Introduction to Sports Biomechanics: Analysing Human Movement ...

THE GEOMETRY OF ANGULAR MOTION
MORE ON MOVEMENT PATTERNS – THE GEOMETRY OF MOTION
In the previous section we considered linear motion – the movement patterns of a
point. The sports performer or sports object can be represented as a point situated at the
centre of mass. The linear motion of this point is defined independently of any rotation
taking place around it. The centre of mass generally serves as the best, and sometimes
the only, point about which rotations should be considered to occur. All human motion
however involves rotation, or angular motion, for example the movement of a body
segment about its proximal joint.
Angular motion is far more complex than linear motion. The rules that apply to the
rotation of a rigid body can be directly applied to an object such as a cricket bat or, as an
approximation, body segments. They can also be applied to a non-rigid body that,
instantaneously, is behaving as though it was rigid, such as a diver holding a fully
extended body position or a gymnast holding a tuck. Such systems are classified as
quasi-rigid bodies. Applications of the laws of angular motion to non-rigid bodies,
such as the complicated kinematic chains of segments that are the reality in most
human movements, have to be made with considerable care. The theory of the rotation
of even rigid bodies in the general case is complicated and many problems in this
category have not yet been solved.
The movement variables in angular motion are defined similarly to those for
linear motion. Angular displacement is the change in the orientation of a line
segment. In two-dimensional motion, also known as planar motion because it
takes place in a two-dimensional plane, this will be the angle between the initial and
final orientations regardless of the path taken. Angular velocity and acceleration
are, respectively, the rates of change with time of angular displacement and angular
velocity.
Joint angles are the most important examples of angular motion – first, as here, when
we look at the change of the angle over time and then, in this next section, for other
combinations of variables. Joint angle patterns are, in general, far more important
than linear motion patterns because they open the way to so many fascinating representations
of human movement patterns.
The angle–time pattern of Figure 3.9, a time-series pattern, shows how the knee
angle changes with time over one stride of treadmill running. As with the linear motion
example of Figure 3.6, we can learn a lot about this pattern by studying its geometry –
the gradients and curvatures of the graph – as we move through time from left to right.
As this analysis focuses on the qualitative aspects rather than the numbers, you need to
remember the angle convention that we adopted in Chapter 1: here, a fully extended
knee would be a larger angle than with the knee flexed – the angle increases upwards in
the figure.
Before you read on, satisfy yourself that you can:
Identify where the knee is flexing and where it is extending in Figure 3.9(a).
Determine the gradient of the graph in each region of the overall pattern (Clue –
would you be going uphill or downhill walking along the pattern?)
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