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A real-time NURBS motion interpolator for position control of a slide equilateral triangle parallel manipulator

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Abstract

This study presents a real-time non-uniform rational B-spline (NURBS) motion interpolator command generation for position control of a new design to achieve a six-degree-of-freedom (6dof) slide equilateral triangle parallel manipulator (SETPM). The existing method utilizes the approximate method to obtain the characteristics of curves of the velocity and acceleration for the feed-forward compensation in the joint space. However, the NURBS motion interpolator command generation is related to the geometric characteristics of curves including position, tangent, and curvature to the motion dynamics of the SETPM including position, velocity and acceleration for applied directly the feed-forward compensation in the global space. The inverse dynamics controller (IDC) is the power of control law. However, implementing the inverse dynamics control laws requires accurately knowing the system dynamic model parameters and computing the complete equations of motion in real time. To reduce the time for calculating the inverse dynamic, this study proposes a feed-forward compensation with feedback proportional derivate (PD) control to take the place of inverse dynamics control for reducing both the inverse dynamic calculation time and the tracking error. The proposed real-time NURBS motion interpolator command generation and feed-forward compensation with feedback PD control are also successfully applied to a slide equilateral triangle parallel manipulator on a PC-based system to achieve high motion precision.

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References

  1. Faroukia RT, Manni C, Sestini A (2001) Real-time interpolator for Bezier conic. Comput Aided Geom Des 18:639–655

    Article  Google Scholar 

  2. Bahr B, Xiao X, Krishnan K (2001) A real scheme of cubic parametric curve interpolations for CNC systems. Comput Ind 45:309–317

    Article  Google Scholar 

  3. Lartigue C, Thiebaut F, Maekawa T (2001) CNC tool path in terms of B-spline curves. Comput-Aided Des 33:307–319

    Article  Google Scholar 

  4. Yeh SS, Hsu PL (1999) The speed-controlled interpolator for machining. The speed-controlled interpolator for machining parametric curves. Comput-Aided Des 31:349–357

    Article  MATH  Google Scholar 

  5. Cheng MY, Tsai MC, Kuo JC (2002) Real-time NURBS command generators for CNC servo controllers. Int J Mach Tools Manuf 42:801–813

    Article  Google Scholar 

  6. Tsai MC, Cheng CW, Cheng MY (2003) A real-time NURBS surface interpolator for precision three-axis CNC machining. Int J Mach Tools Manuf 43:1217–1227

    Article  Google Scholar 

  7. Cheng CW, Tsai MC (2004) Real-time variable feed rate NURBS curve interpolator for CNC machining. Int J Adv Manuf Technol 23:865–873

    Google Scholar 

  8. Tikhon M, Ko TJ, Lee SH, Kim HS (2004) NURBS interpolator for constant material removal rate in open NC machine tools. Int J Mach Tools Manuf 44:237–245

    Article  Google Scholar 

  9. Zhang Q, Greenway RB (1998) Development and implementation of a NURBS curve motion interpolator. Robot Comput-Integr Manuf 14:27–36

    Article  Google Scholar 

  10. Gough VE, Whitehall SG (1962) Universal tire test machine. In: Proc 9th Int Tech Congress FISITA, pp 117–137

  11. Stewart D (1965) A platform with six degrees of freedom. In: Proc Instn Mech Engrs, vol. Part 180–1(15):371–386

  12. Salcudean SE, Drexel PA, Ben-Dov D, Tayor AJ, Lawrence PD (1994) A six degree-of-freedom, hydraulic, one person motion simulator. IEEE Conference on Robotics and Automation, 8–13 May, vol. 3, pp 2437–2443

  13. Cleary K, Brooks T (1993) Kinematic analysis of a novel 6-DOF parallel manipulator. In: Proc IEEE International Conference on Robotics and Automation, vol. 1, 2–6 May, pp 708–713

  14. Uchiyama M, Imura K, Pierrot F, Dauchez P, Unno K, Toyama O (1992) A new design of a very fast 6-DOF parallel robot. Proc of 23rd Int Symp On Industrial Robots, pp 771–776

  15. Han CS, Hudgens JC, Tesar D, Traver AE (1991) Modeling, synthesis, analysis, and design of high-resolution micromanipulator to enhance robot accuracy. In: Proc IEEE/RSJ International Workshop on Intelligent Robots and Systems, 3–5 Nov. vol. 2, pp 1157–1162

  16. Fukuda T, Arai F (2000) Prototyping design and automation of micro/nano manipulation system. In: Proc IEEE International Conference on Robotics and Automation, 24–28 April, vol. 1, pp 192–197

  17. Grace KW, Colgate JE, Glucksberg MR, Chun JH (1993) A six degree of freedom micromanipulator for ophthalmic surgery. In:Proc IEEE International Conference on Robotics and Automation, 2–6 May , vol. 1, pp 630–635

  18. Tsai LW (1999) Robot analysis: the mechanics of serial and parallel manipulators. Wiley, New York

    Google Scholar 

  19. Piegl L, Tiller W (1997) The NURBS book, 2nd edn. Springer, Berlin Heidelberg New York

    Google Scholar 

  20. Tsay DM, Huey CO Jr (1993) Application of rational B-splines to the synthesis of cam-follower motion programs. J Mech Des Trans ASME 115(3):621–626

    Article  Google Scholar 

  21. FANUC Corp (1991) FANUC AC servo amplifier-maintenance manual

  22. Chou JJ, Yang DCH (1991) Command generation for three-axis CNC machining. ASME J Eng Ind 113:305–310

    Google Scholar 

  23. Asada H, Slotine JJE (1985) Robot analysis and control. Wiley, New York

    Google Scholar 

  24. Lee SH, Song JB, Chun WC, Hong D (2003) Position control of a Stewart platform using inverse dynamics control with approximate dynamics. Mechatronics 13(6):605–619

    Article  Google Scholar 

  25. Geike T, McPhee J (2003) Inverse dynamics analysis of parallel manipulators with full mobility. Mech Mach Theory 38:549–562

    Article  MATH  MathSciNet  Google Scholar 

  26. Kelly Rafael, Salgado Ricardo (1994) PD control with computed feed-forward of robot manipulators: a design procedure. IEEE Autom 10(4):566–571, August

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Taiwan University of Science and Technology, 43, Keelung Road, Sec. 4, Taipei, Taiwan, 106, Republic of China

    Hua-Yi Chuang & Kuo-Hua Chien

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  1. Hua-Yi Chuang
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  2. Kuo-Hua Chien
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Correspondence to Hua-Yi Chuang.

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Chuang, HY., Chien, KH. A real-time NURBS motion interpolator for position control of a slide equilateral triangle parallel manipulator. Int J Adv Manuf Technol 34, 724–735 (2007). https://doi.org/10.1007/s00170-006-0647-7

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  • DOI: https://doi.org/10.1007/s00170-006-0647-7

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