Figure 5 - uploaded by Ping Wang

Content may be subject to copyright.

Source publication

When a table tennis ball is hit by a racket, the ball spins and undergoes a complex trajectory in the air. In this article, a model of a spinning ball is proposed for simulating and predicting the ball flight trajectory including the topspin, backspin, rightward spin, leftward spin, and combined spin. The actual trajectory and rotational motion of...

## Context in source publication

**Context 1**

... the ball spins through a certain angle, its coordi- nates can be obtained by the spin of point P and trans- lation of the coordinate system. 19 Figure 5 shows point P spinning around the unit vector O ball N that passes through the origin O ball with the angle of c. The coordi- nates of point N are (a, b), so the rotation matrix R(c) is given by equation (9) ...

## Similar publications

When a table tennis ball is hit by a racket, the ball spins and undergoes a complex trajectory in the air. In this article, a
model of a spinning ball is proposed for simulating and predicting the ball flight trajectory including the topspin, backspin,
rightward spin, leftward spin, and combined spin. The actual trajectory and rotational motion of...

## Citations

... Studies such as [36,51] mostly rely on image processing techniques to determine or predict the physical behavior of tennis balls or their flight trajectory. Ke et al. [36] proposed to use machine learning and neural networks to determine the impact coordinates of a tennis ball under certain conditions. ...

Topspin is one of the most widely used hitting techniques in a tennis match and it is an effective tool to win over the opponent. Hence, flight path simulation of a spinning ball can be a tremendous analysis tool to help tennis players perfect their game. This article proposes a fuzzy logic model based on the principles of kinematics and mechanics. This study analyzes the physical characteristics of a spinning ball during the flight process, which are divided into two categories: the characteristics of the ball on impact (including the floating and rotating it causes) and the landing rebound characteristics. These two characteristics are considered as the constraints of the flight path simulation and the inputs of the fuzzy logic model. Fuzzy logic is used to fuzzify the impact and landing rebound information of the ball based on the knowledge base, solve the problem, and finally defuzzify the results into crisp outputs, that is, accurate flight trajectory. The simulation results show that the estimation error of the proposed model is lower than 3.7 cm/s and 0.9°, and the success rate of accurate topspin execution is 100%, indicating that the proposed model is effective to train tennis players.

... However, the monitoring of this technology is still an isolated field. First of all, the palms and finger joints are small joints, and a single high-speed camera cannot capture the motion at all [11][12][13]. In addition, athletes' palms need to remain in a square shape before entering the water. ...

Transparent stretchable wearable hybrid nano-generators present great opportunities in motion sensing, motion monitoring, and human-computer interaction. Herein, we report a piezoelectric-triboelectric sport sensor (PTSS) which is composed of TENG, PENG, and a flexible transparent stretchable self-healing hydrogel electrode. The piezoelectric effect and the triboelectric effect are coupled by a contact separation mode. According to this effect, the PTSS shows a wide monitoring range. It can be used to monitor human multi-dimensional motions such as bend, twist, and rotate motions, including the screw pull motion of table tennis and the 301C skill of diving. In addition, the flexible transparent stretchable self-healing hydrogel is used as the electrode, which can meet most of the motion and sensing requirements and presents the characteristics of high flexibility, high transparency, high stretchability, and self-healing behavior. The whole sensing system can transmit signals through Bluetooth devices. The flexible, transparent, and stretchable wearable hybrid nanogenerator can be used as a wearable motion monitoring sensor, which provides a new strategy for the sports field, motion monitoring, and human-computer interaction.

... The video data must have clear images to calculate the ball's rotation and a high camera frame rate to correctly judge the rotation speed. Furthermore, the camera hardware must be advanced, limiting the generation system's development significantly [8]. Therefore, real-time monitoring and controlling prediction are urgent problems in sophisticated environments. ...

A DCNN-LSTM (Deep Convolutional Neural Network-Long Short Term Memory) model is proposed to recognize and track table tennis’s real-time trajectory in complex environments, aiming to help the audiences understand competition details and provide a reference for training enthusiasts using computers. Real-time motion features are extracted via deep reinforcement networks. DCNN tracks the recognized objects, and the LSTM algorithm predicts the ball’s trajectory. The model is tested on a self-built video dataset and existing systems and compared with other algorithms to verify its effectiveness. Finally, an overall tactical detection system is built to measure ball rotation and predict ball trajectory. Results demonstrate that in feature extraction, the Deep Deterministic Policy Gradient (DDPG) algorithm has the best performance, with a maximum accuracy rate of 89% and a minimum mean square error of 0.2475. The accuracy of target tracking effect and trajectory prediction is as high as 90%. Compared with traditional methods, the performance of the DCNN-LSTM model based on deep learning is improved by 23.17%. The implemented automatic detection system of table tennis tactical indicators can deal with the problems of table tennis tracking and rotation measurement. It can provide a theoretical foundation and practical value for related research in real-time dynamic detection of balls.

... Motion capture technology uses the principle of computer graphics to track, measure, and record the three-dimensional motion of the main joints of human body in the form of images through multiple cameras arranged in space, and has been widely used in lm production, mechanical control, simulation training and teaching, human posture research, ergonomics and other elds [22, 23 24, 25, 26, 27]. Highspeed motion capture system can not only capture the trajectory of a ying ball, but also calculate the ball speed, which is widely used in the monitoring of sports training [21,28,29]. ...

Background: A perfect stroke is essential for winning table tennis competition. A perfect stroke is closely related to reasonable stroke structure, which directly affects the stroke effect. The main purpose of this study was to examine the correlations between the structural characteristics of stroke and the stroke effect.
Methods: Forty-two young table tennis players were randomly selected from China Table Tennis College (M age = 14.21 ± 2.13; M height = 1.57 ± 0.14 m; M weight = 46.05 ± 6.52 kg, right-hand racket, shake-hands grip, no injuries in each joint of the body). The high-speed infrared motion capture system was used to collect the data of stroke structural characteristics, and the high-speed camera was used to measure the spin speed of the stroke. The influence of striking structural characteristics on striking effect was examined.
Results: The time duration of backswing and forward motion were significantly correlated with ball speed (r = -0.403, p < 0.01; r = -0.390, p < 0.01, respectively) and spin speed (r = -0.244, p = 0.027; r = -0.369, p < 0.01, respectively). The linear velocity of right wrist joint was positively correlated with ball speed (r = 0.298, p < 0.01) and spin speed (r = 0.238, p = 0.031). The angular velocity of right elbow joint and right hip joint were positively correlated with ball speed (r = 0.219, p = 0.013; r = 0.427, p < 0.01, respectively) and spin speed (r = 0.172, p = 0.048; r = 0.277, p = 0.012, respectively). The angular velocity of right knee joint had a significantly negative correlation with placement (r = -0.246, p = 0.026). The angular velocity of right ankle joint had a significantly positive correlation with the ball speed (r = 0.443, p < 0.01).
Conclusions: The time allocation of the three phases of backspin forehand stroke had an important impact on stroke effect, especially the ball speed and spin speed. The ball speed of the stroke was mainly affected by the translation of the right wrist joint. The spin speed of the stroke was mainly affected by the translation of the right wrist joint. The placement of the stroke was mainly affected by the rotation of the right knee joint.

... Here there exists a unique polynomial q(t) using the n th order. Equation (14) establishes the relation matrix pf vectors q and a, which is known as the Vandermonde matrix T [29]. Using the pseudo inverse matrix of T, Equation (15) gives coefficient a where a minimum squared-error exists between the coefficient equation and the trajectory data. ...

Sports robots have become a popular research topic in recent years. For table-tennis robots, ball tracking and trajectory prediction are the most important technologies. Several methods were developed in previous research efforts, and they can be divided into two categories: physical models and machine learning. The former use algorithms that consider gravity, air resistance, the Magnus effect, and elastic collision. However, estimating these external forces require high sampling frequencies that can only be achieved with high-efficiency imaging equipment. This study thus employed machine learning to learn the flight trajectories of ping-pong balls, which consist of two parabolic trajectories: one beginning at the serving point and ending at the landing point on the table, and the other beginning at the landing point and ending at the striking point of the robot. We established two artificial neural networks to learn these two trajectories. We conducted a simulation experiment using 200 real-world trajectories as training data. The mean errors of the proposed dual-network method and a single-network model were 39.6 mm and 42.9 mm, respectively. The results indicate that the prediction performance of the proposed dual-network method is better than that of the single-network approach. We also used the physical model to generate 330 trajectories for training and the simulation test results show that the trained model achieved a success rate of 97% out of 30 attempts, which was higher than the success rate of 70% obtained by the physical model. A physical experiment presented a mean error and standard deviation of 36.6 mm and 18.8 mm, respectively. The results also show that even without the time stamps, the proposed method maintains its prediction performance with the additional advantages of 15% fewer parameters in the overall network and 54% shorter training time.

In sports science research, the dynamic non-uniform blur caused by the movement of running athletes is a challenging problem in computer vision, that seriously affects the judgment accuracy of the finish-line photography system. With the rapid development of deep learning technology, image preprocessing, object identification, and object classification have been widely used and studied. This work proposes multi-scale convolutional neural network image deblurring to eliminate dynamic blur generated by the athletes in the shooting process. This network comprises three end-to-end convolutional neural subnetworks of different scales to recover the blurry athlete image caused by various factors on the field. The system effectively extracts the detailed edge of the image on each scale from coarse to fine. Many experiments show that this method can deblur the image captured by the finish-line photography system in real-time and rapidly achieve a better visual effect in the athlete’s dynamic image.

Background:
An optimal stroke is essential for winning table tennis competition. The main purpose of this study was to examine the correlations between the stroke characteristics and the stroke effect.
Methods:
Forty-two young table tennis players were randomly selected from China Table Tennis College (M age= 14.21; M height= 1.57m; M weight= 46.05 kg, right-hand racket, shake-hands grip, no injuries in each joint of the body). The high-speed infrared motion capture system was used to collect the data of stroke characteristics, and the high-speed camera was used to measure the spin speed of the stroke. The influence of stroke characteristics on stroke effect was analyzed.
Results:
The time duration of backswing and forward motion were significantly correlated with ball speed (r=-0.403, P<0.01; r=-0.390, P<0.01, respectively) and spin speed (r=-0.244, P=0.027; r=-0.369, P<0.01, respectively). The ball speed was positively correlated with the linear velocity of right wrist joint (r=0.298, P<0.01), and the angular velocity of right elbow joint (r=0.219, P=0.013), right hip joint (r=0.427, P<0.01) and right ankle joint (r=0.443, P<0.01). The spin speed was positively correlated with the linear velocity of right wrist joint (r=0.238, P=0.031), and the angular velocity of right elbow joint (r=0.172, P=0.048) and right hip joint (r=0.277, P=0.012). The placement had a negative correlation with the angular velocity of right knee joint (r=-0.246, P=0.026).
Conclusions:
The time allocation of the three phases of backspin forehand stroke had an important correlation with stroke effect, especially the ball speed and spin speed. The movement of the right wrist joint and right ankle joint were mainly correlated with the ball speed of the stroke. The spin speed of the stroke was mainly correlated with the movement of the right wrist joint. The placement of the stroke was mainly correlated with the rotation of the right knee joint.