Research article - (2009)08, 235 - 246 |
Kinematic Analyses of the Golf Swing Hub Path and its Role in Golfer/Club Kinetic Transfers |
Steven M. Nesbit, Ryan McGINNIS |
Key words: Golf biomechanics, golf swing kinematics, golf swing kinetics |
Key Points |
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Subjects |
Four amateur golfers, three males and the one female had their golf swings analyzed for this study. All subjects are right-handed and their relevant data are given in |
Subject Swing Data |
Much of the kinematic and kinetic data output by the computer model ( |
Hub Path Geometry |
In the discussions that follow, the reader should refer to |
Hub Path Velocity and Acceleration |
The maximum hub path linear (grip) velocities were found to be very similar among the subjects (11.5, 11.1, 11.2, 11.3) m·s-1. For all subjects, the velocity increased significantly during the first phase + (39.7, 37.4, 38.0, 42.8)%, but more rapidly during the second phase +(60.3, 62.6, 62.0, 53.4)%. A slight but distinct increase in the slope of the velocity profile was evident at the transition between phase I and phase II for all subjects. The increasing path radius during phase II appears to enhance the rate of increase in hub velocity. Three of the four subjects reached their peak grip velocity values at the end of the phase II. The grip velocity remained nearly constant during phase III for the male scratch subject, reduced slightly for the male 5H and male 13H subjects, and increased slightly for the female 18H subject. Relationships between the linear acceleration components of Equations (5) and (6), and hub radius phases can be better identified when the accelerations are resolved into tangential and normal components. Referring to The differences in the profiles and maximum values of the normal acceleration for the subjects resulted primarily from differences in the hub path radius profiles since the velocity profiles were similar. For all subjects, the normal acceleration increased during all phases; + (32.4, 30.2, 35.8, 46.7)% during phase I, + (34.5, 41.7, 27.4, 33.4)% during phase II, and + (33.1, 28.1, 31.8, 19.1)% during phase III. Three of four subjects reached 100% of their maximum normal accelerations at ball contact (the female 18H subject reached 99.2%). The increase during phase III was a result of the significant reductions in hub radii for all subjects since their linear velocities were relatively constant during this phase. The normal acceleration was (nearly) maximum at ball contact for all subjects even in cases when hub path linear velocity was not maximum. This occurrence was a result of all subjects reaching a local minimum radii at ball contact. The rate of increase of normal accelerations was fairly uniform over the three phases for three of the subjects. This uniformity requires a complex interaction between hub path velocity and radius during the downswing. |
Hub Path Interface Kinetics: Torque |
The maximum swing torque values differed considerably among the subjects (42.1, 36.8, 24.6, 24.0) Nm. All subjects initiated the downswing with a relatively high percentage of their maximum swing torque (44.6, 29.7, 28.8, 16.3)%. The subjects increased their swing torque over phase I + (31.4, 37.0, 58.3, 67.9)% reaching (66.0, 66.7, 87.1, 84.2)% of maximum at the end of the phase. Even though the swing torques were relatively high during phase I, there was little outward movement of the club relative to the hub path. The low club handle velocity coupled with the initial large hub path radius minimized the centrifugal loading on the club thus reducing the tendency of the club moving outward. The subjects further increased their torque over phase II + (24.0, 33.3, 12.9, 15.8)% and all reached 100% of maximum torque at the end of the phase. For all subjects, the initiation of phase II coincided with their first local hub radius minimum, while applying the majority of their respective maximum swing torque, and reaching about half of their respective maximum grip velocity. Acting together these effects increased the centrifugal loading on the club and initiated the rapid outward or uncocking movement of the wrists/club relative to the hub path. During phase II, as the club moved outward, the wrist torques continued to increase accelerating the angular motion of the club. The increase in hub path radius during this phase may be a result of the golfer shifting the effort from controlling the hub path to applying maximum wrist torque, or it could simply be a third-law reaction to the rapid outward movement of the club. During phase III, all subjects experienced a significant reduction in swing torque -(100, 91.8, 72.4, 65.5)% and reached (0, 8.2, 27.6, 34.4)% of maximum at ball contact. During phase III when the hub radius reduced rapidly, the wrist torques decreased toward zero at ball contact. During this phase, the wrist torques continued to contribute somewhat to the acceleration of the club. |
Hub Path Interface Kinetics: Force |
Relationships between the linear force and hub radius phases can be better identified when the force is resolved into its tangential and normal components (see The tangential component is initially (12.3, 10.3, 6.6, 4.9)% of maximum and increased + (41.0, 49.0, 56.7, 66.7)% and reached (53.3, 59.3, 63.3, 71.6)% of maximum at the end of phase I. The tangential force continued to increase during phase II + (46.7, 40.7, 36.7, 28.4)% and all subjects reached 100% of maximum at the end of phase II. During phase III the tangential force drops rapidly - (100, 93.3, 96.7, 92.2)% and reached (0, 6.7, 3.3, 7.8)% of maximum at ball contact. The normal component which is initially zero increased during all three phases; + (7.7, 14.2, 16.2, 23.7)% during phase I, + (16.1, 17.1, 22.1, 27.8)% during phase II, and +(75.7, 68.7, 61.7, 48.5)% during phase III. All subjects reached 100% of maximum at ball contact. The function of the linear force appears to change as the downswing progresses. During phase I, the majority of the force is tangent to the path and primarily functions to accelerate the club. The subjects apply the majority of their respective maximum tangent force by the end of phase I while applying little of their respective maximum normal force in controlling the hub path. Only modest effort is required to reduce the path radius during this phase because of the low club velocity. The tangential force continues to increase during phase II and reaches maximum at the end of the phase which coincides with the subjects reaching their local maximum radii. During this phase the normal force increases more slowly and reaches between a quarter and half of maximum by the end of the phase. Even though the club head velocity is quite high at this point (86.4-92.6% of maximum), the increasing value of the hub radius and the angular position of the club relative to the hub path diminish the centrifugal force loading from the club. The function of the linear force during this phase transforms from simply accelerating the club to simultaneously accelerating the club, controlling the path, and reacting to the centrifugal loading of the club. During phase III the tangential force drops toward zero while the normal force increases to maximum values at ball contact. The primary action of the linear force during this phase is controlling the path and reacting to the large centrifugal loading from the club as it reaches its maximum club head velocity and coincident minimum hub radius. The rapidly reducing hub path radius nearing ball contact assists in transferring energy to the club even though the direction of the force is nearly perpendicular to the direction of the club head velocity (Miura, |
Hub Path Interface Kinetics: Work and Power |
The work (and power) done on the club by the golfer during the downswing is resolved into linear and angular contributions (see Equation (7). The linear work comes primarily from the action of the arms and the angular work from the action of the wrists (Nesbit and Serrano, There were significant differences in total work (355, 289, 288, 235) Nm and linear work (206, 155, 140, 114) Nm among the subjects. The angular work was more consistent (146, 134, 148, 121) Nm. The ratio of linear work to angular work for the subjects was (1.41, 1.16, 0.95, 0.94) which highlights the relative use of the arms/wrists in doing work on the club. During phase I the subjects generated (35.5, 37.3, 50.1, 60.4)% of their total work, which consisted of (58.5, 53.3, 44.6, 54.5)% of their linear work, and (17.6, 21.7, 56.3, 69.0)% of their angular work. During phase II, the subjects increased their total work by + (39.0, 47.9, 33.2, 34.1)%, of which the linear work increased by + (32.9, 43.1, 41.5, 42.7)%, and the angular work increased by + (69.7, 72.5, 23.6 26.4)%. There were smaller addition amounts of work done during phase III. Total work increased by + (10.5, 4.8, 16.7, 3.5)%, of which the linear work increased by + (8.6, 5.6, 13.9, 2.8)%, and the angular work increased by + (12.7, 3.8, 20.1, 4.6)%. All subjects reached 100% of their total, linear, and angular work at ball contact. All subjects did the most linear work during phase I which emphasizes the importance of the arms in accelerating the club during this portion of the downswing. During this phase, the relative high value of the linear displacement combined with moderate values of the tangential force yielded the high value of linear work. All subjects continued to do positive linear work through phase II though not as much as during phase I. Here the tangential forces became maximum, however they were applied to only about 30% of the hub path. The small amount of additional linear work done during phase III reflects the rapidly diminishing tangential force and small linear displacement during this phase. The majority of the angular work was done during phases I and II for the subjects which emphasizes the importance of the wrists in accelerating the club during these phases of the downswing. The angular work results from the combined effects of swing torque applied over the angular displacement of the club. These results reveal the effectiveness of the male scratch and male 5H subjects in delaying the outward movement or uncocking of the club through coordinating the timing of their swing torques with the radius profile of the hub path which has been shown to yield higher club head velocities (Nesbit, There were large differences among the subjects in total power (3875, 3005, 2310, 1720) Nm·s-1, linear power (2775, 2316, 1402, 1188) N.m/s and angular power (1150, 890, 1078, 698) Nm·s-1, as well as in the ratio of linear power (arms) to angular power (wrists) (2.41, 2.60, 1.30, 1.70). Starting from zero power, the total power reached (30.6, 26.7, 45.2, 51.0)% of maximum, the linear power reached (37.6, 34.1, 44.9, 55.5)% of maximum, and the angular power reached (22.0, 19.6, 47.2, 47.0)% of maximum at the end of phase I. During phase II, the subjects increased their total power by + (69.4, 73.3, 54.8, 49.0)%, their linear power by + (62.4, 65.9, 55.1, 44.5)%, and their angular power by + (78.0, 80.4, 52.8, 53.0)%. By the end of phase II, all subjects had reached 100% of their maximum total, linear, and angular power. During phase III, the power dropped rapidly, and at ball contact the total power was (0, 0, 5.2, 8.8)% of maximum, linear power was (0, 0, 2.1, 6.0)% of maximum, and angular power was (0, 0, 11.3, 14.8)% of maximum. Phase II appears to be the most important portion of the downswing relative to power generation. All subjects are at peak power output the end of phase II thus applying maximum effort in accelerating the club (both linearly and angularly) at this point in the downswing. This peak coincides with the subjects reaching a local maximum hub radius. It would seem logical that an increasing radius during this phase would reduce the effort required to control the path, thus making more effort available to the golfer to generate power thus enhancing the kinetic transfer from the golfer to the club. |
Club Head Velocity |
Maximum club head velocities differed significantly among the subjects (52.0, 49.7, 46.3, 42.1) m·s-1. The subjects generated (30.3, 32.2, 37.5, 46.5)% of their maximum club head velocity during phase I. During phase II the subjects increased their velocity by + (60.1, 56.3, 48.9, 46.1)% reaching (90.4, 88.5, 86.4, 92.6)% of their maximum by the end of the phase. The subjects further increased their club head velocities during phase III by + (9.6, 11.5, 13.6, 7.4)% and all subjects achieved 100% of maximum at ball contact. All subjects showed an increase in club head velocity during the entire downswing. The rate of velocity increase transitions from phase I to phase II for three of the subjects (the female 18H subject sees a uniform increase over the two phases). At this point in the downswing, the slope of the velocity curve shows a relatively sharp increase which expected since this change in phase coincides with the initiation of the outward movement of the club. At the transition from phase II to phase III, the club head velocity begins to level off as it reaches its maximum value at call contact. The specific effects of hub path radius on club head velocity are difficult to isolate since club head velocity represents a summary of the effectiveness of the golfer in generating and transferring energy through the various kinetic quantities to the club which individually are related to the hub radius to different degrees as discussed. |
Hub Path Modification and Optimization for Scratch Golfer |
In an effort to better understand the role of the hub path in the golf swing, modifications were made to the hub path of the scratch golfer and the effects upon the club head velocity and kinetic quantities were determined. Two hub path modifications were analyzed then compared to the original swing. First, the hub path was constrained to follow a constant radius path set at the average (0.58 m), larger than the average (0.68 m), and smaller than the average radius (0.48 m) for this subject (The average radius was determined by matching the original swing club head velocity using a constant radius hub path). The swing was kinematically controlled to execute the original swing with the exception of the altered hub path. Second, an optimum hub path was searched for within the band of possible hub paths constrained by the maximum and minimum radial values exhibited by the subject. Once a hub path “trial ”was selected within the band, the swing was again kinematically controlled to execute the original swing with the exception of the altered hub path. The goal of the optimization was to identify the hub path that yielded the highest club head velocity. A constraint on the optimization was that none of the kinetic values (force, torque, work, and power) from the original subject swing could be exceeded. The results of the constraining the hub path to constant radius motion are presented in The optimization algorithm searched through 80 million iterations in identifying a hub path for this subject that yielded an increased club head velocity (+4.1%) with equal or lower kinetic quantities to execute ( |
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The X-Y coordinate system is in the plane of the swing and fixed to the ground (global coordinate system). The N-T coordinate system (local coordinate system) is attached to, and moves with grip point A along the hub path, and orients normal to the path pointing towards the center of curvature (N-component), and tangent to the path in the direction of motion (T-component). The following equations of motion were developed from The acceleration of the club mass center is given by the following relative acceleration vector expression: This equations yields the following scalar components in the X and Y directions: Data to kinematically drive the model are obtained from subject golf swings. A motion capture system (Motion Analysis Corporation, Santa Rosa, CA, USA) with eight Falcon HR 240 cameras and Eva 6.02 software is used to collect and process data from the golfers’ swings. The system tracks passive-reflective markers that are placed on the golfer and the club. Only the data from the markers on the club are necessary to drive this model. The three markers on the club are arranged in a rigid triad that is attached to the shaft just below the handgrip. Two of the markers are aligned with the long axis of the club shaft, and the third is offset perpendicular to the club shaft and parallel to the club face (see Numerical differentiation of the swing plane linear and angular position data yields the linear acceleration of the hub path (A From the linear force components and swing torque at the club handle, the total work done by the golfer on the club is determined from the following: Where i indicates the value of the quantity at point i in the hub path, and the ∆ function indicates a change in the associated quantity from hub point i to i + 1. The total power is determined by numerically differentiating the work expression of Equation (7). The total work and power quantities are comprised of the contributions from the linear force (linear work and power) and swing torque (angular work and power). |
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Superimposed illustrations of the subject swings are shown in The hub path during the downswing for all subjects is shown in |
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The following discussions are limited to the downswing portion of the golf swing. Grouped numerical quantities given in parentheses are for the male scratch, male 5H, male 13H, and female 18H subjects respectively and +/- indicates overall increase/decrease. |
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Analysis of the hub path during the downswing found that it is geometrically complex, deviates significantly from a constant radius path, exhibits a continuously changing radius, and experiences considerable movement of the center-of-curvature. While the size and shape of the hub path differed considerably among subjects, a three phase pattern emerged that was based upon path radius max/mins, that aligned well with distinct stages of thedownswing. Significant markers, relative changes, and trends in the kinematic and kinetic quantities occurred within these specific phases of the hub path. Describing the downswing relative to the hub path phasing was found to be logical and informative. The shape of the hub path appears to result from a complex combination of achieving equilibrium between the golfer and the club, and a purposeful configuring of the path to control the outward movement of the club while minimizing the kinetic loading on the golfer yet transferring the maximum kinetic quantities to the club. Artificially controlling and optimizing the hub path of the better golfer in the group indicated that a non-circular hub path was superior to a constant radius path in minimizing the kinetic loading while generating the highest possible club head velocity. This results presented in this study support the notion that the non-circular nature of the hub path is fundamental to the golf swing, and properly configured an essential element in achieving the maximum transfer of energy from the golfer to the club. These finding have important implications for golf instruction, and possibly for equipment design (achieving variable equilibrium paths) and injury prevention (minimizing kinetic loading). |
ACKNOWLEDGEMENTS |
Funding for this project was provided by a grant from the National Science Foundation. |
AUTHOR BIOGRAPHY |
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REFERENCES |
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