Kinematics is the part of mechanics that deals exclusively with motion. It does not consider forces at all.
First a bit of history: Kinematics is usually the first part of a biomechanical analysis and also probably one of the original roots of biomechanics. Eadweard Muybridge (1830-1904) was an English photographer who conceived the idea of studying motion through a series of still pictures. If you Google him you will discover that he, as a red-blooded Victorian gentleman, exercised his interest particularly on horses and scantily dressed ladies. Muybridge was in essence observing motions and using them to study biomechanics, and from his pioneering work sprang the motion capture technology we use today.
The nice thing about kinematics is that you can study movement with your eyes or simple equipment. In this post I want to make two points about it:
- Kinematics is not simple but one of the trickier parts of biomechanics, and this is due to nonlinearity.
- Kinematics is not just a stepping stone to an analysis of forces. It has a lot of value in its own right, particularly in sports.
The video below shows a very simple model, namely a four-bar mechanism. It is the mother of all mechanisms and it does not look very anatomical, but similar mechanisms are present in several different places in the skeleton and also where the body is connected to equipment, for instance a bicycle. Here’s an animation of the basic version of the mechanism.
In the mechanism above, opposite bars have equal lengths and this creates the very simple and predictable behavior of the system that you see in the video.
When we make mathematical models of nature, some phenomena are benevolent and have a predictable behavior. They are often mathematically linear or only weakly nonlinear. Such is not the case with kinematics; it is hugely nonlinear, and this fact is simultaneously a source of our endless fascination with human movement and the difficulties of simulating it.
Just think of our enjoyment of the performance of an elite athlete, i.e. somebody who can perform motions that are seemingly impossible and can only be accomplished by an extremely fine-tuned technique: A fast baseball pitch, a 300 m golf drive, a motorcycle rider racing through a curve at the very limit of tire friction, a soccer kick curving the ball around a wall of defenders and into the corner of the goal outside the reach of the goalie, Roger Federer’s forehand stroke in tennis. All of these examples are possible for trained athletes and fascinate us endlessly because they are completely beyond our reach.
So why are the best athletes able to perform so much better by small but seemingly very difficult adjustments to movements? At least a part of the answer has to do with the nonlinearity of kinematics. If you change the input a little bit, the output may become vastly different. Let us take the four-bar mechanism above and make the left bar just slightly shorter. The video below shows the surprising result.
The small change of dimension has caused a completely different kinematic behavior of the mechanism. And it gets worse. If we furthermore shorten the upper bar just a little bit, we get the following:
So tiny changes to kinematics can change the behavior of the system completely, and this is also the case for the sports performances mentioned above. The change of motion drastically influences the forces in the system, and this is what magically drives the golf ball 300 meters if you can get it completely right. The tiny adjustments make a huge difference in the result.
A general example of this is what we call kinetic chain movements that occur in all sorts of striking and kicking motions in sports. They are particularly interesting and the subject of a blog post somewhere in the near future.
It is all about nonlinearity and its unpredictable nature. It influences all of us and is the reason why events often take a completely different turn from what we expect. Shit simply happens. I leave you this time with a musical commentary, namely Lazyboy’s eloquent review of how crazy the past year was.
Biomechanics For Everybody 