Fig 2 - uploaded by Sasho James Mackenzie
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a Dynamic loft is the change in nominal club loft that results from clubhead deflection. b Dynamic close also occurs as a result of clubhead deflection and is a close in the face of the clubhead relative to the intended clubhead direction
Source publication
Theoretically, shaft stiffness can alter shot distance by increasing clubhead speed or altering clubhead orientation at impact.
A 3D forward dynamics model of a golfer and flexible club simulated the downswing. A genetic algorithm optimized the coordination
of the model’s muscles (four torque generators) to maximize clubhead speed. The maximum torq...
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An understanding of shaft dynamics during the golf swing was gained through a series of theoretical simulations, using a 3D
forward dynamics model. By resolving the resultant force applied at the grip end of the club into a tangential and a radial
(centripetal) component, the mechanisms of shaft deflection were quantified. It was determined that ra...
Citations
... We present results that apply our modeling approach to the inertia tensor that was obtained by geometric scaling [21], from a previously published dataset [22]. Specifically, we did not directly measure the inertia tensor; rather, we used data obtained from a club made by the same manufacturer. ...
This study explores the application of the Laban/Bartenieff Movement System (® LBMS), particularly its Effort component, to analyze the biomechanical dynamics of the golf swing. Focusing on the initiation of the downswing, this paper investigates how the instantaneous screw axis (ISA) with rotational and linear motions contributes to subsequent movements, such as the hip turn. We propose that the physical forces generated by the golf club, characterized by mass moment inertia, extend beyond the body's boundaries, such as through the hand grip. A skilled golfer’s ability to 'allow' these forces to influence body dynamics without opposing them is analyzed through the lens of LBMS's Free Flow Effort, suggesting an indulgent and expansive use of movement energy.
... The shaft of a golf club is the component of the club that most substantially affects swing performance, and a shaft's material properties directly affect its weight and stiffness (Haeufle et al., 2012). Research findings suggest that golfers can optimize their swing and ball flight parameters by suitable selection of drivers with different shaft lengths (Mizoguchi et al., 2005;Kenny et al., 2008;Lacy Jr et al., 2012), flexibility levels (MacKenzie and Sprigings, 2009;Worobets and Stefanyshyn, 2012), kick points (Joyce et al., 2016), and weights (White, 2006;Haeufle et al., 2012;Lacy Jr et al., 2012). However, related research for selection of iron clubs is limited. ...
This study examined the effects of three 7-iron shaft weights on golf swing performance among golfers of varying skill levels. The study included 10 low-handicap (LH; 4.3 ± 2.4) and 10 high-handicap (HH; 29.1 ± 5.4) right-handed golfers as participants. The participants were randomly assigned 7-iron clubs with shaft weights categorized as light (77 g), medium (98 g), or heavy (114 g), and they performed test shots. Kinematic data were captured using a motion analysis system with nine infra-red high speed cameras; a force platform connected to this system was used to record weight transfer patterns. Performance variables were assessed using a FlightScope launch monitor. A two-way mixed-design analysis of variance was used to determine the significance of the performance differences among both participant groups and golf shaft weights. The results indicated that during the backswing, the LH group exhibited significantly greater maximum rightward upper torso rotation, maximum X-factor, and maximum right wrist hinge rotation than did the HH group. During the downswing, the LH group exhibited significantly greater maximum upper torso angular velocity and maximum right wrist angular velocity than did the HH group. Moreover, the LH group produced significantly higher ball speeds, longer shot distances, and lower launch angles than did the HH group. The shaft weight neither greatly altered the golf swing nor displaced the center of gravity of the golfers. The lighter shafts were observed to facilitate faster clubhead speeds and initial ball velocities, thereby resulting in longer shot distances, especially among LH golfers. Although significant differences in swing mechanics and performance exist between HH and LH golfers, lighter shafts can contribute to increased shot distances for all golfers.
... Researchers have tracked markers on both the driver clubhead and grip [60,61]; from movement of the head relative to the grip, the time-varying bending deflections in the plane of motion ("lead/lag") and perpendicular to this plane ("toe up/down") were calculated. The results confirmed the expected forward bend of the shaft (lead) at impact, which increases the effective loft at impact (the "dynamic loft"), plus a significant toe-down deflection (or "droop")-results that are consistent with dynamic models of the flexible shaft [62,63]. ...
... The model results were in good agreement with experimental swings by an elite golfer, with root mean squared errors of 0.66, 1.25, and 1.53° for the arm, torso, and club angles. The authors used their 3D model to (1) confirm the proximal to distal sequencing of joint torques (i.e., torso-shoulder-forearm-wrist) for maximum clubhead speed [111], and (2) show that shaft flexibility affects clubhead orientation at impact, but not clubhead speed [55,62]. The model was also used to demonstrate the effect of clubhead center of mass location and radial grip force on shaft deflection [112] Balzerson et al. [113] further extended this model by including the passive stiffness and damping properties of human joints [114], replacing the discrete shaft model with the continuous flexible beam model of Sandhu et al. [88], and including models of aerodynamic drag on the clubhead, clubhead-ball impact, and subsequent ball trajectories. ...
A narrative review of dynamic models of golf phenomena is presented, as well as current technologies for measuring the motions of a golfer, club, and ball. Kinematic and dynamic models of the golf swing are reviewed, including models with prescribed motions or torques as inputs, and predictive dynamic models that maximize an objective (e.g., driving distance) to determine optimal inputs or equipment designs. Impulse–momentum and continuous contact dynamic models for clubhead–ball and ball–ground impacts are described. The key observations from 172 cited references are extracted and presented, along with suggestions for future research.
... In Herstellerkatalogen werden weder die Toleranzen noch der Bereich des statischen Spine angegeben. Nach Park (Park, 2010) (Maltby, 1995;Maltby Design, 2020) (Chou & Roberts, 1994;Brouillette, 2002;Mase, 2004;Huntley, Davis, Strangwood, & Otto, 2006;Huntley, 2007;MacKenzie & Springings, 2009;Betzler, 2010) ...
Zusammenfassung
Wird ein Pfeil von einem Compound-Bogen abgeschossen, so verursacht die durch das Zuggewicht auf den Pfeil übertragene Abschussenergie eine Biegeknickung (seitliches Ausweichen der Längsachse) des Pfeils. Je nach statischem Spine-Wert des Pfeilschafts, fällt diese Biegung größer oder kleiner aus. Während des freien Pfeilfluges muss die Biegeknickung, welche in Form einer freien Schwingung sichtbar ist, durch die Steifigkeits- und Dämpfungseigenschaften des dynamischen Spines kompensiert werden. Der Pfeil muss sich im freien Flug entsprechend eigenständig stabilisieren, um auf der Zielscheibe eine möglichst kleine Pfeilgruppierung zu erreichen. Darüber hinaus variiert der statische Spinewert entlang des Pfeilumfangs, und bei jedem Pfeil ist eine bestimmte Orientierung vorhanden, in welcher die Durchbiegung am größten bzw. kleinsten ist. Dies wird im Allgemeinen mit Spline bezeichnet. In diesem Beitrag wird mittels experimenteller Untersuchungen dargelegt, welche Auswirkung die Wahl eines zu weichen oder zu steifen Pfeils (dynamischer Spine) im Vergleich zu einem optimalen Pfeil auf die Größe der Pfeilgruppierung und damit auf die Ringzahl besitzt. Zudem werden auch Variationen der Lage und Orientierung des Splines durchgeführt. Hier zeigen die Ergebnisse, dass der Spline keine Auswirkungen auf die Größe der Pfeilgruppierung besitzt. Weiterhin ergeben sich aus den Untersuchungsergebnissen, dass ein zu weicher wie auch ein zu steifer Pfeil zu einer Vergrößerung der Pfeilgruppierung führen und dadurch das Wertungsergebnis entsprechend geringer wird. Mithilfe der durchgeführten Untersuchungen in diesem Beitrag wird der Einfluss des Spine auf die Pfeilgruppierung aufgezeigt, um den Bogenschützen bei der richtigen Materialauswahl zu unterstützen.
... A 275 g driver would be considered extremely light, while a 375 g driver would be considered extremely heavy; yet, there was less than a ½ mph difference in clubhead speed. In a study investigating shaft stiffness, [8] showed that individual players can react quite differently to a club's physical parameters and that important individual differences can be masked by group trend statistics. While 45% of the participants in this study had their highest average clubhead speed with the lightest condition, 65% broke from conventional theory and had a higher average with either the 325 g or 375 g condition. ...
The purpose of the study was to determine the influence of grip mass on driver clubhead kinematics at impact as well as the resulting kinematics of the golf ball. Three club mass conditions (275, 325, and 375 g) were tested by 40 experienced golfers (handicap = 7.5 ± 5.3) representing a range of clubhead speeds (36 to 54 m/s). Each participant executed 12 drives per condition using matched grips and shafts and a single clubhead. Club mass was modified by inserting 50 g and 100 g into the grips of the two heavier conditions. The heaviest condition was associated with the slowest clubhead speed (p = 0.018) and highest vertical launch (p = 0.002), which resulted in no net influence on driving distance (p = 0.91). Lateral dispersion was greatest with the 325 g condition (p = 0.017), as was horizontal impact spot variability on the driver face (p = 0.031). Findings at the individual golfer level were not reliable enough to suggest that grip mass could be effectively used in a fitting environment to either shift ball flight tendencies or improve consistency.
... Previous studies investigating the golf shaft's role in generating clubhead speed have focused primarily on shaft stiffness [1][2][3][4]. These studies have brought attention to the physical interaction between the shaft and golfer biomechanics, which is not easily understood. ...
... Upon further investigation, it was found that shaft bending dynamics played a role in this divergence. Figure 2c demonstrates that lag deflection was sustained longer using a higher balance point, resulting in an increase in kick velocity approaching impact, as shown by Figure 2d (lead/lag deflection are defined in [1], kick velocity is the derivative of lead/lag deflection with respect to time). The difference in mean kick velocity at impact between shafts A and C was 0.32 m/s, which exceeded the mean difference in clubhead speed (0.1 m/s). ...
In this study, a dynamic golfer model was used to investigate the influence of the golf shaft’s balance point (i.e., center of mass) on the generation of clubhead speed. Three hypothetical shaft designs having different mass distributions, but the same total mass and stiffness, were proposed. The golfer model was then stochastically optimized 100 times using each shaft. A statistically significant difference was found between the mean clubhead speeds at impact (p < 0.001), where the clubhead speed increased as the balance point moved closer to the grip. When comparing the two shafts with the largest difference in balance point, a 1.6% increase in mean clubhead speed was observed for a change in balance point of 18.8 cm. The simulation results have implications for shaft design and demonstrate the usefulness of biomechanical models for capturing the complex physical interaction between the golfer and golf club.
... Furthermore, there is a lead/lag deflection decrease and the rotation around the shaft axis. This is in accordance with the typical pattern of shaft deflection, where lead deflection contributes to DL and closing the clubface (MacKenzie & Sprigings, 2009a). Player 2 showed a distinctive swing style, with closed FA in driver trials. ...
The purpose of the study was to investigate clubhead kinematics during the impact phase of a golf swing. Three highly skilled golfers of a distinguished body type were instructed to perform driver, 6-iron and pitching wedge trials. A high-speed imaging system was used to capture the clubhead motion near the impact. Conventional golf swing parameters were analysed for comparison. Additionally, a circular arc was fitted to the clubhead path, and the moving trihedron was introduced as a reference frame for observing the clubhead rotation. Despite differences in their body type, golfers achieved comparable clubhead speed, while the radius of the fitted circular arc was in a narrow range. The moving trihedron, together with conventional parameters of the golf swing, enabled additional insight to the clubhead motion and clubface orientation. Individual swing characteristics, which result in the clubhead motion prior to impact, could clearly be observed, enabling improvement of the golfer’s swing technique.
... The golf swing is a complex unified movement of the human body and golf club. The behaviour of the golf shaft during the swing is crucial to the outcome of the shot as it contributes to the orientation and velocity of the clubhead at impact [1] and in turn, the initial linear and angular velocities of the ball [2]. It is well-understood that the ball's launch conditions can have drastic effects on the outcome of the shot and a meaningful impact on scoring [3,4]. ...
... Motivated by evidence that the golf swing is not planar [8,22], much research has gone into the development of three-dimensional forward dynamic golf swing models featuring flexible shafts. MacKenzie and Sprigings [1] utilized a discretized approach to model the golf club using four rigid sections interconnected by rotational spring-damper elements. Their golf club model was limited to four segments as a result of the lengthy closed-form dynamic equations that pushed the computational resources available at the time. ...
... Although two elastic coordinates led to a 27.6% reduction in relative error in the twisting frequency test, the same level of improvement was not observed in the full golf swing simulations. Similar to previous studies [1,23,24], it was found that shaft twist played a relatively minor role compared to shaft bending; the experimental twist angles rarely exceeded 2 • , whereas the experimental droop and lag angles occasionally surpassed 10 • . Based on this observation, one twist coordinate was used in the full swing simulations to significantly reduce the computational complexity of the model. ...
The intricate physical interaction between the golfer and golf club has driven the development of numerous dynamic golf swing models over the past few decades. Within these golf swing models, the shaft is represented analytically, and simplifications are often made to strike a balance between the demanding computation required for simulating full swings and running optimizations. Despite recent progress in modeling golfer biomechanics, there has been a marked lack of experimental validation surrounding the dynamic behaviour of the analytical shaft models used in golf swing simulations. The purpose of this study was to evaluate the simulated behaviour of an advanced, continuously-parameterized analytical golf shaft model using experimental data collected in constrained mechanical property experiments as well as golf swing motion capture experiments. In the constrained experiments, the model predicted the experimental shaft’s static deflection and bending frequency within a relative error of 1%. In simulations of full swings, the model authentically replicated the unique bending patterns for each of the 20 golfers in the motion capture experiment. The root mean square errors for the shaft droop, lag, and twist angles for all swings (\(N=200\)) were \(1.14^{\circ }\), \(0.83^{\circ }\), and \(0.85^{\circ }\), respectively, and the clubhead speed at the time of impact was predicted to within \(-\,2.9\) to 0.6%. Empowered by symbolic computation, the model is computationally efficient enough for fast simulations of full swings (\(<1\) s CPU time) on a desktop computer, thereby enabling golf shaft design optimization.
... Studies investigating the effects of shaft stiffness on performance include theoretical models [6,7] and experimental studies, utilising either high-speed photogrammetry [8] or, more commonly, the use of strain gauges attached to the shaft [1,7,[9][10][11][12][13][14][15][16][17]. The results of the theoretical studies lack experimental validation whilst overall results are often conflicting [5]; however, it has been shown that shafts of varying flex have distinctly different bending profiles throughout the swing [8,16,18,19]. ...
... The maintenance of the shaft strain profile during the swing, found in this investigation, is compatible with results presented by MacKenzie and Boucher [20] which provide an explanation as to the lack of a systematic effect of shaft stiffness on clubhead speed. Whilst the speed of shaft recoil was greater with a more compliant shaft, a result previously reported in the literature [6], this was offset by a decrease in angular velocity at the grip end of the club. That differences were predominantly in the magnitude of the strain, with the strain profile otherwise remaining relatively consistent, supports the suggestion that optimum shaft stiffness may be individually specific [20]. ...
... That is, the golfers' movement patterns may have been altered with the different stiffness shafts, either due to the golfers adapting their swing or due to differences in reaction forces applied by the shaft. Differences in kinematics might explain the reported decrease in angular velocity at the grip end of the club [20] and the discrepancies with results from computer simulation studies [6]. Whilst golfers are typically blinded to the shaft stiffness in human studies, like in this investigation, it is probable that golfers adjust their movements based on the subjective feel of the club. ...
There is much debate around the role of shaft stiffness in the dynamic response of the club shaft during the golf swing. This study used a novel complex analysis to investigate within- and between-golfer differences in shaft strain patterns for three shaft stiffnesses. Twelve right-handed male golfers, with a handicap less than or equal to five, hit six shots with three driver clubs which differed only in shaft stiffness. Clubs were instrumented to record the shaft strain in the lead/lag and toe/heel directions. The analysis combined these perpendicular components into a single complex function, which enabled the differences between two swings to be characterised by a scale and a rotation component. Within-golfer strain patterns were found to be significantly more consistent than between-golfer, p < 0.01. Whilst some golfers displayed more similar patterns than others, there were no clear groups of golfers with similar patterns of shaft strain. Between the clubs, shaft strain patterns differed in the scale component, p < 0.01, rather than the rotation, p = 0.07.
... These alterations in club fit along with changes in swing weight and moment of inertia caused by using standardised clubs may have affected the perceived feel of these clubs by the golfer and subsequently produced altered swing mechanics (Wallace, Otto, & Nevill, 2007). However, it has been suggested that club properties have only marginal effects on clubhead characteristics and shot outcome (Betzler, Monk, Wallace & Otto, 2012;MacKenzie & Sprigings, 2009). Therefore, it is anticipated that, as the same clubs were used in both conditions and unlimited familiarisation trials were allowed, club characteristics would have had a minimal effect on the results of this study. ...
Analyses of segment kinetic energy (KE) can provide the most appropriate means of exploring sequential movements. As the reliability associated with its measurement has not been reported, the aim of this study was to examine the test-retest reliability of segment KE measures in the golf swing. On two occasions, seven male golfers hit five shots with three different clubs. Body segment inertia parameters were estimated for 17 rigid bodies and 3D kinematic data were collected during each swing. The magnitude and timing of peak total, linear and angular kinetic energies were then calculated for each rigid body and for four segment groups. Regardless of club type, KE was measured with high reliability for almost all rigid bodies and segment groups. However, significantly larger magnitudes of peak total (p = 0.039) and linear (p = 0.021) lower body KE were reported in test 2 than in test 1. The high reliability reported in this study provides support for the use of analyses of segment kinetic energy. However, practitioners should pay careful attention to the identification of anatomical landmarks which define the thigh, pelvis and thorax as this was the main cause of variability in repeated measures of segment kinetic energy.
