I wrote this for some friends of mine who had questions about biomechanics, and figured I’d share it here.
I’ll start with an introduction to what it is I’m studying. Biomechanics is nothing more than the description of mechanics (using the physics definition) as applied to the human body. The study of physical bodies being displaced or subjected to force is rather thorough, and indeed it must be – very large buildings, bridges, machinery, weapons, and other constructions are subject to the myriad laws of the universe. However, when we apply “simple” concepts of velocity, acceleration, and torque to human bodies, things get very complicated for one main reason.
Difficulties in Measurement
Accurately measuring the velocity of a baseball in a pitcher’s hand as it is accelerated towards the plate isn’t too hard. Radar guns do a reasonable job, but high-speed videography can get an answer within a few tenths of a mile per hour. While not very “precise” from a scientific definition, for the purposes of the game of baseball, it’s more than good enough. It becomes more difficult when you start to measure acceleration, which is nothing more than the second derivative of position (velocity is the first, naturally). The ball is not simply being accelerated in the x-plane towards home plate by any pitcher – no, it’s not that simple. Pitchers have a curvilinear approach to the plate with their pitching hand and release the ball on a line tangent to the curvilinear path. Since the ball is being accelerated sideways/upwards in addition to forwards, you can see how this would be hard to model using a single camera, no matter what the sampling rate.
And torque – don’t even get me started! Position, velocity, and acceleration all describe the kinematics of the moving baseball. Kinematics is simply the branch of classical mechanics that describes the motion of bodies – but kinematics does NOT describe the source of the force being imparted to the moving body. Kinematics answers the question of “what,” but Kinetics answers the question of “why.”
Torque is the third order derivative of position, ahead of velocity and acceleration. Put another way, torque is derived from acceleration – perhaps this is obvious. Torque is simple to measure in a basic machine – think about a torque wrench spinning the lugnuts off of a car wheel. You apply force at the distal end of the wrench, which is magnified at the proximal end. Additionally, if the torque is too great, you could snap the lever arm (wrench body) in half. The rate at which the lugnut and the wrench spin is described by kinematics, the force you impart to the wrench is described by kinetics.
Simple enough. But how does it apply to the human body? Well, we can take a relatively simple example to illustrate just how complex things can get. We’ll use forearm pronation/supination as an example. You pronate when you give someone the thumbs down, and you supinate when you give them the thumbs up. Place a steel rod in your hand and extend your arm. If you supinate and pronate your forearm, you are imparting force on the rod and torque is being produced.
But it’s not enough to know that you are imparting a force on the rod, because what biomechanists want to know (or at least, I do) is much more nebulous: How did you produce that force? Well, muscles pull on tendons which pull on bones, and ligaments stabilize the connections between them all. If that sounds like an internal machine, you’re right. In this case, when you turn your thumb down, the pronator teres and pronator quadratus activate to pull the radius towards the ulna (the bones in your forearm) – and there you go, your thumb is down in a display of disapproval. But… tendons and ligaments were subject to some force in this whole endeavor, and so were both of the bones. Quantifying exactly how much force each part received is… tricky. To calculate net force, you need to know the weight of all of the body parts. Since that’s impossible, we need to use estimations from Zatsiorsky and deLeva to turn kinematic equations into kinetic ones. You can derive the average weight of the humerus in an adult male’s body by dividing his total body weight by X% and so forth. As you can probably tell, this is not very precise, nor is it it accurate.
And, thus, this is exactly the problem. No two humans have identical bone cortex density, nor do their muscles pull in the same way (nor are they even of the same composition), nor do tendons/ligaments act in the same manner. The slightest mechanical change in movement can alter how the forces are distributed – both from a peak and total viewpoint.
Now think: What is the effective load on the ulnar collateral ligament (UCL) when the humerus is internally rotating at thousands of degrees per second, when the pitcher is holding a 5 oz. regulation baseball? Tough question. We know the anterior band of the UCL is under heavy stress during the throwing motion, as the ulna and humerus are being literally pulled apart! But quantifying the forces is, again, very hard. The angle of the forearm relative to the humerus is important, as is the position of the wrist – is it radially deviated? – and the rotational position of the forearm – how supinated/pronated is it?
We’re not even touching on the fact that an ideal model could film at an infinite sampling rate producing a perfect three-dimensional model – but the real world is nothing like this. Using the calculus-based concept of Direct Linear Transformation (DLT) – read up if you’re brave http://en.wikipedia.org/wiki/Direct_linear_transformation – we take multiple sources of video calibrated to a control object and can reconstruct a three-dimensional model of the pitcher. But there’s a loooooot of room for error here – the precision of the control object’s dimensions, the sampling rate of the cameras, the ability to synchronize the cameras together on a single frame…
It’s no stretch to say that this is very difficult stuff. Multiple Ph. D. candidates have contacted me asking me how far along my work has come, and when I tell them what I’m doing, all of them are shocked. Even the person running the motion capture laboratory at the University of Washington couldn’t believe what I was able to do with a handful of old research papers written by the original DLT theorists (Dr. Jesus Dapena and Michael Feltner).
So it’s a sole effort that I’m pushing forth, which is fun because it’s uncharted territory, but also very frustrating and terrible because I have no peers. This is not an egotistical statement; rather, it is a realistic one. Everyone performing biomechanics “research” have all moved on to labs costing hundreds of thousands of dollars while we’re still using equipment that would have been used in the 1990’s. As such, we need to do a lot more legwork. (When I say “we,” I mean my assistant and I.)
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