Introduction to Sports Biomechanics: Analysing Human Movement ...

INTRODUCTION TO SPORTS BIOMECHANICS
as those of Figure 3.11) and that we can pair joint angles of interest easily to show
how they co-vary. These graphs show coordination patterns qualitatively, which can
facilitate comparisons, for example between individuals and for one individual during
rehabilitation from an injury. We can also compare patterns between, for example,
running and walking; most of these comparisons have been based on methods to
quantify angle–angle diagrams. Such a reduction of a rich qualitative pattern to a few
numbers seems bizarre to me and ignores the saying ‘a picture is worth a thousand
words’. Few attempts have been made to distinguish patterns qualitatively; one of the
very few is known as ‘topological equivalence’. Two shapes are topologically equivalent
if one can just be stretched – albeit by different amounts in different places – to form
the other; two shapes are not topologically equivalent if one has to be ‘folded’ rather
than just stretched to form the other. Simplistically, this means that if the shapes have
different numbers of loops, they are not topologically equivalent; they are then qualitatively
rather than just quantitatively different, as for the ankle–knee, but not the hip–
knee or ankle–hip couplings when comparing the running angle–angle diagrams in
Figure 3.13 with those for walking in Figure 3.15. You should also note that the
number of changes in the coordination of the two joints during one stride differs
between running and walking. For example, in the previous paragraph, we noted seven
such changes for the hip–knee coupling in running; Figure 3.15(a) shows only six such
changes for walking, all from in-phase to anti-phase or vice versa.
Disadvantages of angle–angle diagrams include their unfamiliarity compared to time
series. Also, it is not obvious from the diagram which way round the figure proceeds –
clockwise or anticlockwise – or where key events, such as toe-off and touchdown in
gait, occur; the latter is also true to some extent for time series. Some criticism can be
Figure 3.16 Angle–angle diagram with time (data) ‘points’. The ‘distance’ on the graph between two successive points shows
how much each angle – for the knee the horizontal ‘distance’, for the hip the vertical ‘distance’ – changes in one time interval
(here 1/50 s).
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