Introduction to Sports Biomechanics: Analysing Human Movement ...

Phase planes
MORE ON MOVEMENT PATTERNS – THE GEOMETRY OF MOTION
made of the loss of ‘time’ as a variable, although marking the data, or time, points as
in Figure 3.16 adds some indication of how the angles change with time. We do, however,
lose access to time-series shape patterns, that is slope = velocity; curvature =
acceleration; such relationships do not apply to angle–angle diagrams.
Perhaps the main criticism of angle–angle diagrams is that they do not show coordination
changes very clearly without painstaking analysis of the patterns, as for the
hip–knee coupling above. Only the ankle–knee coupling of the three joint couplings
that we compared between walking and running was qualitatively different topologically
between the two modes of gait. Phase planes, a totally different approach,
are based on the notion that any system, such as a body segment, can be graphed as
diagrams of two variables; for the phase planes used in human movement analysis, these
variables are usually joint angle and angular velocity. As it turns out, although the
relevance of a phase-plane for a single joint to coordination between joints may seem
hard to fathom, phase planes turn out to be pivotal for our understanding of movement
coordination, as will be evident later in this section.
Example phase planes, for the hip (Figure 3.17(a)) and the knee (Figure 3.17(b))
joints in a running stride, are shown in Figure 3.17. Its description – although not its
analysis – is ‘child’s play’ compared to both angle–time series and angle–angle diagrams.
As we define flexion as a decrease in joint angle and extension as an increase, then flexion
must be from left to right and extension from right to left in Figure 3.17. Similarly, as
we saw in the previous section on time series, a flexion velocity is negative and an
extension velocity is positive; so, flexion must be below the horizontal (zero) line in
Figure 3.17 and extension above it. And that is about that; the diagrams of Figure 3.17
must progress clockwise. Why? Well let’s assume the opposite – they proceed anticlockwise.
In this case, in the top half of Figure 3.17(a) the joint would be flexing –
from right to left – while the angular velocity was positive, indicating extension. We
have proved a contradiction; therefore, our phase planes must progress clockwise with
time.
The value of phase planes starts to become evident when we define the so-called
‘phase angle’ as shown for ‘real data’ in Figure 3.18. We have changed the graph so
that it is ‘centred’ on its mean value, for reasons that need not concern us in this book.
If we now subtract the phase angle – defined anticlockwise from the right horizontal –
for one joint from that for a second joint at the same instant, we define a variable
known as relative phase. Here, we subtract the knee phase angle from that for the
hip, rp = pah – pak. We can do this for every time instant in the cycle to arrive at
values of this relative phase as a function of time, which is known as ‘continuous relative
phase’.
A graph of continuous relative phase as a function of time is shown in Figure 3.19.
Continuous relative phase is simply another coordination ‘pattern’, although more
difficult to interpret than angle–angle diagrams. In Figure 3.19, for example, we see that
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