Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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Dynamics in Carom and Three Cushion Billiards

  • Han Inhwan (Department of Mechano- Informatics & Design Engineering, Hongik University)
  • Published : 2005.04.01
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Abstract

This paper presents the analysis results of dynamics in the billiards game within the frame­work of rigid-body mechanics and a numerical simulation program. The friction exists between the ball and the table bed as well as between the ball and the rail. There are three parts in the dynamic behavior of the ball on the table bed; motion of the ball on the table bed, collision between balls, and collision between the ball and the cushion. During the development of the simulation program, the dynamics problems such as rolling motion and three-dimensional frictional impact motion have been analyzed in detail. The theoretical issues are implemented into a viable graphic simulation program and its efficacy is demonstrated through the experi­mental validation of the billiards game. The resulting analysis results are verified quantitatively and qualitatively using high-speed video camera. Through the experimental tests, it was found that the physical parameters such as coefficients of restitution and friction vary according to the motion variables and corresponding empirical formulations were developed. The simulation and experimental results agree well.

Keywords

References

  1. Cheng, B. -R., Li, J. -T. and Yang, J. -S., 2004, 'Design of the Neural-fuzzy Compensator for a Billiard Robot,' Proc. of IEEE Int'l Conf. on Networking, Sensing and Control, Taipei, Taiwan https://doi.org/10.1109/ICNSC.2004.1297068
  2. Cohen, G. L., 2002, 'Three Cushion Billiards : Notes on the Diamond System,' Sports Engineering, Vol. 5, pp. 43-51 https://doi.org/10.1046/j.1460-2687.2002.00095.x
  3. Han, I. and Gilmore, B. J., 1993, 'Multi-body Impact Motion with Friction-Analysis, Simulation and Experimental Validation,' ASME Trans. Journal of Mechanical Design, Vol.115, pp. 412-422 https://doi.org/10.1115/1.2919206
  4. Han, I. and Cho, J., 1996, 'Analysis of Three-dimensional Rigid-body Collisions with Friction-Collisions Between Ellipsoids (in Korean),' Trans, of the Korean Society of Mechanical Engineers, Vol. 20, No. 5, pp. 1486-1497
  5. Jeong, M. -Y. et al., 2003, 'Chaotic Behavior on Rocking Vibration of Rigid Body Block Structure under Two-dimensional Sinusoidal Excitation,' KSME International Journal, Vol. 17, No. 9, pp. 1249-1260
  6. Onoda, G. Y., 1989, 'Comment on 'Analysis of billiard ball collisions in two dimensions,' by R. E. Wallace and M.C. Schroeder [Am. J. Phys. 56, 815-819 (1988)],' Am J. Phys., Vol.57, No. 5, pp. 476-478 https://doi.org/10.1119/1.16008
  7. Petit, R., 2004, 'The Art of Billiards Play,' http://vrbilliard.tripod.com/practice.html.
  8. Routh, E. J., 1891, Dynamics of a System of Rigid Bodies, MacMillan and Co., London, pp. 265-269
  9. Wallace, R. E. and Schroeder, M. C, 1988, 'Analysis of Billiard Ball Collisions in Two Dimensions,' Am. J. Phys., Vol. 56, No. 9, pp. 815-819 https://doi.org/10.1119/1.15455
  10. Witters, J. and Duymelinck, D., 1986, 'Rolling and Sliding Resistive Forces on Balls Moving on a Flat Surface,' Am. J. Phys., Vol. 54, No. 1, pp. 80-83 https://doi.org/10.1119/1.14747
  11. Witters, J. and Duymelinck, D., 'All About Billiards,' http://allsportsbid.com.