Modeling the Swing - Nesbit

Dave Tutelman  --  January 16, 2012

Steven Nesbit is a professor of Mechanical Engineering at Lafayette College. He and his graduate students are a prolific source of interesting swing modeling. But their models are of a different sort. Before we delve into his studies, let's review the kinds of models one encounters in the biomechanics of sports.

Different Kinds of Models

Starting with a very brief note on the names of the three types of models, they are:
  • Kinematic models
  • Kinetic models, divided into:
    • Forward dynamics kinetic models.
    • Inverse dynamics kinetic models.
Now a little more detail, in a table view.

Type of model
Kinematic model
Study of motion only.
Coleman & Rankin - Swing is not planar.
Study of motion and the  forces that created the motion.
Simple model: apply forces and see the motion produced.
Double pendulum.
MacKenzie & Sprigings.
Study of motion and the  forces that created the motion.
Complex model: view motion and deduce the forces that produced the motion.
Nesbit, with Serrano and others.

Finally, the full verbal explanation:

A kinematic model studies motion. No forces or torques, nothing about what made the motion happen that way, just the motion itself. We have already seen a kinematic study in the Coleman-Rankin paper, "A three-dimensional examination of the planar nature of the golf swing". This involved frame-by-frame analysis of video to see exactly where in space the neck (pivot), shoulder joint, wrist, and clubhead are during a swing. Pure motion; no forces are ever discussed.

A kinetic model studies both motion and the forces required to create that motion. There are two kinds of kinetic models.

A forward dynamics kinetic model is a model of the kind we have already seen, the double-pendulum of Jorgensen, or the three-dimensional triple pendulum of MacKenzie. A forward dynamics model is usually a relatively simple model. Its intent is to represent the important aspects of the swing, and its purpose is to "experiment" with the effects of those important aspects. In order to keep the experiments pure, we need a mechanical or mathematical model; a real golfer cannot be trusted to change only the one factor of interest and nothing else. In order to keep the experiments manageable, the model should not have any more complexity than needed to investigate that aspect. (Einstein on physics: "Everything should be as simple as possible, but not simpler.")

An inverse dynamics kinetic model is usually considerably more complex, used to determine the forces applied to make an observed motion. Instead of representing the important aspects a golf swing, it represents the major parts of the human body and the forces applied. In the case of Nesbit's studies of the golf swing, the repesentation of the body is joint-oriented; that means that the "forces" involved are actually torques at the joints. (BTW, the human body isn't the only system that can be studied by inverse dynamics. But we are studying a golf swing here, so our system is the human body plus a golf club.)

Here's the way an inverse dynamics study works. You start with kinematic data -- a description of pure motion. Ideally, this description includes the motions of all the joints in your representation of the body. Then you employ a computer program to deduce the joint torques that must have been applied to produce those motions. The computer program tries a torque-vs-time curve for each of the joints, and sees what motion is produced. Then it iteratively changes the torque curves to home in on the motion the kinematic data prescribes.

Nesbit's studies are kinematic studies, usually followed by inverse dynamics kinetic models based on the kinematic models. Let's look at a couple of his most important such works.

A Full-Body Model

The papers by Steven Nesbit we will be studying are, "A Three Dimensional Kinematic and Kinetic Study of the Golf Swing" (Nesbit the sole author) and "Work and Power Analysis of the Golf Swing" (jointly with Monika Serrano), both papers in the Journal of Sports Science and Medicine, 2005 No. 4. They are both based on the same model and the same kinematic data, and we will discuss them as if they were a single study.

Nesbit's studies are inverse dynamics kinematic studies. This implies he need three resources. The needed resources are:
  1. A quantitative model of the body, including each body part's dimensions, mass and mass distribution, and the properties at the joints (which ways they can move, how far they can move, how much torque they can exert, etc).
  2. The kinematic data for the motion to be studied, in this case a golf swing.
  3. A computer program that can apply torques to the body model (#1 on the list) and generate a motion, combined with a program that efficiently and iteratively modifies the torques so the motion converges to the measured golf swing (#2 on the list).
Given the resources, the study itself is the art of mixing the resources together -- and, one hopes, gaining some useful knowledge from the mix.
The full-body model that Nesbit uses is based on GeBOD (Generator of Body Data) model, which has been around since the mid 1990s. It seems to have been used mostly for computer-simulated crash test dummies. (They must have been watching my golf swing.) Nesbit has chosen to model a golf swing with a GeBOD model having 15 body parts and 14 joints. In the diagram at right, I have labeled the body parts, in a picture from both the papers. The joints identified are the obvious meetings of the parts, with the addition of wrist joints hinging the club to the ends of the forearms.

The club itself is obviously part of the model. Nesbit chose to add the complexity of a flexible shaft, so he learned something about shaft flex behavior as well. As with MacKenzie, we will ignore shaft flex in this article.

The kinematic data -- the detailed motion of the golf swing -- was obtained by taking videos with multiple cameras from different angles. Key points on the body were fitted out with reflective markers, making it easier to trace the motion in the video frames.

Four golfers were modeled: three men with handicaps of 0 (scratch), 5, and 13, and a woman with an 18 handicap. (There was actually a measured population of 84 golfers. The three men were selected as representative of the diversity of that population.)

The computer program was the ADAMS software from Mechanical Dynamics. It does Finite Element Analysis (FEA) of mechanical systems. The GeBOD model of the human body is essentially a mechanical system suitable for FEA.


The results of this sort of study are things like graphs of energy or power vs time, or compared across all the joints. Here are a few examples from Nesbit & Serrano:

This bar chart shows the total work done (energy exerted) at each joint in the study. The first and most obvious lesson here is that the lion's share of the work is done by the body: the hips, lumbar, and thoracic joints. Next after that is the right elbow, so we know that golfers are exerting effort to extend the right elbow.
The left ankle and left knee contribute nothing to clubhead speed (the kinetic energy that is the goal of all this work). In fact, they are energy sinks (they absorb energy), but only very slightly so.[1]

This bar chart seems to contradict MacKenzie's results -- that a significant amount of clubhead speed comes from left shoulder torque. (And, in so doing, it would contradict my general assertion that later models didn't contradict earlier models; they just refined them and addressed questions the earlier models did not.) But it needn't be a contradiction. We did discuss (and MacKenzie himself mentioned) the possibility of right arm extension adding to left shoulder torque. Nesbit and Serrano's results say that two thirds or more of MacKenzie's "left shoulder torque" is actually due to right arm extension. It also suggests that all swings contain more "C-Motion" (used to be called "Leecommotion") than you might think.

I noticed another interesting thing from this graph. I have heard time and again that women have to use more lower body (legs, hips, and torso) than men, because they don't have the upper body strength (shoulders, arms, and hands). But such an assertion is belied by this data. The female golfer here is close to the male golfers' performance for most joints, but falls way short for the right hip, lumbar, and thoracic joints. Interestingly, that is where all the swing power is. But the woman in the study neglects those joints -- where folklore says the woman will expend her productive effort. Instead, she comes closer to matching the men in upper body strength -- shoulders, elbows, and wrists. But it doesn't help, because the hips and torso is where the power is really coming from (according to this graph, as well as our earlier, forward-dynamics, models).

Perhaps that is why the woman is an 18 handicap; there are not enough women in the study to know if that is a gender-related difference. Note that the male 13-handicap also trends to that same fault.

Here is another output from the Nesbit-Serrano paper. It is the total amount of work done by the golfer over the course of the downswing. The time scale is with respect to impact; 0.0 seconds is the moment of impact between clubface in ball.

Note that the scratch golfer has not only done the most work (indicating strength and conditioning); he has also timed things so the work peaks at impact (indicating coordination and tempo). It suggests that the scratch golfer is both very fit and able to sequence those fit muscles to make a very efficient swing.
This is even more apparent when we look at power. Power is the rate at which work (energy) is being input into the system. So, at the peak of total energy, the power should be zero, and going from positive to negative. Why? Because before the peak, energy was being input to the system (positive work); after the peak energy is leaving the system (negative work).

We can see from the power curve that only the scratch golfer crosses through zero power at impact (0.0 sec). The 5-handicap gets there a little early (already peaked, and is going down). The other two golfers reach zero power after impact (they are still accelerating at impact; there's unused clubhead speed still "in the tank" when the clubhead gets to the ball).
Male Scratch
Male 5 Hcp
Male 13 Hcp
Female 18 Hcp
Left Ankle
Right Knee Left Knee Right Ankle
Right Ankle
Left Ankle Right Knee Left Ankle
Left Knee
Left Knee Left Ankle Right Knee
Right Knee
Right Ankle Right Ankle Left Knee
Left Hip
Right Hip Lumbar Right Hip
Right Hip
Left Hip Left Hip Left Hip
Lumbar Thoracic Thoracic
Left Shoulder Right Hip Lumbar
Left Shoulder
Thoracic Left Shoulder Left Shoulder
Right Shoulder
Right Shoulder Right Shoulder Right Shoulder
Left Wrist
Left Wrist Right Wrist Right Elbow
Left Elbow
Right Wrist Left Wrist Left Elbow
Right Elbow
Left Elbow Left Elbow Right Wrist
Right Wrist
Right Elbow Right Elbow Left Wrist
And yet another display: the order of timing of the peak effort for each joint. I have changed the display from the graph in the paper to a color-coded table here. For example, the male scratch golfer's first joint to have peak effort is the Left Ankle, the second the Right Ankle, etc.

My color code is based on the idea that whatever the scratch player is doing is correct. So I colored his order as a rainbow, with gradual changes from one color to the next. Then I colored each joint the same color it was for the scratch player. That way, any joint not in the same sequence as the scratch player is a color out-of-order for the rainbow, making it easier to notice.

The differences are pretty clear; the higher handicap the male golfer, the less in-sequence he is with the scratch golfer. The female golfer in the sample is a different story. Her sequence is actually pretty good; except for a the elbows and wrists, she is never more than one spot out-of-sequence. The elbows and wrists may not be much of a problem; see the next paragraph. Her problem is not one of timing, but of total ability to do work -- strength.

We do not see the same organized ordering, even for the scratch player, once we get beyond the shoulders. The wrist and elbow timing is more random at first glance. But a look at the original graphs in Nesbit & Serrano's paper tell us why. Those four joints fire almost simultaneously, and just before impact. All four of those joints fire within 5 milliseconds of each other (and 15 milliseconds or less before impact).

Lessons from the Model

Most of these lessons are pointed out by Nesbit in his discussion, but a few are my own observations based on the data presented.

Sequence of the joints' firing: Look again at that rainbow-coded table, showing the order of peaking of the effort in the various joints. Particularly, let's look at the scratch golfer, because there is an important lesson there.

A close look shows that the scratch golfer has a very organized and easily described sequence.
  • It is from the ground up, until it reaches the shoulders. This is what the best textbooks say the golf swing should be, but it's really nice to have scientific confirmation.
  • On top of that, at each level (ankles, knees, etc), the left side fires before the right side.
The only place this pattern is broken is beyond the shoulders -- the elbows and wrists. And that's not a problem. They are nearly simultaneous anyway, as noted above.

The importance of wrist cock: This lesson is emphasized by the accompanying graph from Nesbit's paper, to which I have added a little. I have added the red curve, which is the clubhead speed that would have been generated by the same hand speed but never any wrist cock. I only plotted one curve, based on the scratch golfer (the solid line in the black curves).

The difference at impact is about 74% of the clubhead speed. That is, the clubhead speed with a good wrist cock is 74% higher than that with no wrist cock. That's huge! Now in reality, it won't be that large a difference, because the dynamic forces on the hands are somewhat different when you release the wrist cock. But even half that difference is 37%, and reality is more than that.

For a golfer who can swing a driver at 100mph with a full wrist cock, the loss of clubhead speed from no wrist cock is more than 80 yards. That is a lesson of a substantial size. Of course, we saw it very clearly with the simpler models; this was very clear even from the double pendulum model.
The importance of wrist torque: The previous observation was purely kinematic -- only motion, no torque considered. What is the kinetic role of the wrist? If we look back at the graph of total work of the various joints, we see that the wrists contribute very little energy. This reinforces the conclusion of the earlier (forward dynamics) models that wrist torque is not a factor in producing clubhead speed.

We came to this conclusion based on total work at each of the joints. But the researchers also have the torque-vs-time graphs for each joint (not published in the paper). They must also support this conclusion, because Nesbit writes, "Just before impact the wrists momentarily approximate a “free hinge” configuration as the golfer merely holds on to the club as its momentum carries it to impact. By the time impact is reached, all torque components are in opposite directions because the wrists cannot keep up with the rotational speed of the club at this time in the downswing." That is consistent with my conclusions in my article on hitting with the hands. In a private communication, Sasho MacKenzie has also supported this point, citing the torque-speed relationship whereby the faster a joint is turning the less torque it can exert.

Note that this is not as strong a statement as the earlier models made: that wrist torque assisting release is deleterious to clubhead speed. We'll see why it didn't make the stronger statement below, when we discuss the limitations of the model.
The importance of path of the hands: Here's another purely kinematic observation. Nesbit points out that there was a strong correlation between skill (reflected as handicap) and the path of the hands in the downswing. Specifically, he measured the "swing radius ratio", the degree to which the hands follow a tighter curve at impact than earlier in the downswing.

What does this mean? Here are "strobe animations" of two of the swings in the paper: the lowest- and the highest-handicap golfers. I have added two curves to each of the swings:
  • A blue curve, tracing the path of the end of the grip early in the downswing.
  • A red curve, tracing the path of the end of the grip in the vicinity of impact.
You can see that the scratch golfer has a relatively straight path (very little curvature) in the blue curve, and a lot more curvature in the red curve. The 18-handicapper is just the opposite -- much more curvature early in the downswing than near impact.

Why does this matter? This is another way of delaying centrifugal release until very late in the downswing, and emphasizing it late for maximum clubhead speed. You don't have to use retarding wrist torque to keep the clubhead lag; just minimze the path curvature early and maximize the curvature late.

Note that the double-pendulum model cannot reflect this distinction; it has a fixed upper pivot and a fixed-length upper arm, so the radius of curvature is absolutely constant. Even allowing a lateral acceleration of the "fixed" pivot doesn't give enough variation of swing radius to study this properly. We needed to go to a kinematic study to even see this effect. Nesbit has written a whole paper on just the subject of the curvature of the hand path (Journal of Sports Science and Medicine, 2009, #8, p235, co-authored with Ryan McGinnis).
Strength vs Flexibility: Nesbit concluded that, "Swinging harder does little to generate additional club head velocity. Swinging further (expanded range of motion) has the potential to generate additional club head velocity if the subject possess sufficient muscular power. Exercise programs thus should promote flexibility, and strength training for power as opposed to just strength development. Subject differences in work, power, force, and torque do translate to differences in club velocity, however not to the degree one would expect. "

Let's look at each of these points:
  • Differences in strength do not make for proportional differences in clubhead velocity. We have seen this before, in our lessons from the double pendulum model.
  • Expanded range of motion can generate additional clubhead speed. Again, we saw this when we studied the double pendulum model. That study said specifically that wrist cock gave more velocity gain than did shoulder turn. Nesbit didn't come to that conclusion, but it is probably true.
  • Exercise programs should promote flexibility first. Any strength training should be for power, not just strength. That is certainly a reasonable conclusion to be drawn from the study. I'm not sure how one trains "for power as opposed to just strength development". I imagine it has to do with speed or reps, as opposed to maximum force, but I'm not sure.

What we can and can't learn from the model

As with the previous models, let's step back and see if we can note where the model is extensible and where it has limitations. This is especially interesting, because this study is kinematic and inverse dynamics kinetic, whereas the previous models were forward dynamics kinetic.

Behavior of the body - A shortcoming of the forward dynamics models we've seen so far has been their inability to model any part of the body below the shoulders. Well, it does model them, but only as a single bulk torque for everything from the torso down. Not so for this model! It can tell the hips from the thorax, the knees from the shoulders.

One of the "lessons" from the study is the order in which the joints fire (or at least peak in their power contribution to the swing). The lessons support the notion that the feet provide the first effort (well, the ankles in this case), then the knees, the hips, and the torso, until finally the shoulders are turning. I saw this described in Jack Nicklaus' 1974 book, "Golf My Way". But I saw it in person much earlier. I had the opportunity in 1961 to play an evening round with a state amateur champion, far and away the best golfer I had ever seen to that point in my life. The single thing that impressed me most was that, even to my untrained eye, his legs preceded his hips, which proceeded his torso; his arms were behind that, and the club lagged way behind the arms for almost the whole downswing. I spent the rest of that summer trying to rebuild my swing along those lines.

This inverse dynamics kinetic study of a full-body model puts the scientific stamp of approval on teaching a "ground up" swing. The lower the handicap of the golfer, the more his swing was monotonically ground up. (I say "his" advisedly. The lone female golfer in this study was the second best at this sequence. There are other reasons she had the highest handicap in the group. One of them was the obvious disadvantage in strength, which showed up in the power curves.)

What if? Beats me! - One of the big benefits of the forward dynamics kinetic model is the ability to do "what if" experiments with it. This is much harder with a full-body inverse dynamics kinetic model like Nesbit's. There are too many parameters to easily tweak something and understand what you did. Think about it.
  • The double pendulum has two joints, where you can apply a one-dimensional torque (just clockwise or counterclockwise) to each. Not very many parameters. It is pretty easy to follow cause and effect in a "what if" experiment.
  • The MacKenzie model is somewhat more complicated: three joints and four one-dimensional torques. Still only four parameters, plus some static conditions of the experiment. (Every model has some static conditions, like the mass, moment of inertia, and center of gravity of each of the elements of the model. These are much easier to deal with than a torque that is a function of time. And the torso angle and shoulder angle are static conditions in MacKenzie's model. The actual torques are still around a single axis.)
  • Nesbit's full-body model has 14 joints. (More if you account for the segmented flexible shaft and a few ignored joints in the neck that don't contribute any power to the swing.) Each joint is a ball and socket, allowing three dimensions of torque to be applied. That is over 40 parameters which are functions of time. Completely apart from the computing demands, it is difficult just managing all that input if you want to tweak the model and see what happens.
Models like this do not generally allow for optimization to find a "best" solution. Instead, they examine known "good" solutions. For instance, a scratch golfer obviously has a good swing. So let us find out what he is doing in the swing, by modeling his swing. Want to see what happens if you change something? Take a less-good swing (a higher handicap golfer), and model that swing. Then compare the models.

That is the essence of what this study does -- how it deals with the limitation of complexity.

It is worth noting that the final output of Nesbit's studies is a mathematical model that can be used for forward dynamics studies, even though it was derived from inverse dynamics methods. That is, it consists of a generalized full-body model of any human move (while holding a golf club in both hands), plus a set of about forty input torque curves that constitute a golf swing. Well, four such sets of input torque curves, one for each of the golfers studied. The difficulty of using the model as a forward dynamics model is the sheer number of inputs to consider: how to tweak each one, and how they interact when a real human makes a swing. For instance, changing the firing of some muscles will cause a human to fire other muscles just to maintain balance and stay upright.


  1. Tiger Woods, in his book "How I Play Golf" (Warner Books, 2001), has written, "For More Yards, I 'Snap' My Left Leg: When I need an extra 20 yards, I incorporate a special move in my lower body just before impact. I've found that by snapping my left leg straight, my hips clear faster and speed up the movement of my shoulders, arms and legs. This is an unorthodox move meant solely for power. Byron Nelson and many other great ball strikers concentrate on maintaining a bit of flex in their left leg through impact, as that tends to keep the clubhead moving along the target line longer. But for extra distance, I straighten that left leg as quickly as I can on the through-swing."

    Tiger's extra-power swing described above is a different swing from the one Nesbit uses for kinematic data; it depends on the left knee adding significant work. Physics strongly suggests that Tiger's move can add extra clubhead speed. It raises the left side of the body, increasing the torque that reaches the shoulders. But that was written before Tiger developed left knee problems that sidelined him for multiple surgeries. And perhaps now we know why.

Last modified -- March 6, 2012