Phil Cheetham The 3D Guy

2D and 3D Coordinates for Golf Swing Analysis

2010-01-18T20:29:00.001-08:00

Introduction
This article is meant as an introduction to the basics of measuring position in both two dimensions and three-dimensions; specifically to the golf swing. I wrote it a while ago but would like to bring it back and then continue the idea.

Position Measurement in Two-Dimensions
When we want to measure the position of something on a flat plane, say a piece of paper or the screen of a computer, we can use two perpendicular axes, one along the bottom and one along the left side of the paper. Lets give each of these lines a name, lets call the bottom one the X-axis and the one on the left side the Y-axis. These two lines join at the bottom left corner of the paper and we call this point the origin or (0, 0). It is zero feet along the X-axis and zero feet along the Y-axis. To place a point on the paper we can simply measure a specific distance along the X-axis and a specific distance along the Y-axis and write is as: (x, y). These two numbers completely define a point anywhere on our piece of paper. Now if we chose to move our two lines to the center of the page, that is, we draw a cross with one line up and down and the other left to right, we would now have added a negative X-axis and negative Y-axis. Anything to the left of the center will get a negative X value and anything below the center would get a negative Y value. Further, any point in the left bottom corner would have both X and Y values negative. The combination of the origin, the X-axis and the Y-axis is called a two-dimensional (2D) coordinate system or reference frame. The coordinate system below is labeled with several coordinate pairs as examples.

The Golf Mat as a Two-Dimensional Coordinate System
Now let’s take this piece of paper and lay it down on the floor, and let’s enlarge the paper to about a 5-foot square, paint it green and call it a golf mat coordinate system. If our golfer stood on this mat in the address position we could move the center (or origin) of our two lines between his feet. We can also make the line in the direction of the pin, red and call it the X-axis and make the line that is forward and backward with respect to the golfer, green (a different green than the mat so we can see it) and call it the Y-axis, maybe even position it through the ball for convenience.

Now since we have the golfer standing on a two-dimensional coordinate system we can measure certain things about his stance, for example, we can find the coordinates of the ball are (0, 3), that is, 0 feet along the X-axis and 3 feet along the Y-axis. We can also measure the positions of his right heel (0.8, 0), right toe (0.9, 0.8), left heel (-0.6, 0) and left toe (-0.7, 0.8). Note that all these values are in feet. Now we have some simple two-dimensional information about his stance. From these points we can calculate things like: width of stance, distance away from the ball, position of the ball between the feet, how much each foot is open or closed to the target in degrees, and if we draw a line connecting each heel we can calculate the angle that his stance is open or closed to the target. Note that the Y-coordinate of each heel is zero, which means he is square to the target in this example.

Measurement in Three-Dimensional Space
Now that we have the golf mat as our two-dimensional X-Y plane, lets add another axis and extend our discussion to the world we live in; three-dimensional space. Lets place an imaginary vertical line starting from the origin and going all the way to the ceiling. Lets color this line blue and call it the Z-axis. Now we have three axes, the X, Y and Z-axes and an origin. The origin is now defined with three number as (0, 0, 0), one each for its X, Y and Z values. The combination of the origin and the X, Y and Z-axes is called a three-dimensional (3D) global coordinate system or a global reference frame. We use the word “global” because it is the reference frame from which everything is measured. If we measure a distance along each of these three axes we can define any point in the 3D space around the golfer. Now we have the power to define the position of any point on the golfer’s body or club at the address position, not just the position of his feet and the ball as we did earlier.

Lets not worry how we do it for now but lets just assume we can measure the 3D coordinates of a point on his pelvis at the right thigh and at the left thigh. Lets also measure the position of a point on his left shoulder and a point on his right shoulder. Now we can join the left and right pelvis points with an imaginary line and the left and right shoulder points an imaginary line. From these lines we can measure some more interesting things about his stance. With the pelvis line we can measure whether his hips are open or closed at address, we call this the pelvis rotation angle, and how he is tilted to the right or left, we call this pelvis side bend. We can do the same for his upper body using the line from the left to the right shoulder. Notice that we can get rotation and side bend from this line but we cannot get forward-backward bend. We don’t know how much he is bending forward with his upper body since we only have a line from left shoulder to right shoulder. We need another line or point to figure that out. In fact we need to define a three-dimensional “local reference frame” in his upper body and all the other body parts in order to calculate everything we need for a true 3D analysis. I will explain this in my next article and also explain the term “six-degrees-of-freedom”. Here’s a hint; with a local reference frame on each body segment we can measure three positions - sway, thrust and lift (x, y, z) and three angles, one around each of the axes - forward bend, side bend and axial rotation (θ_x, θ_y, θ_z). Remember, positions are measured in feet (or meters) and angles are measured in degrees.

Changing the Kinematic Sequence with Biofeedback Drills

2009-12-12T15:43:00.001-08:00

I am currently working with an LPGA player to improve her efficiency in the kinematic sequence and get her more swing speed. Remember that the kinematic sequence is the graph of turning speed of pelvis (red), thorax (green), arm (blue) and club (brown). It is measured in degrees/second along the vertical axis and shows time through the swing along the horizontal axis. (Check my earlier blog articles for more detail or amm3d.com). After capturing her swing with the AMM3D golf motion capture system, I analyzed it with the TPI 3D biomechanics report. Below is the graph of her kinematic sequence with a driver. There are many “expert” characteristics in the graph; transition order is good, peaking order is good, accelerations and decelerations generally look good too.

Although she transitions in the correct order; pelvis, thorax, arm, club; you can see that she pauses with her hips before transition (the red curve flattens out), also her transition period is too long, there is minimal downswing loading of any joint and her turning speeds are fanning early in the downswing. This pause really limits the speed contribution of the “stretch-shorten cycle” of the muscles. In and ideal stretch-shorten cycle there should be virtually no time between the eccentric/concentric contraction phases of the muscle; this “amortization” phase or pause should be as short as possible. The lack of downswing joint loading means she is leaving a lot of power on the table and the fanning of the curves means that the relative speed between the body segments is increasing, reducing the amount of force that can be produced in each muscle; (see my article on amm3d.com regarding Riding, Stretching, Fanning, I’ll post it soon on this blog too).

So while she was still in the AMM3D system we began using real-time audio biofeedback to see if we could change the sequence and teach her not to pause at the top; hence allowing the smooth acceleration into and out of transition and improving the stretch-shorten cycle. We set the audio tone to sound if she achieved a good core stretch at the beginning of downswing and worked on half backswing drills. Very quickly she was able to coordinate her downswing loading (aka “X-Factor Stretch”) and the curves became smoother before and after transition. We also saw that thorax, arm and shaft “rode” up together (good energy transfer); however, her total transition time was still very long. This means that the drill was definitely successful but that we still need to work on lessening the transition time from about 0.17 seconds to about 0.8 seconds. This will require a combination of half swing drills and strengthening of the core muscles so they can support fast pelvis firing without leaving the thorax behind. Check out the kinematic sequence graph below, this is from one of the half swing drills.

Drills can definitely change the kinematic sequence very quickly, but conditioning exercises will also need to be done in the gym to support the change. The trick will be to transfer this to the full swing.

Where is Peak Rotation Speed in the Kinematic Sequence of the Golf Swing?

2009-11-26T10:45:00.001-08:00

An article I did earlier this year on where in the downswing the pelvis rotation speed peaks and then decelerates. The interesting this is how early it happens.

The Kinematic Sequence is an indicator of swing efficiency and speed. If you look at just the downswing phase of the swing (the center section) the graph above displays how fast you turn or swing each part of your body for about 0.25 seconds before impact. During the downswing each part accelerates then decelerates in a smooth and sequential order. In an efficient swing the red (pelvis) curve should peak first followed by the green (thorax) curve then the blue (lead upper arm) curve and finally the brown (shaft) curve hits maximum swing speed at impact. Also each curve should peak higher than the previous one.

One thing that is not obvious from the graph: What is the typical body position at each of these peaks? In this article we look at where the pelvis speed peaks. The strange thing from the graph is that it looks like it is about half way down in the swing. Well, in terms of time it may be; but in terms of body position it is not. In fact peak pelvis turning speed occurs surprisingly early in the downswing in terms of body and club position; look at the first image in the diagram above. That’s because at the beginning of the downswing you are moving slow and at the end you are moving very fast.

Let’s look at where 45 touring pros are at this point in the downswing. They are taken from the TPI 3D database. It is very instructive to look at their positions. Look at the angles of the shaft, lead arm, thorax and pelvis. I tried to group them with respect to shaft angle. I couldn’t group them with respect to thorax and pelvis angle but you can study that yourself.

One very important observation is that in most cases the club is still very close to, or before vertical, the pelvis looks pretty close to square, and as I said, peak pelvis speed occurs pretty early in the downswing. That’s where the pelvis is turning the fastest, after this point the pelvis turning speed slows down. Notice that at this point there is still a good wrist set and in many cases also a good shoulder load.

The last four images in this article are definitely the odd ones out.

In a subsequent article I will look at the positions of high handicappers also at peak pelvis speed and you definitely won’t see this consistency and “strength” of position; quite often will see a very late pelvis peak.

So when doing a 3D analysis, in my opinion, it is good to visualize what the golfer should look like at the specific points in the kinematic sequence, the first one being shown here; the point at which the pelvis reaches its peak turning speed.

This was not meant to be a rigorous scientific analysis and you can probably argue some of my groupings, however, it is just meant to give you a feel of where these top golfers are when their pelvis speed peaks and then begins to decelerate as the rest of the segments continue to accelerate. Enjoy studying the pictures on the next few pages.

The first group has the club shaft well before vertical and the lead arm close to horizontal.

Next group is on the next page.
This next group has the club still before vertical but the arm is a little below horizontal.

Next group is on the next page.
This next group has the club shaft a little past vertical and the arm is around 30 to 45 degrees below parallel

These last four have the latest point of peak pelvis speed and hence a larger more released wrist angle. These four guys are not the longest hitters on the tour.

15 Minutes of Biofeedback Training improves the Kinematic Sequence

2009-11-23T15:27:00.001-08:00

I recently captured the swings of a young female playing professional on the AMM3D golf full-body motion capture system using TPI 3D analysis. She had some issues with the kinematic sequence peaking order, it was not optimal; her thorax was peaking before her pelvis. I noticed from the graphs that she had both a little excessive sway in the backswing and a reverse spine angle at the top. After the analysis we worked on some real-time biofeedback; we set it so if she swayed more than an inch the computer would beep; after about 15mins of practice we again captured her swing. She was able to maintain stability without swaying; she also stopped the reverse spine action. Look what happened to the peaking order of her kinematic sequence; perfect! She and her coach were both thrilled. Check out the kinematic sequence graphs below.

The Kinematic Sequence: Signature of Efficiency and Power in the Golf Swing

2009-11-19T10:43:00.001-08:00

This article is a very good introduction to the Kinematic Sequence. It discusses the downswing, the transition and gives a few examples.

In sports such as golf that need to create maximal speed of a distal segment or implement (club, bat, racket etc.), it is generally found through motion analysis techniques, that there is a precisely timed sequence of body segment motions progressing from the proximal (inner), large segments to the distal (outer), smaller segments. In the biomechanics literature this is often called "proximal-to-distal-sequencing", "kinetic linking" or the term I prefer; the "Kinematic Sequence".

Downswing Phase

During the downswing in golf all body segments must accelerate and decelerate in the correct sequence with precise and specific timing so that the club arrives at impact accurately and with maximal speed. The most efficient sequence of motion for the major segments is: pelvis, thorax (upper body), arms and finally club. This motion must occur sequentially with each peak speed being faster but fractionally later than the previous one. This sequence reflects an efficient transfer of energy across each joint and facilitates an increase in energy from the proximal segment to the distal one. The muscles of each joint produce this increase in energy. On the other hand, if the timing of energy transfer is wrong, energy can be lost and hence speed will be lost; also if one body part has to compensation because another is not acting correctly then injury may result.

In the downswing, the larger, inner segments such as the pelvis and thorax move slower with the speed building as the energy progresses to the smaller distal segments such as the arms and club. Note that the pelvis does not continue accelerating through impact, but decelerates before impact.

In order to quantify the differences in the Kinematic Sequence between golfers we compare specific values from the segmental rotational speed curves. For example, we can look at the maximum rotation speeds of each segment; progressive speed gains between segments; sequence of maximum speeds; timing of maximum speeds with respect to impact; average accelerations and decelerations before impact. Using these values we can quickly tell what segment of the body is not performing optimally.

In summary, and looking at the graph on the first page in the downswing phase; between Top (of the backswing) and Imp (impact) the Kinematic Sequence proceeds as follows:

Pelvis (red) accelerates and peaks at a lower speed than the other segments, and then decelerates rapidly.
Thorax (green) accelerates to a higher speed than the pelvis, and then decelerates rapidly.
Lead Upper Arm (blue) accelerates to a higher speed than the thorax, and then decelerates rapidly.
Club (brown) continues accelerating reaching maximum speed at impact.

Notice also that each segment speed peaks slightly later than the previous highest speed, that is, each peak is more to the right of the previous one. The pictures of the golfer show the body position at each of the peak rotational speeds; from left to right, pelvis peak, thorax peak, lead arm peak, and club peak. The pictures should clearly show (looking at the position of the golf club) that the pelvis peaked first, then the thorax, then the arm and then the club. The peak for the thorax and arm will be very close so these two pictures should show the club at almost the same location. There should be a larger time between the pelvis peak and thorax peak; and again between the arm peak and the club peak. The club rotational speed should peak at impact; notice in fact that it is still going up at impact. This means that the club is still accelerating at impact.

Transition Phase

Another important section of the Kinematic Sequence is the Transition Phase. This is the area of the graph surrounding the top of backswing (Top), when the golfer transitions from the backswing to the downswing. The Top of Backswing is considered to be when the club turns around from the backswing to the downswing. The Transition Phase is defined as the period of time between the first body segment turnaround and the last segment (or club) turnaround. The biomechanically efficient Transition Phase starts at the bottom and works up, going from the pelvis to the thorax, the arm and then the club.

In the graph above we have zoomed in on the Transition Phase of a pro swing and the swing progresses in time from left to right. Any part of the curve below the black horizontal zero line is in the backswing, any part that is above this line is in the downswing. Starting from the left of the graph we see that the red (pelvis) line crosses zero first, then the green (thorax) line, then the blue (lead arm) and finally the brown (club). The club crosses exactly at top of backswing because this, as mentioned, is our definition of top; the point at which the club shaft changes direction. Since the x-axis of the graph is time, the distance from when the red curve crosses zero to when the brown line crosses zero is the time from when the pelvis changed direction to when the club changes direction; the Transition Phase. This transition sequence shown is considered biomechanically correct as far as the order is concerned, that is, a good transition order is pelvis, thorax, lead arm, and club.

The amount of time that the red curve is on top of the green curve after it has crossed the zero line gives an indication of how much transitional spine stretch (X-Factor Stretch) is occurring, since when the red is on top of the green it means that the pelvis is rotating faster than the thorax and hence the spine stretch is increasing. This same rule can be applied to each curve or body segment. Look at when the green crosses the zero line. The time that it is on top of the blue line after crossing zero indicates that shoulder stretch is occurring, because the thorax is rotating faster than the lead arm and the shoulder angle must therefore be closing. Finally after the blue curve has crossed zero means that the lead arm is in the downswing. So the time it stays on top of the brown curve after crossing zero indicates how much wrist stretch is occurring.

Due to the structure of muscles and connective tissue, it is advantageous to cause the muscle and joint to get this extra stretch during the transition period. It helps transmit more energy and speed to the following body segment. If the transition sequence described above is not optimal elastic energy from the muscles and joint is lost.

Note that since the above graph is “zoomed in” this transition phase is exaggerated, normally the distance from the red crossing to the brown crossing will not look so large, and in fact if this distance is too large it means that the golfer is taking too long to transition and may be loosing the benefit of the muscle stretch (known as the “Stretch-Shorten Cycle”).

Comparison of Pro’s and Amateurs

If the brown curve (club) gets on top of the other curves soon after top of backswing, then this is a good indication that casting is occurring. In the example graph below, very soon after top of backswing the club is rotating faster in the swing plane than the arm and so the wrist angle is opening, indicating casting. Notice that to the right of the “Top” line, the brown curve is above every other curve. This graph shows an inefficient Kinematic Sequence of a high handicap player.

Let’s put three examples side by side and examine the relationships of each of the four curves during the downswing phase.

From the graphs above it can be seen that “Pro” has relatively smooth accelerations and decelerations with each subsequent segment’s speed peaking higher and later than the previous one. Notice also that the club’s speed peaks at impact and in fact is still going up at impact; this means that the club is still accelerating when it hits the ball. Amateur 1 shows lower speeds; poorer accelerations and decelerations; and the peaks are out of sequence with the arm peaking before the thorax. Amateur 2 has no decelerations of the pelvis and thorax before impact, but has a little deceleration of the arm (followed by a re-acceleration before impact). Both amateurs cast the club and it races ahead of the other body segments; this is evident from the fact that the brown curve is on top of the other curves. This casting action causes the club to peak early and even decelerate a little before impact loosing speed and power. In contrast notice the Pro curves; near the middle portion of the graph the arm (blue) is actually on top of the club (brown). This means that the wrist is cocking more just before release. This action will tend to allow more energy to be supplied to club release from the efficient use of the “stretch-shorten cycle” of the forearm muscles. Since the graphs are scaled equally you can see that the club speed of the pro at impact is higher than that of both amateurs.

Phil Cheetham has been an innovator in sport biomechanics for over 25 years. He is an Olympian in Gymnastics from Australia. Phil is co-founder and CEO of Advanced Motion Measurement, Inc. and director of the Titleist Performance Institute Biomechanics Advisory Board. Dr. Greg Rose and the Titleist team call him the “3D Guy” because his science in 3D Motion Analysis has proved to be the best available to analyze and improve human athletic motion.

The data for this article was captured by the AMM3D Motion Analysis System using TPI 3D protocols.

Phil Cheetham The 3D Guy’s New Blog

2009-11-19T09:31:00.001-08:00

Welcome to my first post on my new blog. This blog will post to several different places, AMM3D website, and Blogger being the first two. I will discuss topics related to AMM3D motion analysis, TPI 3D golf swing biomechanics, the kinematic sequence, the body-swing connection and real-time biofeedback training.