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Physical principles for the golf swing

Biology

Dave Tutelman -- October 3, 2022

Joints

Wait a second! Muscles only pull? Not push? Then how can I reach my hand out and push something using my arm?

That's a fair question, and brings us to the next topic in this biology chapter. The answer to the question is "joints". I said up front that the only muscles we would be discussing here would be skeletal muscles, because they are the only kind of muscle that makes a difference in the golf swing. And the distinguishing feature of a skeletal muscle is that it attaches to the skeleton -- it is connected at each end to a bone. The connection is via a tendon, but the action itself is muscle pulling on bone. How does this work?

Function

Consider this lever. It is strictly mechanical, except that one force on the lever is produced by a muscle pulling at an attachment point on the lever.

This kind of lever is the same as the wrench we looked at when we first introduced torque. The muscle force acts through a moment arm (lever arm) of L_m, and has the job of lifting or holding a weight at a moment arm of L_w. Since L_w is a lot larger than L_m, the muscle needs to pull with a much larger force than the kettlebell weighs.

For instance, suppose the kettlebell weighs 25 pounds, L_m is one inch, and L_w is one foot (12 inches). That means the muscle's force of contraction must be 300 pounds (25*12/1) in order to just hold the lever horizontal, and more to raise the kettlebell upwards.

In case you don't see a human joint right away, let's look at something that looks less like mechanical engineering and more like human anatomy.

This is mechanically identical, but made of flesh and bone instead of metal. It is a human arm, flexed at the elbow.The green centerlines cross at the hinge pivot of the elbow joint. We can think of the distance from this pivot to where the biceps muscle attaches to the forearm bones as L_m, and the distance from the pivot to the hand as L_w.

As noted, the biceps connects to the bones of the forearm at one end. The other end of the biceps connects to bone of the upper arm (the humerus) where it meets the shoulder. That keeps the pull exerted by the muscle parallel to the upper arm. I mentioned above that the muscle has to exert a much larger force than is exerted by the hand as a result of that force. A few implications:

As with any lever system, a gain of force is a loss of distance (motion) and vice versa. Thus the hand will move a much greater distance than the amount the biceps contracts.The attenuation of force by the forearm lever is perhaps a factor of 10 or 15; I used 12 in the example above.
The range of motion, combined with L_m, will limit the total contraction possible for the muscle. For instance, suppose L_m is one inch and the length of the humerus is 14 inches, both pretty reasonable estimates. So the attachment to the forearm is 1in longer when the elbow joint is extended, and 1in less when it is flexed. That's a total range of 2 inches out of a nominal 14in muscle length. If we assume that elbow-extended is the neutral state, that gives a contraction range of only 14% (2"/14"). We needed to know this when we looked at how much work a muscle can do; if you recall, that was limited by how much it can contract, as a percentage of its full length.
Ultimately, the function of a joint is to convert the force exerted by a muscle into a torque around the pivot axis of the joint. The resulting torque can be used to exert a force elsewhere, exerted by the bone that acts as the moment arm for the torque. Keep that in mind as we proceed; it is at the bottom of a lot of biomechanics.

But wait! We wanted to see how we could push if muscles can only pull. The example we just looked at, flexing the elbow joint with the biceps muscle, is still much more of a pull than a push. Let's try again.

Here is another arrangement of forces around a joint. This time the forces are on opposite sides of the pivot, not the same side. So a pull with the muscle causes movement in the opposite direction, a push, at the "payload".

As before, we accomplish this by having the muscle generate a torque at the pivot. The torque is the force exerted by the muscle times the moment arm L_m. And as before, the force at the payload is considerably attenuated because L_m is a lot less than L_w.

We can look back at the classification of levers and see that this is a Class 2 lever, while the previous one, the one that lifted a kettlebell, is a Class 1 lever.

Now let's once again relate this to biological levers.

This image shows how the the arm can be extended at the elbow, rather than flexed as in the previous example. The muscle that contracts is the triceps, and it lies opposite from the biceps against the humerus (the upper arm bone). The triceps connects to the bones of the lower arm on the outside of the elbow joint, instead of the inside the way the biceps does. In that way, it causes the elbow joint to straighten out, to push instead of pull. Let's add to our list of implications:

The lever arm L_m for the triceps muscle is even smaller than the one for the biceps. That implies an even greater ratio of L_w/L_m, and requires more of a muscular contraction force to give the same force at the payload (again, the hand).
In general, skeletal muscles appear on both sides of a joint, so the joint can be torqued in both directions. The muscle on one side contracts while the other relaxes.
Taking this a step further, we have at the elbow -- and indeed at most joints:

A bone that is the lever the muscles are moving.
A center pivot constructed of bone, that is the fulcrum of the lever.
A muscle that extends the lever straight out from its supporting bone. That muscle makes it a Class 2 lever.
Another muscle that flexes the lever -- makes more of an angle to the supporting bone. That muscle makes it a Class 1 lever.

Diagram from visiblebody.com

Types of joints

Any given joint has a certain amount of freedom -- degrees of freedom, or perhaps we could refer to them as dimensions or axes of rotation. We have been looking so far at an elbow, a simple joint with only one degree of freedom. You can extend your arm out straight or "curl" it at the elbow. So you need a one-axis hinge for the joint, and one muscle on each side of the joint to power it. (By "power it" I mean both execute contraction and control the motion.)

Here is a diagram of many of the joints that figure into the golf swing. We can see the elbow represented as a hinge. The knee is also a hinge.

Another important type of joint is the ball and socket, which allows three-dimensional motion, not just one like a hinge. We find it at the shoulders and hips. It allows the bones to sit at different angles to one another, and not just in one plane either like the hinge elbow. In addition, it allows the bone to rotate on its own axis. Of course, there must be a pair of muscles involved for each dimension. The angling can be achieved by two pairs of extensor-flexor muscles at right angles to each other. The axial rotation is achieved by a muscle wrapped around the bone in a shallow spiral. And of course we need a second muscle wrapped the other way to rotate the bone the other way.

The condyloid joint (for instance, in the wrist) is a two-dimensional joint. It allows angles in two dimensions like the ball and socket, but no axial rotation.

The final type of joint I'd like to mention is in the spine. Our spine is made up of a column of small bones called vertebrae, stacked one on top of the other. between each pair of vertebrae is a strong but somewhat flexible piece of cartilage called a disc. If a disc can compress a little bit on one side or the other, then it allows the angle between the vertebrae to change a bit. Even if it is only a couple of degrees, it can be a total of over 60 degrees of total bend, given that there are 33 vertebrae in the spine, and therefor 32 disc joints. So the spine will appear to curve over its length, rather than "fold" at a single pivot. In reality, the curve is the incremental folding of a lot of short segments.

I described the spine as a column. It is often even called the "spinal column". But engineers know columns as deceptively fragile structures. If you compress a narrow column by pushing at its ends, you are not likely to see it fail in compression. Instead, as soon as some section of the column gets out of line a little bit, the whole column bends to one side; it fails not in compression but in bending.

To illustrate, try this with a soda straw. Hold it vertically, with one end on a hard surface, a surface rough enough that the end of the straw will not slide around. Now press down on the tip with your finger or hand. It will seem to be resisting your pressure very well... until it suddenly "goes out of column" and fails. It starts to bend a little bit, and that little bit cascades into a major failure so fast it seems instantly.

That nasty behavior of columns causes engineers to look for ways to reinforce them. Specifically, they reinforce them against sideways bending, or "buckling". Avoiding buckling was especially critical when much of the world's commerce depended on sailing ships. The mast of a sailboat is a tall, thin column, with a lot of compression, and also a lot of force being exerted by the sails to try to pull it "out of column". When that happens, a mast will snap. When you look at all the ropes on an old sailing ship, it is easy to be overwhelmed about their function. The function of a lot of that rigging was stabilization of the mast column. Let's look at a more modern sailing mast (left), which is a lot simpler. It has wire stays (called "shrouds" in this diagram), and rigid struts called "spreaders". The function of the stays and spreaders is to stabilize the shaft, to keep it in column. It does so by pushing sideways (the spreaders) and pulling sideways (the stays), reacting against any tendency of the mast column to buckle.

There are vaguely similar structures in the spinal column, with very similar functions (though they look very different). There are protruding bones and facet joints which play the part of spreaders, and the muscles that span the protruding bones apply tension and act as stays. Yes, it's a lot more complicated than that. But unless you want to look closely at the biomechanics of spinal injuries, we don't need to understand the spine in much more detail than this.

Tendons, ligaments, and cartilage

We know what tendons are; they connect muscle to bone. Their relation to joints is that they are the "transmission" that connects the "engine" (the muscle) to the "wheels", where the joints are "bearings". (Hey, I said up front we were going to treat the body as mechanical components to be used in engineering the golf swing. Hence the analogies.)

Here's a diagram that shows other components of the joints, ligaments and cartilage. The joint itself is the knee. The function of each of the components is:

Tendons, as we already know, connect muscle (red) to bone (tan).
Ligaments stabilize the joint and even hold it together. Ligament is flexible but strong tissue that connects bone to bone. In the knee joint shown, the ligaments hold the upper leg bone (the femur) to the lower leg bone (the tibia).
Cartilage is flexible and compression-resistant, and provides cushioning for the bone. We can also consider it as "lubricant" for the joint though, strictly speaking, the lubrication is a function of liquid hyaluronic acid that the cartilage usually encapsulates. Cartilage has other functions as well, but these are the functions relevant to what we are discussing here, the biomechanics of athletic motion.

But there is a specialized cartilage function worth discussing in the most complex moving structure in the body, the spine. In between the 33 pieces of backbone, the vertebrae, there are structures called discs. provide cushioning, adhesion, and lubrication of the joints between the vertebrae. And cartilage is involved in each of those functions.

Cushioning - Normally, this would be a function of cartilage alone. But the spine bears the whole weight of the upper half of the body; every dynamic motion we make is likely to create an F=ma that will increase the compressive load on the spine. So the cartilage encapsulates a thick, gelatinous core that increases the cushioning.
Adhesion - This is the natural function of cartilage. As we saw earlier, the spine is protected from large loads on the column by external muscles separated from the spinal column itself by bones that act as "spreaders". But even in repose or light load, when the muscles should be relaxed, the vertebrae still need to be held together. The cartilage in the discs act as a thick layer of glue to accomplish this. Think of the discs as made of double-sided foam tape, and you will have some idea of their function.
Lubrication - The vertebrae just tilt with respect to one another, unlike hinge or ball-and-socket joints where one bone slides on another. So the lubrication needs are quite different. They are met by the flexibility of the disc itself, which is mostly cartilage.

Terminology

In order to understand articles and talks about golf biomechanics, you will probably need to understand a bunch of terms that biomechanists, physical therapists, patent lawyers, and other tech-talkers use. Sorry, but it is necessary, and a fair amount of it just has to be memorized. So let's dive in.

The first terms we introduce are proximal and distal. I have to be honest; until I got into golf biomechanics (quite a few years into retirement) the only place I ever encountered those terms was reading patents. Patents are notoriously hard to read, and sprinkling them with terms like "distal" do not make it easier. But there is a real use for these two when discussing the structure of the body, or even the motion of a golf club. Proximal and distal make a distinction between nearer (in proximity) and more distant parts of a structure. For instance, when discussing the bones on the two sides of the elbow joint:

"Proximal" refers to the upper arm, the humerus, since it is on the side of the elbow closer to the core of the body, the trunk.
"Distal" refers to the forearm, since it is farther from the core of the body than the elbow.

In general, biomechanics and anatomy use the trunk as the "base" from which to decide whether something is closer (proximal) or farther (distal). When discussing the golf swing, things get more ambiguous when discussing the legs and feet. For many athletic maneuvers, including the golf swing, most biomechanists consider the base not to be the trunk but the ground. For instance, many discussions of the kinematic sequence (we haven't seen that yet, but we will) start at the ground, and go from proximal to distal as:

Feet
Lower legs, then upper.
Hips
Thorax (chest)
Arm, usually the lead arm (upper arm, then forearm)
The golf club itself.

It is worth remembering that the "distance" is measured along the chain of bones and joints, not directly measured distance. For instance, think of the golf clubhead. If we measured straight-line distance instead of along the chain, it would still be the most distal element at the top of the backswing. But at impact it would be equal to the feet as most proximal. Since it is the last element in the chain, it is still distal.

We already used the terms extension and flexion of a joint when talking about the elbow. A joint is put into extension when the motion of the distal element extends the length of the proximal element. (We could not have expressed that without first defining proximal and distal.) Flexion, therefore, is the motion opposite to extension.

The diagram shows the directions for a couple of other joints, the knee and the ankle. They follow the definition, too.

But it gets ambiguous when a joint has three dimensions of motion, and sometimes even with two. There can be movement in either of two planes that extends the length of the limb in question -- and sometimes there is not even a limb involved. So the names attached can be arbitrary, or at least seem arbitrary to someone trying to memorize the names. But we are going to mention two that we will be talking about in the golf swing:

The spine, which is actually a pretty large collection of joints, is said to be extending when the back is arching, and flexing when the back is hunching.
The wrist is so important to the golf swing that we will treat it separately below.

Here is a good video that attaches consistency to even more joint motions, in case you are interested in going further. But what we have so far, plus the wrist motions described below, should get you through most of the interesting literature on the golf swing.

Finally, we get to the wrist. Things you need to know about the wrist:

It is the single most talked about joint in golf swing biomechanics, at least as of 2023 when this is being written. I don't expect that to change soon, but it might. In any event, it has been key for over a decade now.
The wrist has three dimensions of motion, so we need three pairs of terms to describe the motion.

The diagram shows the six motions and their names. Here are my own mnemonics when I forget the names. But after a while you just remember.

Flexion and extension for the wrist violate the mnemonics that work for the elbow, knee, and ankle. I have just had to memorize them.
The forearm is two bones, the "radius" and the "ulna". The radius is on the same side of the hand as the thumb, so I have learned to associate "radius" with "thumb". Bending of the hand to the thumb side is "radial deviation", and the other side is the other name.
Think of your hand as a hand puppet. For that to work, the palm is the front of the puppet. Now the hand represents your whole body, with arms, legs, and head. "Prone position" is lying on your belly, and "supine" is lying on your back. But I do have a mnemonic for which is which. I remember from rifle training what shooting from a prone position is: you lie on your belly. So pronation means moving to get the belly of the hand puppet (the palm of the hand) facing down.

Yeah, kind of lame. If you can think of something that helps you more, then use it. Eventually they will just become familiar, if you spend enough time reading and talking about biomechanics.

Last modified -- Apr 3, 2023