Motion Programs with Better Characteristic Values

  • Kuan-Lun HsuEmail author
  • Jia Yu Chung
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


Motion characteristics are dimensionless peak values of velocity, acceleration, jerk, and acceleration multiplied by velocity of a motion program. In general, these peak values of a synthesized motion program should be as low as possible. Some trigonometric motion programs are widely used since they have a good compromise of all motion characteristics. A property in common for trigonometric motion programs is that their acceleration functions can be expressed as a qualitative shape of a sinusoidal function. The interval of the sinusoidal function is divided into several zones having different linear slopes. The acceleration function can be easily shaped by specifying presented phase angle function to synthesize desired motion programs. To improve kinematic quantities of trigonometric motion programs, this paper proposes an alternative phase angle function to obtain synthesized motion programs with a simultaneous reduction in all the characteristic values. The synthesis process and results are illustrated by examples.


motion programs motion characteristics phase angle function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The first author would like to express his gratitude to Prof. Dr. Long-Iong Wu. His illuminating instruction makes this paper possible. In addition, the first author is grateful for the substantial support of National Taiwan University. Most importantly, the Young Scholar Fellowship Program of Ministry of Science and Technology of Taiwan (108-2636-E-002-012) encourages the first author to fearlessly devote to his research. All supports made this research work possible.


  1. 1.
    Neklutin, C. N.: Mechanisms and Cams for Automatic Machines. American Elsevier Pub. Co., New York (1969).Google Scholar
  2. 2.
    Chen, F. A.: Mechanics and Design of Cam Mechanisms. Pergamon Press, New York (1982).Google Scholar
  3. 3.
    Jensen, P. W.: Cam Design and Manufacture. 2nd edn. Marcel Dekker, Inc., New York (1987).Google Scholar
  4. 4.
    Reeve, J.: Cams for Industry. John Wiley and Sons Ltd, London (1995).Google Scholar
  5. 5.
    Rothbart, H. A.: Cam Design Handbook. McGraw-Hill, New York (2004).Google Scholar
  6. 6.
    Norton, R. L.: Cam Design and Manufacturing Handbook. 2nd edn. Industrial Press, New York (2009).Google Scholar
  7. 7.
    Zigo, M.: A general numerical procedure for the calculation of cam profiles from arbitrarily specified acceleration curves. Journal of Mechanisms 2(4), 407–414 (1967).Google Scholar
  8. 8.
    Chen, F. Y.: An algorithm for computing the contour of a slow speed cam. Journal of Mechanisms 4(2), 171–175 (1969).Google Scholar
  9. 9.
    Chen, F. Y.: A refined algorithm for finite-difference synthesis of cam profiles. Mechanism and Machine Theory 7(4), 453–460 (1972).Google Scholar
  10. 10.
    Angeles, J.: Synthesis of plane curves with prescribed local geometric properties using periodic splines. Computer-Aided Design 15(3), 147–155 (1983).Google Scholar
  11. 11.
    Lakshminarayana, K., Kumar, B. N.: A note on dwell-cam follower-motion synthesis. Mechanism and Machine Theory 22(1), 65–70 (1987).Google Scholar
  12. 12.
    Tsay, D. M., Huey, C. O.: Cam Motion Synthesis Using Spline Functions. Journal of Mechanisms, Transmissions, and Automation in Design 110(2), 161–165 (1988). 10Google Scholar
  13. 13.
    Tsay, D. M., Huey, C. O.: Spline Functions Applied to the Synthesis and Analysis of Nonrigid Cam-Follower Systems. Journal of Mechanisms, Transmission and Automation in Design 111(4), 561–569 (1989).Google Scholar
  14. 14.
    Tsay, D. M., Huey, C. O.: Application of rational B-splines to the synthesis of camfollower motion programs. Journal of Mechanical Design 115(3), 621–626 (1993).Google Scholar
  15. 15.
    Sandgren, E., West, R. L.: Shape Optimization of Cam Profiles Using a B-Spline Representation. Journal of Mechanisms, Transmissions, and Automation in Design 111(2), 195–201 (1989).Google Scholar
  16. 16.
    Yoon, K., Rao, S. S.: Cam motion synthesis using cubic splines. Journal of Mechanical Design 115(3), 441–446 (1993).Google Scholar
  17. 17.
    Ting, K. L., Lee, N. L., Brandan, G. H.: Synthesis of polynomial and other curves with the Bezier technique. Mechanism and Machine Theory 29(6), 887–903 (1994).Google Scholar
  18. 18.
    Neamtu, M., Pottmann, H., Schumaker, L.: Designing NURBS cam profiles using trigonometric splines. Journal of Mechanical Design 120(2), 175–180 (1998).Google Scholar
  19. 19.
    Srinivasan, L. N., Ge, Q. J.: Designing dynamically compensated and robust cam profiles with Bernstein-Bézier harmonic curves. Journal of Mechanical Design 120(1), 40–45 (1998).Google Scholar
  20. 20.
    Kim, J. H., Ahn, K. Y., Kim, S. H.: Optimal synthesis of a spring-actuated cam mechanism using a cubic spline. Proceedings of the Institution of Mechanical Engineers. Journal of Mechanical Engineering Science 216(9), 875–883 (2002).Google Scholar
  21. 21.
    Qiu, H., Lin, C. J., Li, Z.Y., Ozaki, H., Wang, J., Yue, Y.: A universal optimal approach to cam curve design and its applications. Mechanism and Machine Theory 40(6), 669–692 (2005).Google Scholar
  22. 22.
    Nguyen, V. T., Kim, D. J.: Flexible cam profile synthesis method using smoothing spline curves. Mechanism and Machine Theory 42(7), 825–838 (2007).Google Scholar
  23. 23.
    Mandal, M., Naskar, T. K.: Introduction of control points in splines for synthesis of optimized cam motion program. Mechanism and Machine Theory 44(1), 255–271 (2009).Google Scholar
  24. 24.
    Naskar, T. K., Mandal, M.: Introduction of control points in B-splines for synthesis of ping finite optimized cam motion program. Journal of Mechanical Science and Technology 26(2), 489–494 (2012).Google Scholar
  25. 25.
    Cardona, S., Zayas, E. E., Jordi, L., Català, P.: Synthesis of displacement functions by Bezier curves in constant-breadth cams with parallel flat-faced double translating and oscillating followers. Mechanism and Machine Theory 62, 51–62 (2013).Google Scholar
  26. 26.
    Hidalgo-Martinez, M., Sanmiguel-Rojas, E., Burgos, M. A.: Design of cams with negative radius follower using Bezier curves. Mechanism and Machine Theory 82, 87–96 (2014).Google Scholar
  27. 27.
    Yan, H. S., Tsai, M.C., Hsu, M. H.: A variable-speed method for improving motion characteristics of cam-follower systems. Journal of Mechanical Design 118(2), 250–258 (1996).Google Scholar
  28. 28.
    Yan, H. S., Tsai, M. C., Hsu, M. H.: An experimental study of the effects of cam speeds on cam-follower systems. Mechanism and Machine Theory 31(4), 397–412 (1996).Google Scholar
  29. 29.
    Cheng, W. T.: Synthesis of universal motion curves in generalized model. Journal of Mechanical Design 124(2), 284–293 (2002).Google Scholar
  30. 30.
    Flocker, F. W., Bravo, R. H.: A closed–Form solution for minimizing the cycle time in motion programs with constant velocity segments. Journal of Mechanical Design 135(1), 014502 (2012).Google Scholar
  31. 31.
    Zhou, C., Hu, B., Chen, S., Ma, L.: Design and analysis of high-speed cam mechanism using Fourier series. Mechanism and Machine Theory 104, 118–129 (2016).Google Scholar
  32. 32.
    Volmer, J.: Getriebetechnik. VEB Verlag Technik, Berlin (1972).Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNational Taiwan UniversityTaipeiTaiwan, R.O.C.

Personalised recommendations