Thank you art for your insight into your research findings.
Michael Finney's "distal parts" are the upper torso which is accelerating into and through impact causing the slowing of the "hips" or pelvic turn. Makes since to me.
never really said that.....
here's some light reading for everyone.......notice how many times non-scientists and non-PHDed golf theorists are referenced - i'll help you - THEY AREN'T......enjoy....
Chapter Two: Literature Review
The following literature review has been separated into three sections. The first section of this review will look at generalized segmental human motion. The intention of this section is to explore what is known about the general pattern of segment sequencing in human movements such as kicking, jumping and overhand throwing. The second section of this review looks at considerations when using a segment-based framework versus a joint framework when analyzing energetics in human movement. The final section of the review examines the development of golf biomechanics, focusing specifically on studies in optimization of club speed.
2.1 Optimizing Speed in Segmental Human Motion
Movement patterns in segmented human motion have been studied in biomechanics for a variety of motions including kicking, jumping, and overhand throwing. The following section focuses on optimal patterns of motion for a linked system of body segments. This is a topic that has been debated in biomechanics research for the past thirty years. To begin, we will look at a kinematic chain of body segments as generalized link mechanism. Figure 2.1.1 illustrates an example of a 2D, 2 segment linkage-mechanism as described by Vinogradov (2000).
6

v =ω ×r b11
v =v +ω ×r cb22
7
Figure 2.1.1: Example of a 2D, 2 segment linkage. Points a and b are the proximal and distal joints respectively. c represents the linkage distal end point. r1 and r2 are the respective lengths of the first and second segments; while ω1 and ω2 are the respective angular velocities.
The velocity of point b relative to a coordinate system fixed to the external reference frame is shown in equation 2.1.1 (Vinogradov, 2000). The velocity of the end point c is given by equation 2.1.2. For a linked mechanism, the velocity of a segment end point is not only dependent on the angular velocity of that segment, but also on the velocity of the endpoints of all of the segments that precede it. In Figure 2.1.1, the linkage contains only one preceding segment but in human motion it is possible to have many more.
2.1.1
2.1.2
2.1.1 Simultaneous Peaking of Body Segment Angular Velocities
Authors have argued over the optimal pattern of timing for joint angular velocities in a linked system. Koniar (1973) has argued for what he called the “principal of superposition of angular speeds in joints”. In order to achieve maximum performance for a given action, Koniar said that all segments should reach a maximum angular velocity at precisely the same moment. He measured 20 athletes with electro-goniometers and found that subjects jumped highest when segmental angular velocities peaked simultaneously. No mention was made as to the sampling frequency or smoothing methods used in this investigation.
Koniar wasn’t the only author to describe this “principle” of simultaneous segmental speed peaks. Gowitzke and Millner (1988) stated that “in theory, each joint action should impart maximal linear velocity at the instant of release”. These authors noted that this phenomenon wasn’t seen in hitting or throwing sports. They speculated that it would be possible to estimate the degree of coordination for a given performance by comparing peak end point velocity with a theoretical end velocity if all segments were to peak at the same time.
Joris et al (1985) described a simultaneous maximality of body segment angular velocities as “the Hocmuth Optimization Principal”. In a study of over hand throwing in handball, those authors set out to determine if simultaneous peaking of segment angular velocities actually improved performance. They found that this pattern could only be possible in a purely theoretical, kinematic sense; that is, if the segments contained no mass. Of course, this constraint does not hold true for real human movement. The authors found that distal segments seemed to go through periods of highest acceleration when the
8
9 preceding segments underwent a deceleration. Joris et al stated that Newton’s third law could likely explain the deceleration of proximal segments. Those authors reasoned that “for every action on a more distal segment ...” (i.e. joint torque) “there is an equal but opposite reaction on the more proximal segment.” In their experiment, they found that optimal performance was found when segmental angular velocities peaked in a proximal
to distal (P-D) fashion.
2.1.2 Proximal to Distal Sequencing of Body Segment Motion
Bunn (1972) was the original author to refute the concept of simultaneous peaking of limb angular velocities. In his “guiding principles of human motion”, he stated that optimum speed of a kinematic chain’s distal end point can only be reached when body segment angular velocities peak in a P-D fashion. According to Bunn, “... movement of each member should start at the moment of greatest velocity, but least acceleration of the preceding member”. He reasoned that proximal joints could attain higher angular velocities if their distal counterparts would remain flexed later in motion. Although he did not provide equations to prove his work, Bunn argued that higher limb angular velocities could be easier to attain if the radius of gyration of the linked system is kept small (ie. when a joint is flexed). He felt it would be possible to capitalize on this increased angular velocity by quickly lengthening the system’s radius of gyration pre- impact. He observed that the knee seemed to be flexed until late before ball contact for maximum kicking velocity in human kicking motions.
Figure 2.1.2 shows hypothetical profiles of angular velocity for a planar, multi- segment chain. Figure 2.1.2 a) represents the motion pattern that Koniar referred to as the
10 Superposition of Angular Speeds. Figure 2.1.2 b) represents the Summation of Speed
Principal as described by Bunn (1972).
Figure 2.1.2: Hypothetical segmental velocity profiles in a 3 link chain. In part a) all segments peak simultaneously. Part b) shows a proximal to distal progression of angular velocity peaks.
Putnam (1993) supported what she referred to as Bunn’s “summation of speed principal”. She wrote that striking and throwing motions must follow a proximal to distal progression. This is due to what Putnam refers to as “motion dependent interaction... between links”. In a Lagrangian model of two-link motion, Putnam found that angular kinematics of connected links did not solely depend on external moments applied (ie. muscle torques); but also on resultant joint “interactive moments” between links. It is speculated that these so called moments are actually due to reaction forces occurring at the joints; and the virtual or inertial forces acting on the segment CG (center of gravity). Putnam noted that the interactive moments were dependent on the relative angular position, angular velocity, and angular acceleration of each segment in series. Putnam found that interactive moments due to relative angular velocity were greatest when segments were orthogonal. Conversely, interactive moments due to relative angular

11 acceleration were greatest when segments were co-linear. In both cases, interactive moments caused the proximal segments to slow down while the distal segments sped up. In any case, Putnam showed that the kinematics of inter-segmental movement had an
interdependent relationship with the loading of those segments.
Herring and Chapman (1992) carried out a 2D, three segment, over-hand
throwing optimization. In the study, relative timing and direction of external joint torques were manipulated to find an optimal strategy for the longest possible throw. They found that a proximal to distal (P-D) sequencing was essential in obtaining the highest overall distal end point velocity. This was not only true of the onset timing of torques, but also in timing and magnitude of segmental angular velocities. The authors also found that negative torques applied to proximal segments can enhance distal end speed if applied just prior to release. Of note, Herring and Chapman found that P-D sequencing was a very robust solution for optimal segmental movement. Their optimization tended towards this type of movement pattern for a wide range of limb lengths, inertial properties, and applied muscle torques. They concluded that the linked, segmental nature of human limbs predisposes our movement systems to P-D sequencing.
Feltner and Dapena (1989) created a 3D, two segment, over-hand throwing model. They attempted to address the “cause-effect” interdependent mechanisms that link segment kinematics and kinetics. The purpose of their investigation was to show resultant joint forces and torques as a function of relative segment kinematics. They also showed how segment kinematics can be determined as a function of joint forces / torques in addition to gravity and neighbouring segment kinematics. The authors showed that
12 kinematics of a double pendulum represent an extremely multifaceted, interdependent
system that does not rely solely on external impulses alone.
In summary, there have been two generalized motion patterns introduced that
attempt to predict an optimum solution for speed generation in multi-segmented movement. Koniar (1973) introduced the concept of simultaneous peaking of angular velocities between body segments to reach optimum speed generation. Bunn (1972) presented a contrasting solution. He stated that segments should peak in a proximal to distal manner to achieve maximal distal end point velocity. Since these concepts were established, only Koniar’s own study has quantitatively supported the concept of simultaneous peaking. The papers of Gowitzke and Millner (1988) and Joris et al (1985) supported the concept of simultaneous peaking in theory, but their results showed that humans displayed a pattern of P-D peaking in real movement.
Simulation work has gone on to support the concept of P-D patterning in segmented human movement. Putnam (1993) showed this pattern to be a function of the inertial property of our limbs. Simulation work by Herring and Chapman (1992) showed that a P-D pattern of segmental motion was a robust solution for a wide range of system parameters in their speed optimization study. Finally, the simulation work of Feltner and Dapena (1989) showed that a system involving 3D motion in linked segments is extremely complex and interdependent; and cannot be defined by external loading alone.
It seems that a pattern of P-D peaking in segmental human motion has been established as an optimal solution for speed generation. However, previous studies in the literature have shown that humans seem to have evolved to use this type of patterning in movements such as kicking, jumping and throwing. In these movements, there are no
13 external implements involved as a part of the dynamic, segmented chain. This is an important distinction. In general, human segments decrease in mass as you move along the body in a proximal to distal manner. In golf, the system may be slightly different. The club is an external implement that is swung as to be another segment in the dynamic linkage. Although the mass of the club is most likely less than that of the arms segment, the length of the club requires a large radius to be created between the club CG and the focus of club rotation. The result of this is a distal segment that may have more inertia than what humans have evolved to move optimally. Therefore, it remains to be seen
whether a P-D pattern of segmented motion exists in the golf swing.
2.1.3 Out of Plane Segmental Motion
Marshall (2002) compiled a review article looking specifically at patterns of limb movement in regards to throwing and striking sports. He found that the literature tended to support the P-D sequencing as predicted by Bunn’s summation of speed principle. Marshall noted that P-D sequencing was generally a pattern found in flexion and extension of linked segments. In a paper by Marshall and Elliot (2000), it was found that long-axis rotation of segments did not follow a classic P-D pattern. In addition, internal rotation was estimated to have a large end point velocity contribution in throwing and racquet sports. Proximal internal rotation was found to have a contribution of between 46-54% of racquet head speed in tennis, while distal segment internal rotation contributed between 5-12%.
Marshall has shown that P-D sequencing may not be an optimal solution for movement occurring outside of the principal motion plane. The golf swing is a complex,
€
14 3D movement that occurs on multiple planes of motion. It is possible that out of plane motions have an effect on overall CHS. Therefore, in addition to angular velocity of golf segments, it would be worthwhile to explore measurements of motion that take out of
plane movements into account.
2.2 Joint vs. Segment Energetics
Winter (1987) said that transfer of energy flow in human movement can be analyzed either by a “segment by segment” or “joint by joint” framework. In joint energetics, mechanical power is calculated using resultant loads at segment end points. Winter set forth the following equations describing joint power calculations. Equation 2.2.1 describes the power at a joint for a given muscle moment M; where ωj describes the angular velocity of a given segment. In addition to muscular energy, Winter noted that power can enter a joint “passively” through reaction forces at segment endpoints. Equation 2.2.2 describes power derived from resultant joint forces; where v is a vector describing the velocity vector of the joint center. Joint power calculations can indicate joint energy generation or absorption; depending on whether the power sign is positive or negative respectively.
P = M • ( ω − ω ) m21
 PJF =Fv
2.2.1
2.2.2
€
€
a segment’s inertial tensor and vector ω is the angular velocity.
ET = EP + KEtranslational + KErotational EP =m⋅g⋅h
KEtranslational =12m⋅v2 KErotational =12I⋅ω2
2.2.3 2.2.4 2.2.5
2.2.6
15 These equations describe sources of segmental energy, either due to muscle moments or joint contact forces. Their direction implies whether a segment absorbs, or generates energy. Segment energetics on the other hand, are a direct measurement of the quantity of energy a segment contains. Stefanyshyn (1996) has described the following equations concerning segmental energy. In equation 2.2.3, a segment’s total energy ET is the sum of its potential EP, translational kinetic KEtranslational and rotational kinetic KErotational energies. EP is found by multiplying a segment’s mass by the acceleration of gravity and the height of its center of mass (eq. 2.2.4). Translational kinetic energy is found by multiplying half of a segment’s mass by the square of the absolute speed of its CG (eq. 2.2.5). Rotational kinetic energy is described in equation 2.2.6 where matrix I is
In studying segments and joints, which framework is utilized is dependent on the € question being answered. A joint energetics framework is useful to determine if power is created from muscular work or joint contact work. Joint energetics can also be useful to
16 calculate a direction of energy flow (Winter, 1987). However, if the goal of the study is to obtain direct measurements of the destinations of energy created, then segmental
energetics may be a stronger approach.
There are other variables to consider when choosing between a joint or segmental
framework. Winter (1987) stated that joint power calculation accuracy depends on a number of assumptions made in the biomechanical model. This method relies on the assumption of spherical joints between segments. It also assumes that the relative position of the center of mass to the segment origin is consistent. Joint power measurements are also dependent on the estimation of muscle moments applied at the joint. In addition, if a muscle were to span two joints, care must be taken when describing energy flow between segments. For these reasons, it may be useful to evaluate the energy calculations in a joint framework against that found studying segment energetics.
If joint energies are a measure of the sources of mechanical power, then segment energies are a measure of the destinations of this power (Stefanyshyn, 1996). To get an idea of the accuracy of power in a given movement; joint energies and resulting segmental energies should reach a balance. Winter (1987) stated that measurements of joint energetics and segmental energetics have balanced in studies of walking and running. Such a comparison has yet to be made in the golf swing. The joint energy models of Nesbit and Serrano (2005), Sprigings and Neal (2000) and Sprigings and Mackenzie (2002) have all used simulations to determine the profiles of joint torques and joint forces. These profiles come from forward dynamic simulations that are optimized to mimic the kinematics of real swings. These joint power calculations have yet to be compared to segmental energy profiles to estimate the accuracy of their findings.
2.3 Kinetic Energy in Cracking Whips
In an article entitled Whip Waves, McMillen and Goriely (2003) explored the mechanics of cracking whips. The authors modelled a leather bullwhip as an elastic rod of decreasing mass and cross-sectional area. One cracks a whip by throwing the handle and creating a forward moving loop known as a buckling discontinuity (see Figure 2.3.1). The loop moves through the whip as a wave. Energy and momentum are conserved after the initial handle throw. Speed increases as the wave moves through whip elements of decreasing mass and decreasing radius. By the time the wave reaches the end of the whip, the tailpiece has undergone an acceleration of up to 50,000 times that of gravity. Krehl et al (1998) developed a sophisticated motion capture system to film the end velocity of the distal whip tip. Those authors found that the speed generated in the whip was nearly 2.2 times the speed of sound. McMillen and Goriely (2003) contend that the air pushed at the front of the whip creates a supersonic wave that sounds like a large crack.
a) b)
Figure 2.3.1: a) Blackforest whip cracker at Shrovetide (from Krehl et al, 1998). The photo was taken just prior to cracking. Notice the forward moving loop near the end of the whip. b) 2D whip wave model from McMillen and Goriely (2003). The wave is moving through the whip with forward velocity c.
17

18 In modelling whip motion as a wave, McMillen and Goriely (2003) found that energy flow in the whip is dependent upon the mass and radius of its elements. If the whip elements became larger along the direction of the wave flow, the wave would slow down and its energy would be stored as potential energy. The wave model slowly
reversed and flowed back in the direction of smaller elements.
Whip cracking can be compared to various types of human motion. The elements
of a whip, like that of the body, decrease in mass and rotational inertia distally along the system length. Movement is initiated at the proximal root, and the speed created at the distal end is dependent on the efficiency of energy transfer along its elements. However, energy and angular momentum are not conserved in a system of human links. Muscles acting across joints are able to create additional work on distal segments. The question remains: If humans are able to create additional work along our musculo-skeletal chains while the leather whip is limited to the initial throw energy, why do we not achieve movements approaching the speed of sound? The following section will address high- speed motion and efficient energy transfer in musculo-skeletal chains.
2.3.1 Musculo-skeletal Whip Cracking
Researchers at the Royal Tyrrell Museum have studied whether it was possible for certain species of dinosaurs to create sonic booms with their tails (Myhrvold and Currie, 1997). Those authors examined the tail vertebrae of a Sauropod species called Apatosaurus. They found that the tail vertebrae were of sufficient number, length, and decreasing inertia to have behaved like a bullwhip. Furthermore, CAT scan studies of the distal vertebrae showed signs of diffuse idiopathic skeletal hyperostosis (ie. bone scars) that the
19 authors believe stem from using the tail as a noise generator. In a simulated reconstruction of the Apatosaurus tail whip, the authors reported that the distal end was able to reach a whipping speed of 540 m/s, roughly 1.5 times the speed of sound. For this species it would have been possible to create supersonic shock waves by wagging its tail. Apparently efficient transfers of kinetic energy may be possible in musculo-skeletal
chains.
Whip-like motion is of interest in human movement because of the creation of
high speed with a high level of efficiency. However, our bodies do not have the number of segments or the sheer length found in the tail of an Apatosaurus. Is it then possible for human movement to resemble that of a whip?
Joris et al (1985) studied the motion of body segments in female handball throwers. Those authors noted that the upper arm throw consists of a whip-like, sequential movement of 6 body segments. For the group of athletes studied, the fastest throws came from players whose distal segments peaked in velocity following the proximal segments in a sequential pattern. Interestingly, the segment velocities decreased substantially after peaking. The decrease in a proximal segment velocity occurred simultaneously with large increases in distal segment velocities. In this way, the transfer of energy in human segments during handball throwing resembles that of a whip. It has yet to be determined if this whip-like transfer of kinetic energy is visible in the golf swing.
20
2.4 Golf Biomechanics
The application of biomechanics in the sport of golf emerged in the mid 1960’s when the Spalding Brothers of Byron, Illinois took a series of stroboscopic photographs of a golf swing. Since then, the focus of this field has been in performance improvement or injury reduction by means of furthering the understanding of the mechanics of golf movement. The focus of this review will be on golf biomechanics research that has contributed to performance improvement, specifically the understanding of speed generation in the swing. Table 2.4.1 is an abbreviated list of selected articles in golf biomechanics literature, and their role in developing an understanding of the generation of speed. The relative contribution of these articles will be explained in further detail in the following sections.
Table 2.4.1: Timeline of selected Golf Biomechanics articles and their contribution to the understanding of speed creation in the golf swing.
Y ear Author(s) Contribution
1967 Williams
• Stroboscopic motion analysis; first to propose delay of wrist un-cocking; proposed relative timing more important than muscle torque.
1968 Cochrane and Stobbs
• Search for the perfect swing; Lagrangian double pendulum swing model; proposed maximal shoulder torques & free hinge timing of wrist un- cocking for optimal speed.
1970 Jorgensen
• First mathematical proofs that delay of wrist un- cocking is important in speed creation.
1974 Cooper et al
• Qualitative full body kinematics + force plate data; concluded segments follow P-D sequencing; quantified golfer interaction with ground.

21
1977 Pyne
• Showed that angular velocity of the hands is not constant during the downswing;
• Used double pendulum to study effect of club 1979 Budney and Bellows parameters; found performance enhancement with
decreased shaft weight.
1981 Vaughn
• 3D kinematics and kinetics from motion analysis, inverse dynamics; resultant force on grip along shaft of club towards golfer; late slowing of hands increased CHS.
1982 Milburn
• 2D kinematics from motion analysis; ‘centrifugal force’ responsible for wrist un-cocking; positive acceleration of club came at expense of deceleration of arm.
• 3D kinematics and kinetics from motion analysis; 1985 Neal and Wilson found shoulder joint loads were greater and acted
earlier than loads at wrist.
McLaughlin and • 3D angular position of segments from motion 1994 Wilson analysis; used Principal Component Analysis to
find that delay of wrist onset important for CHS.
1994 McTeigue
• 3D hip and torso kinematics; large subject group of professional players; quantified ‘X-factor’.
1998 Burden et al
• 3D kinematics from motion analysis; results supported P-D sequencing in full body movement.
• Ran speed optimizations of 2D double pendulum 1999 Pickering and Vickers model; found wrist delay and forward ball
positioning to improve performance.
• Three segment simulation model; found greater 2000 Sprigings and Neal realism in simulated shoulder torques; linked wrist
delay with torso rotation.
Sprigings and • Three segment simulation model, calculated joint 2002 Mackenzie powers; found P-D sequencing of joint power
generation.
2005 Coleman and Rankin
• 3D kinematics from motion analysis; reasoned that downswing motion from multiple segments does not fit well into single plane.

22
2005 Nesbit
• 3D, full body kinematics and kinetics from multi model simulation; found that most work done on club by pulling force exerted on grip by arms segment.
2005 Nesbit and Serrano
• 3D, full body kinematics and kinetics from multi model simulation; calculated full body joint power contribution towards CHS; wrist torques found to be relatively unimportant.