A Model for Straight-Line Pocketing of an Object Ball in Billiards

DOI: https://doi.org/10.62517/jes.202602402

Author(s)

Zhenming Zhang, Jie Deng*

Affiliation(s)

Shenghua Zizhu Academy, Shanghai, China *Corresponding Author

Abstract

In this paper, the problem of speed and aiming for straight-line pocketing of the object ball in billiards will be considered. The simplified motion model will be introduced taking into account the initial speed of the object ball, its effective deceleration and the effective opening half-width. Based on this model, a combined speed and direction criterion for reaching the pocket opening along a straight path is derived. For aligned motion and a zero minimum arrival speed, the initial-speed threshold is proportional to the square root of the normal distance to the pocket opening. The angular tolerance decreases approximately in inverse proportion to this distance in the small-angle limit. The proposed model can inform shot-speed selection and aiming-direction planning for billiards robots.

Keywords

Billiards; Effective Deceleration; Geometric Criterion; Angular Tolerance; Billiards Robot

References

[1] Witters J, Duymelinck D. Rolling and sliding resistive forces on balls moving on a flat surface. American Journal of Physics. 1986; 54(1):80–83. [2] Hierrezuelo J, Carnero C. Sliding and rolling: the physics of a rolling ball. Physics Education. 1995; 30(3):177–182. [3] Florea OA, Rosca IC. Analytic study of a rolling sphere on a rough surface. AIP Advances. 2016; 6(11):115111. [4] Özkanlar A. Billiard physics: Motion of a cue ball after hit by a cue stick horizontally. The Physics Educator. 2020; 2(1):2050003. [5] Wallace RE, Schroeder MC. Analysis of billiard ball collisions in two dimensions. American Journal of Physics. 1988; 56(9):815–819. [6] Doménech-Carbó A. Independent friction-restitution description of billiard ball collisions. Mechanics Research Communications. 2023; 131:104149. [7] Shih C. Aiming strategy error analysis and verification of a billiard training system. Knowledge-Based Systems. 2010; 23(7):732–742. [8] Smith M. PickPocket: A computer billiards shark. Artificial Intelligence. 2007; 171(16–17):1069–1091. [9] Landry JF, Dussault JP. AI optimization of a billiard player. Journal of Intelligent & Robotic Systems. 2007; 50(4):399–417. [10] Mathavan S, Jackson MR, Parkin RM. Ball positioning in robotic billiards: A nonprehensile manipulation-based solution. IEEE/ASME Transactions on Mechatronics. 2016; 21(1):184–195. [11] Park JK, Park J. Intelligent Carom Billiards Assistive System for automatic solution path generation and actual path prediction with principal component analysis-based ball motion detection. International Journal of Advanced Robotic Systems. 2022; 19(4):1–20.