Research Papers: Design of Mechanisms and Robotic Systems

An Optimization Approach Toward a Robust Design of Six Degrees of Freedom Haptic Devices

[+] Author and Article Information
Aftab Ahmad

Department of Machine Design,
KTH Royal Institute of Technology,
Stockholm 100 44, Sweden
e-mail: aftaba@kth.se

Kjell Andersson

Department of Machine Design,
KTH Royal Institute of Technology,
Stockholm 100 44, Sweden
e-mail: kan@kth.se

Ulf Sellgren

Department of Machine Design,
KTH Royal Institute of Technology,
Stockholm 100 44, Sweden
e-mail: ulfs@md.kth.se

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 9, 2014; final manuscript received December 30, 2014; published online February 6, 2015. Assoc. Editor: Xiaoping Du.

J. Mech. Des 137(4), 042301 (Apr 01, 2015) (14 pages) Paper No: MD-14-1012; doi: 10.1115/1.4029514 History: Received January 09, 2014; Revised December 30, 2014; Online February 06, 2015

This work presents an optimization approach for the robust design of six degrees of freedom (DOF) haptic devices. Our objective is to find the optimal values for a set of design parameters that maximize the kinematic, dynamic, and kinetostatic performances of a 6-DOF haptic device while minimizing its sensitivity to variations in manufacturing tolerances. Because performance indices differ in magnitude, the formulation of an objective function for multicriteria performance requirements is complex. A new approach based on Monte Carlo simulation (MCS) was used to find the extreme values (minimum and maximum) of the performance indices to enable normalization of these indices. The optimization approach presented here is formulated as a methodology in which a hybrid design-optimization approach, combining genetic algorithm (GA) and MCS, is first used. This new approach can find the numerical values of the design parameters that are both optimal and robust (i.e., less sensitive to variation and thus to uncertainties in the design parameters). In the following step, with design optimization, a set of optimum tolerances is determined that minimizes manufacturing cost and also satisfies the allowed variations in the performance indices. The presented approach can thus enable the designer to evaluate trade-offs between allowed performance variations and tolerances cost.

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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].
Zhang, P., Yao, Z., and Du, Z., 2013, “Global Performance Index System for Kinematic Optimization of Robotic Mechanism,” ASME J. Mech. Des., 136(3), p. 031001. [CrossRef]
Liu, X.-J., Jin, Z.-L., and Gao, F., 2000, “Optimum Design of 3-DOF Spherical Parallel Manipulators With Respect to the Conditioning and Stiffness Indices,” Mech. Mach. Theory, 35(9), pp. 1257–1267. [CrossRef]
Su, Y., Duan, B., and Zheng, C., 2001, “Genetic Design of Kinematically Optimal Fine Tuning Stewart Platform for Large Spherical Radio Telescope,” Mechatronics, 11(7), pp. 821–835. [CrossRef]
Zhang, Y., and Yao, Y., 2006, “Kinematic Optimal Design of 6-ups Parallel Manipulator,” Proceedings of the 2006 IEEE International Conference on Mechatronics and Automation, Luoyang, Henan, June 25–28,IEEE, New York, pp. 2341–2345. [CrossRef]
Ottaviano, E., and Ceccarelli, M., 2002, “Optimal Design of Capaman (Cassino Parallel Manipulator) With a Specified Orientation Workspace,” Robotica, 20(2), pp. 159–166 [CrossRef].
Boudreau, R., and Gosselin, C. M., 2001, “La synthèse d'une plate-forme de Gough–Stewart pour un espace atteignable prescript,” Mech. Mach. Theory, 36(3), pp. 327–342. [CrossRef]
Miller, K., 2004, “Optimal Design and Modeling of Spatial Parallel Manipulators,” Int. J. Rob. Res., 23(2), pp. 127–140. [CrossRef]
Lee, L.-F., Narayanan, M. S., Mendel, F., Krovi, V. N., and Karam, P., 2010, “Kinematics Analysis of In-Parallel 5-DOF Haptic Device,” 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Montreal, Canada, July 6–9, IEEE, New York, pp. 237–241. [CrossRef]
Cruz-Valverde, C., Dominguez-Ramirez, O. A., Ponce-de León-Sánchez, E. R., Trejo-Mota, I., and Sepúlveda-Cervantes, G., 2010, “Kinematic and Dynamic Modeling of the Phantom Premium 1.0 Haptic Device: Experimental Validation,” Proceedings of the Electronics, Robotics and Automotive Mechanics Conference (CERMA), Morelos, Sept. 28–Oct. 1, IEEE, New York, pp. 494–501. [CrossRef]
Lee, J. H., Eom, K. S., and Suh, I. I., 2001, “Design of a New 6-DOF Parallel Haptic Device,” Proceedings of the 2001ICRA, IEEE International Conference on Robotics and Automation, IEEE, New York, Vol. 1, pp. 886–891. [CrossRef]
Cui, H., Zhu, Z., Gan, Z., and Brogardh, T., 2005, “Kinematic Analysis and Error Modeling of TAU Parallel Robot,” Rob. Comput. Integr. Manuf., 21(6), pp. 497–505. [CrossRef]
Zhu, Z., Li, J., Gan, Z., and Zhang, H., 2005, “Kinematic and Dynamic Modelling for Real-Time Control of TAU Parallel Robot,” Mech. Mach. Theory, 40(9), pp. 1051–1067. [CrossRef]
Dasgupta, B., and Mruthyunjaya, T., 1998, “A Newton–Euler Formulation for the Inverse Dynamics of the Stewart Platform Manipulator,” Mech. Mach. Theory, 33(8), pp. 1135–1152. [CrossRef]
Abdellatif, H., and Heimann, B., 2009, “Computational Efficient Inverse Dynamics of 6-DOF Fully Parallel Manipulators by Using the Lagrangian Formalism,” Mech. Mach. Theory, 44(1), pp. 192–207. [CrossRef]
Tsai, L.-W., 2000, “Solving the Inverse Dynamics of a Stewart–Gough Manipulator by the Principle of Virtual Work,” ASME J. Mech. Des., 122(1), pp. 3–9. [CrossRef]
Mendes Lopes, A., and Almeida, F., 2009, “The Generalized Momentum Approach to the Dynamic Modeling of a 6-DOF Parallel Manipulator,” Multibody Syst. Dyn., 21(2), pp. 123–146. [CrossRef]
Nguyen, C. C., and Pooran, F. J., 1989, “Dynamic Analysis of a 6-DOF CKCM Robot End-Effector for Dual-Arm Telerobot Systems,” Rob. Auton. Syst., 5(4), pp. 377–394. [CrossRef]
Ahmadi, M., Dehghani, M., Eghtesad, M., and Khayatian, A. R., 2008, “Inverse Dynamics of Hexa Parallel Robot Using Lagrangian Dynamics Formulation,” Proceedings of the INES 2008, International Conference on Intelligent Engineering Systems, Miami, FL, Feb. 25–29, IEEE, New York, pp. 145–149. [CrossRef]
Pashkevich, A., Klimchik, A., and Chablat, D., 2009, “Nonlinear Effects in Stiffness Modeling of Robotic Manipulators,” In Proceedings of International Conference on Computer and Automation Technology, pp. 168–173.
Ur-Rehman, R., Caro, S., Chablat, D., and Wenger, P., 2010, “Multi-Objective Path Placement Optimization of Parallel Kinematics Machines Based on Energy Consumption, Shaking Forces and Maximum Actuator Torques: Application to the Orthoglide,” Mech. Mach. Theory, 45(8), pp. 1125–1141. [CrossRef]
Zang, C., Friswell, M., and Mottershead, J., 2005, “A Review of Robust Optimal Design and Its Application in Dynamics,” Comput. Struct., 83(4), pp. 315–326. [CrossRef]
Tannous, M., Caro, S., and Goldsztejn, A., 2014, “Sensitivity Analysis of Parallel Manipulators Using an Interval Linearization Method,” Mech. Mach. Theory, 71, pp. 93–114. [CrossRef]
Caro, S., Binaud, N., and Wenger, P., 2009, “Sensitivity Analysis of 3-RPR Planar Parallel Manipulators,” ASME J. Mech. Des., 131(12), p. 121005. [CrossRef]
Caro, S., Wenger, P., Bennis, F., and Chablat, D., 2006, “Sensitivity Analysis of the Orthoglide: A Three-DOF Translational Parallel Kinematic Machine,” ASME J. Mech. Des., 128(2), pp. 392–402. [CrossRef]
Parkinson, A., Sorensen, C., and Pourhassan, N., 1993, “A General Approach for Robust Optimal Design,” ASME J. Mech. Des., 115(1), pp. 74–80. [CrossRef]
Du, X., Venigella, P. K., and Liu, D., 2009, “Robust Mechanism Synthesis With Random and Interval Variables,” Mech. Mach. Theory, 44(7), pp. 1321–1337. [CrossRef]
Phadke, M. S., 1995, Quality Engineering Using Robust Design, Prentice Hall PTR, Upper Saddle River, NJ.
Chen, W., and Lewis, K., 1999, “Robust Design Approach for Achieving Flexibility in Multidisciplinary Design,” AIAA J., 37(8), pp. 982–989. [CrossRef]
Caro, S., Bennis, F., and Wenger, P., 2005, “Tolerance Synthesis of Mechanisms: A Robust Design Approach,” ASME J. Mech. Des., 127(1), pp. 86–94. [CrossRef]
Beyer, H.-G., and Sendhoff, B., 2007, “Robust Optimization: A Comprehensive Survey,” Comput. Methods Appl. Mech. Eng., 196(33), pp. 3190–3218. [CrossRef]
Zhang, C. C., and Wang, H.-P. B., 1997, “Robust Design of Assembly and Machining Tolerance Allocations,” IIE Trans., 30(1), pp. 17–29. [CrossRef]
Li, M., Azarm, S., and Aute, V., 2005, “A Multi-Objective Genetic Algorithm for Robust Design Optimization,” Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, ACM, New York, pp. 771–778. [CrossRef]
Angeles, J., and López-Cajún, C. S., 1992, “Kinematic Isotropy and the Conditioning Index of Serial Robotic Manipulators,” Int. J. Rob. Res., 11(6), pp. 560–571. [CrossRef]
Gao, F., and Gruver, W. A., 1997, “Performance Evaluation Criteria for Analysis and Design of Robotic Specimens,” Proceedings of the ICAR'97, 8th International Conference on Advanced Robotics, Monterey, CA, July 7–9, IEEE, New York, pp. 879–884. [CrossRef]
Asada, H., 1984, “Dynamic Analysis and Design of Robot Manipulators Using Inertia Ellipsoids,” Proceedings of the 1984 IEEE International Conference on Robotics and Automation, IEEE, New York, Vol. 1, pp. 94–102. [CrossRef]
Menon, C., Vertechy, R., Markót, M. C., and Parenti-Castelli, V., 2009, “Geometrical Optimization of Parallel Mechanisms Based on Natural Frequency Evaluation: Application to a Spherical Mechanism for Future Space Applications,” IEEE Trans. Rob., 25(1), pp. 12–24. [CrossRef]
Lee, J. H., Yi, B.-J., Oh, S.-R., and Suh, I. H., 1998, “Optimal Design of a Five-Bar Finger With Redundant Actuation,” Proceedings of the 1998 IEEE International Conference on Robotics and Automation, IEEE, New York, Vol. 3, pp. 2068–2074.
Park, G.-J., Lee, T.-H., Lee, K. H., and Hwang, K.-H., 2006, “Robust Design: An Overview,” AIAA J., 44(1), pp. 181–191. [CrossRef]
Han, J. S., and Kwak, B. M., 2001, “Robust Optimal Design of a Vibratory Microgyroscope Considering Fabrication Errors,” J. Micromech. Microeng., 11(6), pp. 662–671. [CrossRef]
Chase, K. W., Greenwood, W. H., Loosli, B. G., and Hauglund, L. F., 1990, “Least Cost Tolerance Allocation for Mechanical Assemblies With Automated Process Selection,” Manuf. Rev., 3(1), pp. 49–59. [CrossRef]
Tsai, L.-W., 1999, Robot Analysis: The Mechanics of Serial and Parallel Manipulators, Wiley-Interscience, New York.
Ahmad, A., Andersson, K., Sellgren, U., and Khan, S., 2012, “A Stiffness Modeling Methodology for Simulation-Driven Design of Haptic Devices,” Eng. Comput.30(1), pp. 125–141. [CrossRef]


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Fig. 2

Optimization approach toward a robust design

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Fig. 3

Kinematic structure of 6-DOF TAU haptic device

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Fig. 4

PDF of performance indices using RDO: (a) PDF of VIn, (b) PDF of GIIn, (c) PDF of GTRIn, (d) PDF of GKIn, (e) PDF of GMIn, and (f) PDF of GNFIn

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Fig. 5

Manufacturing cost to allowed variation in performance indices

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Fig. 6

Deterministic design optimization

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Fig. 7

PDF of performance indices using DDO: (a) PDF of VIn, (b) PDF of GIIn, (c) PDF of GTRIn, (d) PDF of GKIn, (e) PDF of GMIn, and (f) PDF of GNFIn

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Fig. 8

PDF of performance indices using RDO and DDO: (a) PDF of VIn, (b) PDF of GIIn, (c) PDF of GTRIn, (d) PDF of GKIn, (e) PDF of GMIn, and (f) PDF of GNFIn

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Fig. 9

Comparison of sensitives of standard deviation (a) and confidence bound (b) of performance indices using RDO, optimum manufacturing tolerances, and DDO



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