- Open Access
Kinematic evaluation of movement smoothness in golf: relationship between the normalized jerk cost of body joints and the clubhead
© Choi et al.; licensee BioMed Central Ltd. 2014
Received: 10 October 2013
Accepted: 20 February 2014
Published: 26 February 2014
When the human body is introduced to a new motion or movement, it learns the placement of different body parts, sequential muscle control, and coordination between muscles to achieve necessary positions, and it hones this new skill over time and repetition. Previous studies have demonstrated definite differences in the smoothness of body movements with different levels of training, i.e., amateurs compared with professionals. Therefore, we tested the hypothesis that skilled golfers swing a driver with a smoother motion than do unskilled golfers. In addition, the relationship between the smoothness of body joints and that of the clubhead was evaluated to provide further insight into the mechanism of smooth golf swing.
Two subject groups (skilled and unskilled) participated in the experiment. The skilled group comprised 20 male professional golfers registered with the Korea Professional Golf Association, and the unskilled group comprised 19 amateur golfers who enjoy golf as a hobby. Six infrared cameras (VICON460 system) were used to record the 3D trajectories of markers attached to the clubhead and body segments, and the resulting data was evaluated with kinematic analysis. A physical quantity called jerk was calculated to investigate differences in smoothness during downswing between the two study groups.
The hypothesis that skilled golfers swing a driver with a smoother motion than do unskilled golfers was supported. The normalized jerk of the clubhead of skilled golfers was lower than that of unskilled golfers in the anterior/posterior, medial/lateral, and proximal/distal directions. Most human joints, especially in the lower body, had statistically significant lower normalized jerk values in the skilled group. In addition, the normalized jerk of the skilled group’s lower body joints had a distinct positive correlation with the normalized jerk of the clubhead with r = 0.657 (p < 0.01).
The result of this study showed that skilled golfers have smoother swings than unskilled golfers during the downswing and revealed that the smoothness of a clubhead trajectory is related more to the smoothness of the lower body joints than that of the upper body joints. These findings can be used to understand the mechanisms behind smooth golf swings and, eventually, to improve golf performance.
Golf requires accuracy controlling the ball’s direction and flight distance . The flight distance of the driver shot is one of the most important parts of the game because it sets the tone for the rest of the game and heavily influences the strategies for the following shots. In addition, the downswing phase takes place a considerable amount of energy consumption to generate high clubhead velocity . Therefore, analyzing, understanding, and mastering the downswing can improve the overall game performance and management .
A golf swing involves complex and continuous rotational movements of each joint in the body, and the muscle contraction sequence and timing of the impact between the club and ball are important components of a successful swing . Okuda et al. proposed that the sequential rotation of each joint involved in golf swing , called proximal-to-distal sequencing (PDS) , is the most important factor for successful golf shots. This series of movements builds momentum from the proximal to distal segments, and skilled golfers have been shown to be highly effective and efficient in these movements by a variety of studies [7–10]. Thus, a successful golf swing can be achieved by rotating the joints and harmoniously coordinating these movements.
A fast, accurate, consistent, and smooth movement has a high coupling in the body joints and segments and extends to successful performance . According to Bril et al., skilled or dexterous action consists of smoothness, flexibility, precision, speed, adaptability, regularity, and optimization, and functionally coordinating these conditions is crucial . Smoothness is achieved by purposefully repeating a movement and making necessary corrections to improve the motion . The success of a human movement is judged by the smoothness of the motion, which can be quantified as jerk .
Jerk is defined as a change in acceleration rate over time and is the third derivative of displacement. The smoothest motion has the lowest jerk. There have been many attempts to describe the smoothness in a variety of movements. Hreljac compared the jerk in the heel of skilled middle- to long-distance runners to that of other athletes (from soccer or tennis) during running and fast walking . The runners had significantly lower jerk than did other athletes, and Hreljac concluded that the runners tended to exhibit smoother movements than non-runners during both running and fast walking. In addition, by analyzing jerk, Yan et al. found that the arm movement involved in overarm throwing becomes smoother as one becomes an adult . More recently, Sakata et al. studied the effect of age-related changes in the smoothness of lower body joints during lifting, and demonstrated high jerk values in the ankle and hip joints of older subjects, pointing to less smooth movements in this group .
An attempt to analyze the smoothness of golf putting was recently performed by Choi et al., who compared jerk among 3 groups: professional, recreational, and novice golfers . They found a significant difference between the novice golfers and the other groups. Nevertheless, studies investigating the smoothness of golf swing movements are quite rare , and none have analyzed the smoothness of a driver swing.
In this study, using jerk, which quantitatively represents the smoothness of a motion, differences between skilled and unskilled golfers were analyzed during the downswing with a driver. We tested the hypothesis that the jerk of the clubhead during the driver downswing is lower in skilled golfers than in unskilled golfers. In addition, basic data to investigate the mechanism of a smooth clubhead movement was proposed by analyzing the correlations between the jerk of individual body joints and that of the clubhead.
Subjects & apparatus
Subject characteristics (Mean ± SD)
(Males, N = 20)
(Males, N = 19)
37.3 ± 9.1
40.3 ± 11.7
173.8 ± 5.2
171.6 ± 5.7
71.5 ± 12.0
71.8 ± 8.6
16.7 ± 6.7
p < 0.01
Peak clubhead speed (m/s)
39.2 ± 4.6
36.3 ± 10.0
Downswing duration (sec.)
0.307 ± 0.04
0.327 ± 0.04
Thirty-five optical markers were attached to anatomical landmarks of the golfers. The placement of each marker was based on the modified Helen Hayes markerset protocol [17, 18], and an additional marker was attached to the clubhead for the jerk analysis. Before the experiment, subjects completed a warm up with large dynamic movements and static stretches , and each subject was able to adapt to the laboratory environment with a practice swing. Each participant performed 3 swings, and the best shot, decided by how the participant felt about the shot and also by the quality of the reconstructed 3D data, was used in the analysis . The analysis was limited to the downswing, which is the interval from the top of the backswing to the point of impact between the club and the ball. The top of the backswing was defined as the moment when the point of maximum clubhead rotation .
Data & statistical analysis
A Mann-Whitney test was applied for comparative assessments of the skilled and unskilled groups, and correlation analysis was performed to define the relationship between the NJ of each human joint and that of the clubhead. All statistics were calculated using the SAS statistical analysis program (SAS version 9.1), and the significance level was set at p < 0.05.
3D trajectories of a clubhead between skilled and unskilled golfers
NJ of human joints
Comparisons of the NJs of all joint angles between the skilled and unskilled golfers during the downswing
215.0 ± 92
496.3 ± 242
107.1 ± 57
240.3 ± 167
105.9 ± 50
254.5 ± 124
298.5 ± 109
459.7 ± 258
194.0 ± 59
310.7 ± 185
98.4 ± 40
177.5 ± 97
187.9 ± 84
324.9 ± 140
162.7 ± 50
346.8 ± 108
147.7 ± 49
288.5 ± 280
297.1 ± 145
331.7 ± 129
237.7 ± 127
391.8 ± 219
211.1 ± 124
241.6 ± 130
180.3 ± 60
216.7 ± 80
177.8 ± 47
222.1 ± 70
280.4 ± 158
359.8 ± 204
204.9 ± 88
169.3 ± 88
151.5 ± 70
237.8 ± 103
343.6 ± 136
372.7 ± 183
115.4 ± 61
125.4 ± 43
282.4 ± 146
286.9 ± 125
197.4 ± 92
252.4 ± 177
275.7 ± 139
315.3 ± 184
300.4 ± 176
353.4 ± 143
105.9 ± 55
186.4 ± 222
213.9 ± 151
227.1 ± 83
211.7 ± 134
247.4 ± 164
518.3 ± 142
728.9 ± 326
215.8 ± 135
272.1 ± 166
312.0 ± 135
421.0 ± 48
320.5 ± 194
239.6 ± 100
455.3 ± 331
214.4 ± 85
329.5 ± 149
282.9 ± 100
480.4 ± 213
627.6 ± 466
635.5 ± 439
1120.4 ± 552
1951.9 ± 1442
1622.9 ± 1686
1211.3 ± 685
1241.7 ± 2197
Correlation analysis between NJ of clubhead and human joints
Correlation coefficient between the cumulative NJs of the joints and the NJ of clubhead during the downswing of skilled and unskilled golfers ( p-value )
On the basis of the general observation that experts or professionals seem to have smoother motions [13, 14, 16], this study was analyzed whether skilled golfers have a smoother golf driver swing than unskilled golfers. To quantify smoothness, jerk, the third derivative of displacement, and the NJ of the clubhead trajectory and of the rotational of all body joints during the downswing were calculated. Also, to better understand the mechanism of a smooth swing, the correlations between the NJs of each joint and the clubhead were calculated.
Since the jerk is the third differentiated trajectory value, random noise can accumulate. Jerk is reportedly sensitive to data smoothing methods . Hreljac tried to minimize this potential error by using a double data smoothing method by filtering raw trajectory data and then filtering acceleration to calculate the jerk in heel movements during running and fast walking . We tested a variety of cut-off frequencies and double data smoothing methods and selected a cut-off frequency for a low-pass filter by visually inspecting the frequency spectrum of each marker. Absolute differences jerk value depended on the data smoothing method, but relative differences between groups and the results of the statistical analysis were always consistent. Even though jerk is sensitive to data smoothing, the filter and cut-off frequency used in this study were appropriate for comparing the two groups.
High jerk values can be interpreted in 2 ways: strong muscles or decreased smoothness . Puniello et al. proposed that the jerk for the vertical trajectory of box lifting is significantly and positively correlated with hip extensor strength . Sakata et al. proposed that the jerk values of the ankle and hip joints increased because the smoothness of lower body joints was lower in the aged group . In general, professional athletes are much stronger than amateurs, and according to previous studies, professional athletes have better muscle balance in the lower body, better weight shifts during movements, and more coordinated sequential muscle activation than amateurs [5, 25]. In the current study, the skilled group had lower jerk in most joints and the clubhead, indicating smoother movements.
This study revealed that although 3D tracing of the downswing movement, when graphed, seemed similar between the skilled and unskilled groups (Figure 3), there was significant and noticeable differences between groups when jerk was taken into account (Figure 4). According to the Newton’s second law ‘F = ma’, force and acceleration have a proportional relationship when the mass is fixed. Therefore, jerk, the derivative of acceleration, can be defined as the variation of applied forces. The graph of jerk values (Figure 4) showed bigger fluctuation with wider distance between each peak and trough and steeper slopes, which implies an unbalanced force distribution to the club and unnecessary physical exertion during the downswing. The unskilled golfers exhibited higher NJ in most of joints and clubhead, which suggests less smoothness of movements due to inefficient motor control .
Another novel suggestion from this study is that the clubhead smoothness during the downswing is highly related to the smoothness of the lower body joints. Most previous literature dealing with golf swing mechanisms has analyzed the upper limbs [27, 28]; only a few have studied the importance of the lower body. However, the fact that a robust lower body is required in upper body-oriented activities, such as pitching and hitting in baseball, is established and well accepted. Continuous movement of upper body joints, such as the PDS, is required in golf for a long drive, but the current study shows that smooth lower body movement is important for a smooth swing. Therefore, building a strong and durable lower body through adequate lower limb training is essential for controlling smoothness. Furthermore, future kinematic and kinetic studies are necessary to establish the precise mechanism that leads to a smooth clubhead trajectory.
Skilled golfers had lower clubhead NJ in the golf driver downswing. This result implies that clubhead movements in skilled golfers were smoother than in unskilled golfers.
Skilled golfers had lower NJ in most joint than did unskilled golfers, although not all differences were statistically significant. The differences between groups for most lower body joints were statistically significant. The differences for most upper body joints were not statistically significant.
The NJs of the joints and the clubhead were positively correlated in the skilled group, and the cumulative NJ of the lower body had the highest correlation with the clubhead (r = 0.657, p < 0.01). The unskilled group did not have as strong of a correlation. This result can be used in future studies to investigate the mechanism behind smooth clubhead movement leading to smoother and more efficient golf swings.
This study confirmed that the jerk of the golf driver swing can be used as a quantitative measure to show differences in smoothness and that swing smoothness should be used in teaching golf. Nevertheless, this study has 2 limitations: only the downswing was analyzed and only the driver swing was analyzed. Future work should analyze the entire swing using various golf clubs. Fundamental and in-depth research on the mechanisms generating smoothness is also necessary.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2013R1A1A2009495), and the Research Fund of the Catholic University of Korea.
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