Modeling the Swing - Nesbit
-- 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.
Kinds of Models
|Starting with a very brief note
names of the three types of models, they are:
Now a little more detail, in a table view.
models, divided into:
|Study of motion
& Rankin - Swing is not planar.
|Study of motion
and the forces that created the motion.
Simple model: apply forces and see the motion produced.
MacKenzie & Sprigings.
|Study of motion
and the forces that created the motion.
Complex model: view motion and deduce the forces that produced the
with Serrano and others.
|Finally, the full verbal
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.
model studies both motion and the forces required to create
that motion. There are two kinds of kinetic models.
dynamics kinetic model
is a model of the kind we have already
seen, the double-pendulum
, or the three-dimensional
. A forward dynamics model is usually a relatively simple
model. Its intent is to represent
the important aspects
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
experiments manageable, the model should not have any more complexity
than needed to investigate that aspect. (Einstein on physics:
should be as simple as possible, but not simpler.")
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
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.
Nesbit's studies are inverse dynamics kinematic studies. This implies
he need three resources. The needed resources are:
Given the resources, the
study itself is the
art of mixing the resources together -- and, one hopes, gaining some
useful knowledge from the mix.
- 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).
- The kinematic
data for the motion to be studied, in this case a golf swing.
- 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).
|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
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.
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.)
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 &
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.
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.
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.
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
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).
And yet another display: the order
of timing of the peak effort for
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
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.
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).
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
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.
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.
- 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.
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
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.
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.
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
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:
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.
- 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.
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
"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).
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
- Expanded range of motion
can generate additional clubhead speed. Again, we saw this when
we studied the double
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
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
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.
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.
- 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.
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.
- 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
modified -- March 6, 2012