands.
Zhou, X. , Xu, Y. , Yao, J. , Zheng, K. , and Zhao, Y. , 2016, “Stiffness Modeling and Comparison of the 5-UPS/PRPU Parallel Machine Tool With Its Non-Redundant Counterpart,” Proc. Inst. Mech. Eng., Part B, 231(9), pp. 1646–1657. [CrossRef]
Fang, X. , Zhang, S. , Xu, Q. , Wang, T. , Liu, Y. , and Chen, X. , 2015, “Optimization of a Crossbar Parallel Machine Tool Based on Workspace and Dexterity,” J. Mech. Sci. Technol., 29(8), pp. 3297–3307. [CrossRef]
Xie, F. , Liu, X. J. , and Wang, J. , 2012, “A 3DOF Parallel Manufacturing Module and Its Kinematic Optimization,” Rob. Comput.-Integr. Manuf., 28(3), pp. 334–343. [CrossRef]
Stewart, D. , 1965, “A Platform With Six Degrees of Freedom,” Proc. Inst. Mech. Eng., 180(1), pp. 371–386. [CrossRef]
Karasic, G. , and Asada, H. , 2011, “Flip-and-Slide Magnetic Paired Robots for Aircraft Manufacturing and Maintenance,” IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9–13, pp. 694–700.
Menon, M. , and Asasda, H. , 2009, “Actuation and Position Estimation of a Passive Mobile End Effector From Across a Thin Wall for Heavy-Duty Aircraft Manufacturing,” IEEE International Conference on Robotics and Automation (ICRA), Kobe, Japan, May 12–17, pp. 985–991.
Wan, X. J. , Li, Q. , and Wang, K. , 2017, “Dimensional Synthesis of a Robotized Cell of Support Fixture,” Rob. Comput.-Integr. Manuf., 48, pp. 80–92. [CrossRef]
Merlet, J. P. , 2006, “Designing a Parallel Manipulator for a Specific Workspace,” Int. J. Rob. Res., 16(4), pp. 545–556. [CrossRef]
Boudreau, R. , and Gosselin, C. M. , 1999, “The Synthesis of Planar Parallel Manipulators With a Genetic Algorithm,” ASME J. Mech. Des., 121(4), pp. 533–537. [CrossRef]
Laribi, M. A. , Romdhane, L. , and Zeghloul, S. , 2007, “Analysis and Dimensional Synthesis of the Delta Robot for a Prescribed Workspace,” Mech. Mach. Theory, 42(7), pp. 859–870. [CrossRef]
Li, Y. , and Xu, Q. , 2004, “Optimal Kinematic Design for a General 3-PRS Spatial Parallel Manipulator Based on Dexterity and Workspace,” 11th International Conference on Machine Design and Production, Antalya, Turkey, Oct. 13–15, pp. 571–584. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.718.2319&rep=rep1&type=pdf
Min, K. L. , and Park, K. W. , 2000, “Workspace and Singularity Analysis of a Double Parallel Manipulator,” IEEE/ASME Trans. Mechatronics, 5(4), pp. 367–375. [CrossRef]
Yoshikawa, T. , 1985, “Manipulability of Robotic Mechanisms,” Int. J. Rob. Res., 4(2), pp. 3–9. [CrossRef]
Endo, H. , 2015, “Application of Robotic Manipulability Indices to Evaluate Thumb Performance During Smart Phone Touch Operations,” Ergonomics, 58(5), pp. 736–747. [CrossRef] [PubMed]
Zhao, Y. , 2013, “Dimensional Synthesis of a Three Translational Degrees of Freedom Parallel Robot While Considering Kinematic Anisotropic Property,” Rob. Comput.-Integr. Manuf., 29(1), pp. 169–179. [CrossRef]
Zhao, Y. , 2013, “Dynamic Optimum Design of a Three Translational Degrees of Freedom Parallel Robot While Considering Anisotropic Property,” Rob. Comput.-Integr. Manuf., 29(4), pp. 100–112. [CrossRef]
Cirillo, A. , Cirillo, P. , Maria, G. D. , Marino, A. , Natale, C. , and Pirozzi, S. , 2017, “Optimal Custom Design of Both Symmetric and Unsymmetrical Hexapod Robots for Aeronautics Applications,” Rob. Comput.-Integr. Manuf., 44, pp. 1–16. [CrossRef]
Salisbury, J. K. , and Craig, J. J. , 1981, “Articulated Hands Force Control and Kinematic Issues,” Int. J. Rob. Res., 1(1), pp. 4–17. [CrossRef]
Angeles, J. , and Angeles, J. , 2007, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms ( Mechanical Engineering Series, Vol. 2), p. 98. [CrossRef]
Zhang, Z. C. D. , 2012, “Stiffness Optimization of a Novel Reconfigurable Parallel Kinematic Manipulator,” Robotica, 30(3), pp. 433–447. [CrossRef]
Yang, D. C. H. , and Lai, Z. C. , 1985, “On the Dexterity of Robotic Manipulators-Service Angle,” ASME J. Mech. Des., 107(2), pp. 262–270.
Zhang, D. , and Gao, Z. , 2015, “Performance Analysis and Optimization of a Five-Degrees-of-Freedom Compliant Hybrid Parallel Micromanipulator,” Rob. Comput.-Integr. Manuf., 34(1), pp. 20–29. [CrossRef]
Yao, J. , Gu, W. , Feng, Z. , Chen, L. , Xu, Y. , and Zhao, Y. , 2017, “Dynamic Analysis and Driving Force Optimization of a 5-DOF Parallel Manipulator With Redundant Actuation,” Rob. Comput.-Integr. Manuf., 48, pp. 51–58. [CrossRef]
Merlet, J. P. , 2005, “Jacobian, Manipulability, Condition Number and Accuracy of Parallel Robots,” ASME J. Mech. Des., 128(1), pp. 199–206. [CrossRef]
Cardou, P. , Bouchard, S. , and Gosselin, C. , 2010, “Kinematic-Sensitivity Indices for Dimensionally Nonhomogeneous Jacobian Matrices,” IEEE Trans. Rob., 26(1), pp. 166–173. [CrossRef]
Wu, C. , Liu, X. J. , and Wang, J. , 2009, “Force Transmission Analysis of Spherical 5R Parallel Manipulators,” ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots (ReMAR), London, June 22–24, pp. 331–336. https://ieeexplore.ieee.org/document/5173850/
Huang, T. , Wang, M. , Yang, S. , Sun, T. , Chetwynd, D. G. , and Xie, F. , 2014, “Force/Motion Transmissibility Analysis of Six Degree of Freedom Parallel Mechanisms,” ASME J. Mech. Rob., 6(3), p. 031010. [CrossRef]
Song, Y. , Gao, H. , Sun, T. , Dong, G. , Lian, B. , and Qi, Y. , 2014, “Kinematic Analysis and Optimal Design of a Novel 1T3R Parallel Manipulator With an Articulated Travelling Plate,” Rob. Comput.-Integr. Manuf., 30(5), pp. 508–516. [CrossRef]
Wang, J. , and Masory, O. , 1993, “On the Accuracy of a Stewart Platform—Part I: The Effect of Manufacturing Tolerances,” IEEE International Conference on Robotics and Automation, Atlanta, GA, May 2–6, pp. 114–120.
Kim, H. S. , and Choi, Y. J. , 2015, “The Kinematic Error Bound Analysis of the Stewart Platform,” J. Field Rob., 17(1), pp. 63–73.
Ropponen, T. , and Arai, T. , 1995, “Accuracy Analysis of a Modified Stewart Platform Manipulator,” IEEE International Conference on Robotics and Automation, Nagoya, Japan, May 21–27, pp. 521–525.
Jiang, Y. , Li, T. , Wang, L. , and Chen, F. , 2018, “Kinematic Error Modeling and Identification of the Over-Constrained Parallel Kinematic Machine,” Rob. Comput.-Integr. Manuf., 49, pp. 105–119. [CrossRef]
Li, T. , and Ye, P. , 2003, “The Measurement of Kinematic Accuracy for Various Configurations of Parallel Manipulators,” IEEE International Conference on Systems, Man and Cybernetics, Washington, DC, Oct. 5–8, pp. 1122–1129.
Ryu, J. , and Cha, J. , 2003, “Volumetric Error Analysis and Architecture Optimization for Accuracy of HexaSlide Type Parallel Manipulators,” Mech. Mach. Theory, 38(3), pp. 227–240. [CrossRef]
Gosselin, C. M. , 2002, “Dexterity Indices for Planar and Spatial Robotic Manipulators,” IEEE International Conference on Robotics and Automation, Cincinnati, OH, May 13–18, pp. 650–655.
Lou, Y. , Liu, G. , and Li, Z. , 2008, “Randomized Optimal Design of Parallel Manipulators,” IEEE Trans. Autom. Sci. Eng., 5(2), pp. 223–233. [CrossRef]
Bai, S. , 2010, “Optimum Design of Spherical Parallel Manipulators for a Prescribed Workspace,” Mech. Mach. Theory, 45(2), pp. 200–211. [CrossRef]
Fattah, A. , and Ghasemi, A. M. H. , 2002, “Isotropic Design of Spatial Parallel Manipulators,” Int. J. Rob. Res., 21(9), pp. 811–826. [CrossRef]
Klein, C. A. , and Blaho, B. E. , 1987, “Dexterity Measures for the Design and Control of Kinematically Redundant Manipulators,” Int. J. Rob. Res., 6(2), pp. 72–83. [CrossRef]
Kim, J. O. , and Khosla, K. , 2002, “Dexterity Measures for Design and Control of Manipulators,” IEEE/RSJ International Workshop on Intelligent Robots and Systems '91 (IROS), Intelligence for Mechanical Systems, Osaka, Japan, Nov. 3–5, pp. 758–763.

Figures

Grahic Jump Location
Fig. 1

(a) Sketch of multirobotized cells of fixture cooperation for holding automobile body side assembly and (b) sketch of multirobotized cells of fixture cooperation for thin-walled workpiece

Grahic Jump Location
Fig. 2

(a) Parallel mechanism CAD model and (b) kinematic pair layout of a limb in the support mechanism

Grahic Jump Location
Fig. 3

Equivalent analysis model of eight-SPU mechanism

Grahic Jump Location
Fig. 4

The workspace of initial architecture parameters

Grahic Jump Location
Fig. 5

Condition number at z=200 mm

Grahic Jump Location
Fig. 6

Singular values distribution at the height z=200 mm

Grahic Jump Location
Fig. 10

Workspace for accuracy performance indices (α=0,β=0,γ=0)

Grahic Jump Location
Fig. 11

Comparison singular values of kinematic performance indices with the accuracy performance indices z=200 mm

Grahic Jump Location
Fig. 12

Comparison condition numbers of kinematic performance indices with the accuracy performance indices z=200 mm

Grahic Jump Location
Fig. 13

Workspace for comprehensive performance indices (α=0,β=0,γ=0)

Grahic Jump Location
Fig. 14

Comparison condition numbers of the comprehensive indices with kinematic performance indices and accuracy performance indices z=200 mm

Grahic Jump Location
Fig. 15

Comparison singular values of the comprehensive indices with kinematic performance indices and accuracy performance indices z=200 mm

Grahic Jump Location
Fig. 7

Workspace for kinematic performance indices (α=0,β=0,γ=0): (a) relationship of MSV and condition in iterations and (b) workspace for kinematic performance indices

Grahic Jump Location
Fig. 8

The condition number from kinematic performance indices at the height Z = 200 mm

Grahic Jump Location
Fig. 9

Minimal singular values from kinematic performance indices at the height Z=200 mm

Grahic Jump Location
Fig. 16

Comparison trajectories before and after optimization: (a) 3D-ellipse trajectory of the different optimization objective functions, (b) the projections of deformation trajectories in Z−O−X plane, and (c) the projections of the deformation trajectories in Z−O−Y plane

Tables

Errata

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