Michael Finney
New
PART 2
2.4.1 2D Golf Models
One of the first scientific papers dealing with motion analysis in the golf swing was a 1967 study by Williams called Dynamics of the Golf Swing – with Conclusions of Practical Interest. In it, Williams took hand and club kinematics measurements from a Spalding Brothers’ stroboscopic photograph of touring professional Bobby Jones. Figure 2.4.1 is a copy of the image used.
Figure 2.4.1: 100 Hz stroboscopic photograph of Bobby Jones hitting a 2 iron. Adapted from Bunn (1972).
Williams made many assumptions in this early study that have since been disproven. For example, he assumed that the clubs and hands travel in the same plane. He also assumed that the hands travel about a fixed rotation point (i.e. the leading shoulder);

23 and that angular velocity of the hands stay constant throughout the second half of the downswing. Aside from these postulations, Williams made some insightful conclusions that are still valid in golf science today. For instance, he was the first researcher to propose that delaying un-cocking of the wrists could account for a large increase in CHS. He also reasoned that relative timing between segments, or swing tempo, would be more important than muscular torque in creating a long hit. Because of errors Williams made in his initial assumptions, mathematical and logical proof of these later assertions would
have to wait nearly thirty years.
In recent reviews of the current state of golf biomechanics, papers by Farrally et
al (2003) and Hume et al (2005) noted that new studies have not significantly improved on the 2D double pendulum golf swing model proposed by Cochran and Stobbs (1968) in their book entitled: A Search for the Perfect Swing. This Langrangian pendulum model put forth in Perfect Swing is still revered in review articles today; and for good reason (apart from A.J. Cochran being a co-author of Farrally’s review). The double pendulum model can allow for a breadth of complex, inter-dependent solutions that closely mimic real life golf motion. In general, golf swing modeling has since been a collection of tweaks and modifications on this ground breaking work. An illustration of the double pendulum is shown in Figure 2.4.2. The proximal segment represents the motion of the lead arm; while the distal segment represents the motion of the club shaft.
24
Figure 2.4.2: The golf swing as a double pendulum. Adapted from Jorgensen (1999). θ and β represent shoulder and wrist angles respectively. Points CH, W, and O represent the positions of the club head, wrist and the system origin respectively.
Early calculations by Cochran and Stobbs (1968) lead them to two general conclusions about optimizing swing speed. First, they found that the arm segment should be ‘driven strongly’. This was interpreted to mean that the external muscle torque operating at the shoulder joint should be maximized. Secondly, they stated that the load applied to the club should happen only “at the stage of the action when it is trying to fly outwards at its own accord”. This was interpreted to mean that the external muscle torque operating at the wrist should onset correspondingly with the outward, centripetal acceleration of the club shaft. No mention is made as to the direction, magnitude, or profile of this wrist impulse.
Perhaps it was a delay on a journal editor’s desk that cost Ted Jorgensen some acclaim in the hallowed history of golf biomechanics. His 1970 paper called Dynamics of the Golf Swing was actually submitted in the same year Perfect Swing was published. In it, Jorgensen belatedly introduced a 2D double pendulum model of the golf swing. Like the work of Cochrane and Stobbs, his calculations lead him to conclude that maximizing
25 shoulder torque could improve CHS. But unlike the work in Perfect Swing, Jorgensen found that delaying the opening of the wrist beyond the timing of a free hinge opening would lead to a great increase in CHS. Jorgensen was the first author to show mathematical proof that the active delay of wrist un-cocking (beyond the timing of a “natural”, free-hinge release) could improve speed generation in golf. This finding was
later repeated by many other authors.
Pyne (1977) expanded on the standard pendulum model by attempting to quantify
the effectiveness of the “wrist snap”. In the practice of Williams and Cochran and Stobbs, Pyne separated the downswing into two general stages: pre and post wrist un- cocking. Pyne attempted to quantify wrist snap efficiency by creating what he called a “club head speed coefficient”. This was a ratio of absolute end point velocity comparing CHS just before wrist un-cocking to CHS at impact. Pyne concluded that “injection speed” (i.e. wrist contribution) could be improved by adding mass to the arm segment, or by optimizing club length. In addition, Pyne was the first author to show that William’s assumption of constant hand angular velocity in the second phase of the down swing was incorrect. He noted that Jimmy Thompson (a “prodigious hitter” in his day) was observed to “stop” his hands before ball contact.
Milburn (1982) looked at the transfer of speed between a golfer’s segments. He studied 2D motion of the lead arm and club segment and noticed a pattern of positive angular acceleration of the club at the expense of angular deceleration of the arm. This finding was in direct support of a P-D sequencing pattern in golf. Milburn stated that this phenomenon was indicative of a free-hinge system. In addition, he felt that the impetus of wrist un-cocking was a “centrifugal” or virtual inertial force that was acting on the
26 double pendulum system. This force tended to pull the club head outwards; and straighten out the arm and club links at the wrist joint. Like earlier researchers, Milburn came to the conclusion that if the golfer were to initially delay the onset of the wrist un-cocking, he
would be more likely to attain maximum segmental angular velocities.
Budney and Bellow (1979), engineering researchers from the University of Alberta, were the first group to examine changes in club parameters on the double pendulum golf model. The authors are one of few groups to report that delayed wrist snap did not appreciably contribute to CHS. Of note, they were the first group to prove that
decreasing club shaft weight could improve energy efficiency for a given swing speed. Pickering and Vickers (1999) looked at joint energetics in the double pendulum model. They found that it was possible for a golfer to have a successful swing without applying an impulse at the wrist. They deemed that this “natural release” was, understandably, the most efficient swing type in lowering muscular energy supplied. Further optimizations were run to determine the timing of wrist release and relative ball position that would allow for greatest impact velocity. It was found that a delayed wrist release coupled with a ball positioning closer towards the lead foot resulted in maximum
CHS.
In summary, scientific work in golf using the double pendulum swing model has
afforded a basic advancement in the understanding of this complex human motion. The preceding articles have shown that the double pendulum itself can be modeled with a variety of segment parameters and joint load profiles that are able to create realistic golf motion. Understandably, work using a two link model has focused primarily on the joint that connects the segments in enquiry; the wrist. The consensus of this work has shown
27 that a delay in opening of the wrist joint improves golf performance by generating increased CHS. It is interesting to note that the late onset of wrist un-cocking in golf corresponds to Bunn’s original observation of delaying knee extension in maximal ball kicking. It seems that the double pendulum golf model agrees with the optimal motion
pattern existing for other sports.
For the two body segments studied in the double pendulum model, a P-D
sequencing of motion seems to be ideal for optimal speed generation. It is still unclear however, if the same holds for a real golf swing; a complex motion involving multiple human body segments and an external implement; moving in three dimensions.
2.4.2 3D Golf Models
Insight into 3D kinematics and kinetics in golf first appeared in the work of Vaughan (1981). In his investigation, club markers were filmed with two orthogonal high-speed film cameras. Resultant forces and torques applied at the hands were calculated from club kinematics using a Newtonian-Euler approach. Vaughan noted that Budney and Bellow (1979) predicted that the wrist should undergo a positive torque throughout the downswing. This torque would be positive about an axis pointing up from the club shaft plane, and would tend to rotate the club towards the target. Vaughan’s results suggested that this torque was negative for the first half of the downswing; which tended to keep the wrists cocked. The external wrist torque then became positive at wrist un-cocking, and remained positive for the remainder of the downswing. Vaughan cautioned that the external wrist torque should not be confused with the wrist muscle torque since the club grip is in contact with both hands. Two contact points on the grip would therefore
28 represent a distributed load. According to Vaughan: “it should be recognized that this normal torque cannot be considered as a valid measure of the ... un-cocking action of the wrists.” This could be a relevant source of error when modeling the wrist as a spherical
joint.
In addition to resultant joint moments, Vaughan also examined resultant joint
forces. He found that the largest component of the grip force at ball impact was applied along the shaft, pulling towards the golfer. He also found that the positive wrist torque was initiated by applying a force at the hands in the opposing direction of the clubface. Of note, Vaughan observed that a late slowing of the hands before impact coincided with a large increase in CHS.
Neal and Wilson (1985) repeated the work done on 3D club loading by Vaughan. A major difference with their paper was that their results were presented in a global reference frame instead of in a local frame fixed to the club. Their torque results supported the findings of Vaughan. The timing of wrist un-cocking coincided with a change from negative to positive wrist torque about the golfer’s frontal axis. The authors also presented results on the resultant joint force acting on the shoulder. When comparing resultant joint loads, peak forces acting on the shoulder joint were of greater magnitude, and occurred earlier in the downswing, than those forces acting at the wrist joint.
McLaughlin et al (1994) measured a variety of 3D golf “kinematic parameters”; actually body segment angular positions at key time points during the swing. The group performed a linear regression and later a principal component analysis on the data to find which parameters had the highest correlation with CHS. Not surprisingly, they found that delayed wrist onset was important in speed generation.
29 Coleman and Rankin (2005) investigated the applicability of 2D multi-segment models in representing 3D motion. They measured 3D kinematics of the left shoulder girdle, left arm and club shaft during the downswing. They found that the motions of these segments did not all lie along the same plane. Coleman and Rankin concluded that 2D models do no realistically represent multi-segment movements in a golf swing, which they found not to occur in a single plane. No mention was made as to whether the
movement of individual segments could be reliably fit with separate planes.
In summary, these papers exploring 3D motion in golf have contributed to the overall understanding of the swing. Vaughn (1981) was the first author to use inverse dynamics based on optical motion analysis in golf. Neal and Wilson (1985) used a similar method to show that loading in the shoulder preceded loading in the wrist in the downswing, in a P-D manner. These two motion analysis studies have laid a foundation in the understanding of joint loading in the swing. The work by McLaughlin et al (1994) and Coleman and Rankin (2005) have repeated the finding of wrist delay and noted that a single 2D plane cannot effectively represent the motion of a golf swing. However, an
optimal motion pattern still remains to be determined in golf for 3D full body movement.
2.4.3 Adding the Spine and Hips
In a golf study by Cooper et al (1974), P-D sequencing of motion onset was observed qualitatively starting with knee joint movement and transferring superiorly and distally to the hip, spine, shoulder, then wrist. This investigation looked at force plate data under each foot during the swing. The authors referred to free moments about the vertical axes of the force plates as “rotational forces”. When viewing a right-handed golfer from
30 above, these rotational ground reaction forces were clockwise at the top of the downswing. They quickly switched to become counter clockwise just prior to ball contact. Although not discussed, their graphs indicated that this phenomenon increased in magnitude and tended to occur later in the swing as the golfer shifted from smaller irons to a driver. This work supports the idea that a golfer interacts with the ground via his feet when creating a golf swing. From this point of view, a golf swing begins with a kinetic
interaction at the ground.
Although Cooper et al looked at other body segments using qualitative
observation; spine and hip rotations had not been quantified in the literature until later. McTeigue (1994) conducted a study on relative spine to hip rotation using large groups of PGA, senior PGA, and amateur players. Kinematic data were collected using a linkage of gyroscopes and potentiometers. His investigation was designed to look at the so called “X-factor”, or range of torso rotation relative to the hips. He found that spine flexibility did not differ between professional and amateur players (although it was limited in the senior PGA group). An interesting result of this study was that of the “hip slide”. McTeigue found that both amateur and professional players underwent a lateral transition of the lead shoulder during the downswing. Professional players accomplished this by shifting their weight from their back to front foot and keeping their torsos vertically aligned. Amateur golfers tended to accomplish the shoulder shift by a lateral bending of the spine.
Burden et al (1998) explored hip and torso rotations in the context of the summation of speed principle. They measured 3D kinematics in a group of eight golfers using a two-camera motion capture system. They claim that their results supported a P-D
31 segment sequence as required by Bunn’s principle. However, this group did not investigate segment angular velocity or angular impulse. The summation of speed, as described by Bunn (1972) and Putnam (1993) described the relative timing of either sequential angular velocity peaks, or sequential torque onsets. This theory did not refer to relative angular positions specifically, as was reported in this article. Also, measurements of shoulder and hip angular positions were made by connecting bi-lateral bony landmarks; and projecting the resulting vector on the ground plane. As the motion of these segments likely does not coincide with the plane of the ground, these projections may have lead to erroneous results. However, this group did find that players who timed
angular position peaks in a P-D fashion were more likely to generate greater swing speed. The 2D double pendulum model was modified with the simulation work of Sprigings and Neal (2000). The authors added a third segment to the standard double pendulum model. They chose lengths and inertial properties to correspond with segment parameters of real golfers; and for the first time, based applied torques on the force- length, force-velocity and activation parameters of human muscles. They supported the finding by Pickering and Vickers that it was possible to have ball contact with a free- hinge wrist joint. Sprigings and Neal were the first authors to simulate a torso segment in the kinetic golf model. They stated that torso rotations were very important in recreating realistic swings. They found the magnitude of applied torques at the shoulder joint could be lowered to a much more realistic level if a component of the angular impulse could be derived from inter-segmental interaction. Also, the authors reported that the angular position and velocity of the torso seemed to have a direct effect on delaying wrist action,
which ultimately lead to higher club speeds.
32 Sprigings and Mackenzie released a study in 2002 to follow the work done on the triple segment golf simulation. Here the authors used the same 3 segment model to identify the mechanical sources of power in the golf swing. The authors used a forward dynamics approach to optimize muscle model variables with measured kinematics. The authors calculated the power at each joint due to muscle torques or joint contact forces. By integrating this power, they calculated joint energies and the mechanical sources of this energy. Their results indicated a P-D sequence of total work done. The authors also noted that the onset of muscular power at the wrist joint precedes the onset of applied positive wrist torque. This means that some of the energy gained by the wrists is due to the resistive torque acting to keep the wrists cocked. Sprigings and Mackenzie noted that muscular power increased distal segment energy at the expense of decreasing energy in the proximal segment, although no direct measurements of segment energy were
reported.
Sprigings and Mackenzie (2002) had applied a high level of realism in the muscle
models used for their simulation. However, they did not account for an onset of muscle torque during the backswing. All muscle load profiles started from zero at the beginning of the downswing. It is quite possible that a golfer’s muscles are able to develop force before the initiation of downward movement. This potential error in muscle work done on the segments leads to the question of how the resulting joint energetics compare to direct physical measurements of energy contained in the segments.
Perhaps the most comprehensive look at the inter-relationship between motion and loading in 3D golf swing has been in work done by Nesbit (2005). In subsequent articles from the same journal; Nesbit introduced a 3D full-body, multi model, integrative
33 motion capture / kinetic analysis system. Nesbit used separate models for the human body, the ground, and the club. Kinematics from video motion capture data were used as input. A full body human segments model came from an ADAMS module called ANDROID (MSC Software Corporation; Santa Ana, CA). It consisted of 15 linked rigid body segments interconnected with spherical joints. The resultant joint torque profiles
were optimized to match realistic kinematics as measured by the video capture system.
In the first article, Nesbit stated that the resultant forces acting on the club were applied at the grip by the arm segments; while the resultant moments acting on the club where due to muscular work done at the wrists. He compared angular work done by the wrists to linear work done by the arms. His results indicate that better golfers tend to do more work by using their arms to pull on the golf club; than by applying a torque at the wrists. He reasoned that greater club head speed is created by reducing the radius of the
path of the hands just prior to impact.
In the second article by Nesbit and Serrano (2005), the authors calculated work
done at each joint in the full body model by using a joint power approach. They then determined the locations of the sources of power in the golf swing. They found that the back and the hip joints generated up to 70% of the total work done in the swing, while 26% of the total work was contributed by the arms (mostly by the right elbow). They concluded that the generation of work, and its transference to the club, is mostly a “bottom-up phenomenon”; moving upward and outward. Of note, the authors noted that proximal segments tended to slow down to become “static support” for their distal counterparts.
34 Nesbit and Serrano (2005) found that the majority of the joint work performed was used in moving the proximal segments. Very little of the total work was actually transferred to the club. Of the work done on the club at the wrist joint, a linear force applied by the arms generated the majority. Wrists torques showed a comparatively
smaller contribution towards an increase in overall CHS.
Interestingly, Nesbit and Serrano showed that total body joint power tended to
switch from positive to negative around the time of impact; but only the scratch golfers were able to zero their power generation exactly at impact. This would result in maximization of club speed. If power became negative pre impact, the body would work to slow the club. If power were still positive post impact, it would mean usable work was wasted. It seemed precise timing of total joint power application was indicative of player ability.
In summary of the golf research presented in this section, an inter-relationship between loading and motion had begun to be established in full body 3D golf movement. Part of this work has stemmed from optical motion analysis studies. The work by Cooper et al (1974) had shown qualitatively that motion in the golf swing should begin at the ground. McTeigue (1994) showed that the torso has a larger range of motion than the hips; and that a difference exists between amateurs and professionals in how the torso rotates at the end of the downswing. The study by Burden et al showed that range of motion, and timing of angular position peaks followed a P-D sequence in successful swings.
The latter research papers presented in this section on 3D, full body golf motion have used simulations of various modelling complexity (Sprigings and Neal, 2000;
35 Sprigings and MacKenzie, 2002; Nesbit, 2005; Nesbit and Serrano, 2005). These studies have given insight into the sources of mechanical power in the golf swing. In their simulations, these authors have used forward dynamic analysis to optimize musculoskeletal models in recreating known kinematics. While the motion of the models has been matched to that of a realistic golf swing, it is currently unknown if the joint loads created by the models are also correct. Therefore, it would be worthwhile to apply a segmental energetics framework to the golf swing to evaluate simulated sources of
mechanical energy with direct measurements of the destinations of that energy,.
2.4.1 2D Golf Models
One of the first scientific papers dealing with motion analysis in the golf swing was a 1967 study by Williams called Dynamics of the Golf Swing – with Conclusions of Practical Interest. In it, Williams took hand and club kinematics measurements from a Spalding Brothers’ stroboscopic photograph of touring professional Bobby Jones. Figure 2.4.1 is a copy of the image used.
Figure 2.4.1: 100 Hz stroboscopic photograph of Bobby Jones hitting a 2 iron. Adapted from Bunn (1972).
Williams made many assumptions in this early study that have since been disproven. For example, he assumed that the clubs and hands travel in the same plane. He also assumed that the hands travel about a fixed rotation point (i.e. the leading shoulder);

23 and that angular velocity of the hands stay constant throughout the second half of the downswing. Aside from these postulations, Williams made some insightful conclusions that are still valid in golf science today. For instance, he was the first researcher to propose that delaying un-cocking of the wrists could account for a large increase in CHS. He also reasoned that relative timing between segments, or swing tempo, would be more important than muscular torque in creating a long hit. Because of errors Williams made in his initial assumptions, mathematical and logical proof of these later assertions would
have to wait nearly thirty years.
In recent reviews of the current state of golf biomechanics, papers by Farrally et
al (2003) and Hume et al (2005) noted that new studies have not significantly improved on the 2D double pendulum golf swing model proposed by Cochran and Stobbs (1968) in their book entitled: A Search for the Perfect Swing. This Langrangian pendulum model put forth in Perfect Swing is still revered in review articles today; and for good reason (apart from A.J. Cochran being a co-author of Farrally’s review). The double pendulum model can allow for a breadth of complex, inter-dependent solutions that closely mimic real life golf motion. In general, golf swing modeling has since been a collection of tweaks and modifications on this ground breaking work. An illustration of the double pendulum is shown in Figure 2.4.2. The proximal segment represents the motion of the lead arm; while the distal segment represents the motion of the club shaft.
24
Figure 2.4.2: The golf swing as a double pendulum. Adapted from Jorgensen (1999). θ and β represent shoulder and wrist angles respectively. Points CH, W, and O represent the positions of the club head, wrist and the system origin respectively.
Early calculations by Cochran and Stobbs (1968) lead them to two general conclusions about optimizing swing speed. First, they found that the arm segment should be ‘driven strongly’. This was interpreted to mean that the external muscle torque operating at the shoulder joint should be maximized. Secondly, they stated that the load applied to the club should happen only “at the stage of the action when it is trying to fly outwards at its own accord”. This was interpreted to mean that the external muscle torque operating at the wrist should onset correspondingly with the outward, centripetal acceleration of the club shaft. No mention is made as to the direction, magnitude, or profile of this wrist impulse.
Perhaps it was a delay on a journal editor’s desk that cost Ted Jorgensen some acclaim in the hallowed history of golf biomechanics. His 1970 paper called Dynamics of the Golf Swing was actually submitted in the same year Perfect Swing was published. In it, Jorgensen belatedly introduced a 2D double pendulum model of the golf swing. Like the work of Cochrane and Stobbs, his calculations lead him to conclude that maximizing
25 shoulder torque could improve CHS. But unlike the work in Perfect Swing, Jorgensen found that delaying the opening of the wrist beyond the timing of a free hinge opening would lead to a great increase in CHS. Jorgensen was the first author to show mathematical proof that the active delay of wrist un-cocking (beyond the timing of a “natural”, free-hinge release) could improve speed generation in golf. This finding was
later repeated by many other authors.
Pyne (1977) expanded on the standard pendulum model by attempting to quantify
the effectiveness of the “wrist snap”. In the practice of Williams and Cochran and Stobbs, Pyne separated the downswing into two general stages: pre and post wrist un- cocking. Pyne attempted to quantify wrist snap efficiency by creating what he called a “club head speed coefficient”. This was a ratio of absolute end point velocity comparing CHS just before wrist un-cocking to CHS at impact. Pyne concluded that “injection speed” (i.e. wrist contribution) could be improved by adding mass to the arm segment, or by optimizing club length. In addition, Pyne was the first author to show that William’s assumption of constant hand angular velocity in the second phase of the down swing was incorrect. He noted that Jimmy Thompson (a “prodigious hitter” in his day) was observed to “stop” his hands before ball contact.
Milburn (1982) looked at the transfer of speed between a golfer’s segments. He studied 2D motion of the lead arm and club segment and noticed a pattern of positive angular acceleration of the club at the expense of angular deceleration of the arm. This finding was in direct support of a P-D sequencing pattern in golf. Milburn stated that this phenomenon was indicative of a free-hinge system. In addition, he felt that the impetus of wrist un-cocking was a “centrifugal” or virtual inertial force that was acting on the
26 double pendulum system. This force tended to pull the club head outwards; and straighten out the arm and club links at the wrist joint. Like earlier researchers, Milburn came to the conclusion that if the golfer were to initially delay the onset of the wrist un-cocking, he
would be more likely to attain maximum segmental angular velocities.
Budney and Bellow (1979), engineering researchers from the University of Alberta, were the first group to examine changes in club parameters on the double pendulum golf model. The authors are one of few groups to report that delayed wrist snap did not appreciably contribute to CHS. Of note, they were the first group to prove that
decreasing club shaft weight could improve energy efficiency for a given swing speed. Pickering and Vickers (1999) looked at joint energetics in the double pendulum model. They found that it was possible for a golfer to have a successful swing without applying an impulse at the wrist. They deemed that this “natural release” was, understandably, the most efficient swing type in lowering muscular energy supplied. Further optimizations were run to determine the timing of wrist release and relative ball position that would allow for greatest impact velocity. It was found that a delayed wrist release coupled with a ball positioning closer towards the lead foot resulted in maximum
CHS.
In summary, scientific work in golf using the double pendulum swing model has
afforded a basic advancement in the understanding of this complex human motion. The preceding articles have shown that the double pendulum itself can be modeled with a variety of segment parameters and joint load profiles that are able to create realistic golf motion. Understandably, work using a two link model has focused primarily on the joint that connects the segments in enquiry; the wrist. The consensus of this work has shown
27 that a delay in opening of the wrist joint improves golf performance by generating increased CHS. It is interesting to note that the late onset of wrist un-cocking in golf corresponds to Bunn’s original observation of delaying knee extension in maximal ball kicking. It seems that the double pendulum golf model agrees with the optimal motion
pattern existing for other sports.
For the two body segments studied in the double pendulum model, a P-D
sequencing of motion seems to be ideal for optimal speed generation. It is still unclear however, if the same holds for a real golf swing; a complex motion involving multiple human body segments and an external implement; moving in three dimensions.
2.4.2 3D Golf Models
Insight into 3D kinematics and kinetics in golf first appeared in the work of Vaughan (1981). In his investigation, club markers were filmed with two orthogonal high-speed film cameras. Resultant forces and torques applied at the hands were calculated from club kinematics using a Newtonian-Euler approach. Vaughan noted that Budney and Bellow (1979) predicted that the wrist should undergo a positive torque throughout the downswing. This torque would be positive about an axis pointing up from the club shaft plane, and would tend to rotate the club towards the target. Vaughan’s results suggested that this torque was negative for the first half of the downswing; which tended to keep the wrists cocked. The external wrist torque then became positive at wrist un-cocking, and remained positive for the remainder of the downswing. Vaughan cautioned that the external wrist torque should not be confused with the wrist muscle torque since the club grip is in contact with both hands. Two contact points on the grip would therefore
28 represent a distributed load. According to Vaughan: “it should be recognized that this normal torque cannot be considered as a valid measure of the ... un-cocking action of the wrists.” This could be a relevant source of error when modeling the wrist as a spherical
joint.
In addition to resultant joint moments, Vaughan also examined resultant joint
forces. He found that the largest component of the grip force at ball impact was applied along the shaft, pulling towards the golfer. He also found that the positive wrist torque was initiated by applying a force at the hands in the opposing direction of the clubface. Of note, Vaughan observed that a late slowing of the hands before impact coincided with a large increase in CHS.
Neal and Wilson (1985) repeated the work done on 3D club loading by Vaughan. A major difference with their paper was that their results were presented in a global reference frame instead of in a local frame fixed to the club. Their torque results supported the findings of Vaughan. The timing of wrist un-cocking coincided with a change from negative to positive wrist torque about the golfer’s frontal axis. The authors also presented results on the resultant joint force acting on the shoulder. When comparing resultant joint loads, peak forces acting on the shoulder joint were of greater magnitude, and occurred earlier in the downswing, than those forces acting at the wrist joint.
McLaughlin et al (1994) measured a variety of 3D golf “kinematic parameters”; actually body segment angular positions at key time points during the swing. The group performed a linear regression and later a principal component analysis on the data to find which parameters had the highest correlation with CHS. Not surprisingly, they found that delayed wrist onset was important in speed generation.
29 Coleman and Rankin (2005) investigated the applicability of 2D multi-segment models in representing 3D motion. They measured 3D kinematics of the left shoulder girdle, left arm and club shaft during the downswing. They found that the motions of these segments did not all lie along the same plane. Coleman and Rankin concluded that 2D models do no realistically represent multi-segment movements in a golf swing, which they found not to occur in a single plane. No mention was made as to whether the
movement of individual segments could be reliably fit with separate planes.
In summary, these papers exploring 3D motion in golf have contributed to the overall understanding of the swing. Vaughn (1981) was the first author to use inverse dynamics based on optical motion analysis in golf. Neal and Wilson (1985) used a similar method to show that loading in the shoulder preceded loading in the wrist in the downswing, in a P-D manner. These two motion analysis studies have laid a foundation in the understanding of joint loading in the swing. The work by McLaughlin et al (1994) and Coleman and Rankin (2005) have repeated the finding of wrist delay and noted that a single 2D plane cannot effectively represent the motion of a golf swing. However, an
optimal motion pattern still remains to be determined in golf for 3D full body movement.
2.4.3 Adding the Spine and Hips
In a golf study by Cooper et al (1974), P-D sequencing of motion onset was observed qualitatively starting with knee joint movement and transferring superiorly and distally to the hip, spine, shoulder, then wrist. This investigation looked at force plate data under each foot during the swing. The authors referred to free moments about the vertical axes of the force plates as “rotational forces”. When viewing a right-handed golfer from
30 above, these rotational ground reaction forces were clockwise at the top of the downswing. They quickly switched to become counter clockwise just prior to ball contact. Although not discussed, their graphs indicated that this phenomenon increased in magnitude and tended to occur later in the swing as the golfer shifted from smaller irons to a driver. This work supports the idea that a golfer interacts with the ground via his feet when creating a golf swing. From this point of view, a golf swing begins with a kinetic
interaction at the ground.
Although Cooper et al looked at other body segments using qualitative
observation; spine and hip rotations had not been quantified in the literature until later. McTeigue (1994) conducted a study on relative spine to hip rotation using large groups of PGA, senior PGA, and amateur players. Kinematic data were collected using a linkage of gyroscopes and potentiometers. His investigation was designed to look at the so called “X-factor”, or range of torso rotation relative to the hips. He found that spine flexibility did not differ between professional and amateur players (although it was limited in the senior PGA group). An interesting result of this study was that of the “hip slide”. McTeigue found that both amateur and professional players underwent a lateral transition of the lead shoulder during the downswing. Professional players accomplished this by shifting their weight from their back to front foot and keeping their torsos vertically aligned. Amateur golfers tended to accomplish the shoulder shift by a lateral bending of the spine.
Burden et al (1998) explored hip and torso rotations in the context of the summation of speed principle. They measured 3D kinematics in a group of eight golfers using a two-camera motion capture system. They claim that their results supported a P-D
31 segment sequence as required by Bunn’s principle. However, this group did not investigate segment angular velocity or angular impulse. The summation of speed, as described by Bunn (1972) and Putnam (1993) described the relative timing of either sequential angular velocity peaks, or sequential torque onsets. This theory did not refer to relative angular positions specifically, as was reported in this article. Also, measurements of shoulder and hip angular positions were made by connecting bi-lateral bony landmarks; and projecting the resulting vector on the ground plane. As the motion of these segments likely does not coincide with the plane of the ground, these projections may have lead to erroneous results. However, this group did find that players who timed
angular position peaks in a P-D fashion were more likely to generate greater swing speed. The 2D double pendulum model was modified with the simulation work of Sprigings and Neal (2000). The authors added a third segment to the standard double pendulum model. They chose lengths and inertial properties to correspond with segment parameters of real golfers; and for the first time, based applied torques on the force- length, force-velocity and activation parameters of human muscles. They supported the finding by Pickering and Vickers that it was possible to have ball contact with a free- hinge wrist joint. Sprigings and Neal were the first authors to simulate a torso segment in the kinetic golf model. They stated that torso rotations were very important in recreating realistic swings. They found the magnitude of applied torques at the shoulder joint could be lowered to a much more realistic level if a component of the angular impulse could be derived from inter-segmental interaction. Also, the authors reported that the angular position and velocity of the torso seemed to have a direct effect on delaying wrist action,
which ultimately lead to higher club speeds.
32 Sprigings and Mackenzie released a study in 2002 to follow the work done on the triple segment golf simulation. Here the authors used the same 3 segment model to identify the mechanical sources of power in the golf swing. The authors used a forward dynamics approach to optimize muscle model variables with measured kinematics. The authors calculated the power at each joint due to muscle torques or joint contact forces. By integrating this power, they calculated joint energies and the mechanical sources of this energy. Their results indicated a P-D sequence of total work done. The authors also noted that the onset of muscular power at the wrist joint precedes the onset of applied positive wrist torque. This means that some of the energy gained by the wrists is due to the resistive torque acting to keep the wrists cocked. Sprigings and Mackenzie noted that muscular power increased distal segment energy at the expense of decreasing energy in the proximal segment, although no direct measurements of segment energy were
reported.
Sprigings and Mackenzie (2002) had applied a high level of realism in the muscle
models used for their simulation. However, they did not account for an onset of muscle torque during the backswing. All muscle load profiles started from zero at the beginning of the downswing. It is quite possible that a golfer’s muscles are able to develop force before the initiation of downward movement. This potential error in muscle work done on the segments leads to the question of how the resulting joint energetics compare to direct physical measurements of energy contained in the segments.
Perhaps the most comprehensive look at the inter-relationship between motion and loading in 3D golf swing has been in work done by Nesbit (2005). In subsequent articles from the same journal; Nesbit introduced a 3D full-body, multi model, integrative
33 motion capture / kinetic analysis system. Nesbit used separate models for the human body, the ground, and the club. Kinematics from video motion capture data were used as input. A full body human segments model came from an ADAMS module called ANDROID (MSC Software Corporation; Santa Ana, CA). It consisted of 15 linked rigid body segments interconnected with spherical joints. The resultant joint torque profiles
were optimized to match realistic kinematics as measured by the video capture system.
In the first article, Nesbit stated that the resultant forces acting on the club were applied at the grip by the arm segments; while the resultant moments acting on the club where due to muscular work done at the wrists. He compared angular work done by the wrists to linear work done by the arms. His results indicate that better golfers tend to do more work by using their arms to pull on the golf club; than by applying a torque at the wrists. He reasoned that greater club head speed is created by reducing the radius of the
path of the hands just prior to impact.
In the second article by Nesbit and Serrano (2005), the authors calculated work
done at each joint in the full body model by using a joint power approach. They then determined the locations of the sources of power in the golf swing. They found that the back and the hip joints generated up to 70% of the total work done in the swing, while 26% of the total work was contributed by the arms (mostly by the right elbow). They concluded that the generation of work, and its transference to the club, is mostly a “bottom-up phenomenon”; moving upward and outward. Of note, the authors noted that proximal segments tended to slow down to become “static support” for their distal counterparts.
34 Nesbit and Serrano (2005) found that the majority of the joint work performed was used in moving the proximal segments. Very little of the total work was actually transferred to the club. Of the work done on the club at the wrist joint, a linear force applied by the arms generated the majority. Wrists torques showed a comparatively
smaller contribution towards an increase in overall CHS.
Interestingly, Nesbit and Serrano showed that total body joint power tended to
switch from positive to negative around the time of impact; but only the scratch golfers were able to zero their power generation exactly at impact. This would result in maximization of club speed. If power became negative pre impact, the body would work to slow the club. If power were still positive post impact, it would mean usable work was wasted. It seemed precise timing of total joint power application was indicative of player ability.
In summary of the golf research presented in this section, an inter-relationship between loading and motion had begun to be established in full body 3D golf movement. Part of this work has stemmed from optical motion analysis studies. The work by Cooper et al (1974) had shown qualitatively that motion in the golf swing should begin at the ground. McTeigue (1994) showed that the torso has a larger range of motion than the hips; and that a difference exists between amateurs and professionals in how the torso rotates at the end of the downswing. The study by Burden et al showed that range of motion, and timing of angular position peaks followed a P-D sequence in successful swings.
The latter research papers presented in this section on 3D, full body golf motion have used simulations of various modelling complexity (Sprigings and Neal, 2000;
35 Sprigings and MacKenzie, 2002; Nesbit, 2005; Nesbit and Serrano, 2005). These studies have given insight into the sources of mechanical power in the golf swing. In their simulations, these authors have used forward dynamic analysis to optimize musculoskeletal models in recreating known kinematics. While the motion of the models has been matched to that of a realistic golf swing, it is currently unknown if the joint loads created by the models are also correct. Therefore, it would be worthwhile to apply a segmental energetics framework to the golf swing to evaluate simulated sources of
mechanical energy with direct measurements of the destinations of that energy,.
