Introduction to Sports Biomechanics: Analysing Human Movement ...

INTRODUCTION TO SPORTS BIOMECHANICS
112
Rigid body An idealisation of a body of finite size in which deformation is neglected. In
other words, the distance between any two given points of a rigid body remains
constant with time regardless of any external forces exerted on it.
Slope The ratio of the ‘rise’ (change in the y-component) to the ‘run’ (change in the
time component) on a variable–time curve. In movement analysis, effectively the
same as the gradient.
Tangent (line) A line that touches but does not intersect a curved line or surface and that
is perpendicular to the radius of curvature of the arc of the curve where the tangent
touches the line or surface.
Time series A list of numbers assumed to measure some process sequentially in time.
Variability A measure of statistical dispersion, indicating how the possible values are
spread around the expected value. See also movement variability.
FURTHER READING
Kelso, J.A.S. (1995) Dynamic Patterns: The Self-Organization of Brain and Behavior, Cambridge,
MS: MIT Press (Chapter 1: How Nature Handles Complexity). Most of you won’t find this
plain sailing, but not because of any mathematics – there are no equations in this chapter –
but because of the novelty of much of the material. Stick with it; this book has had far more
influence than any biomechanics text on the way I now approach the analysis of sports
movements. You too might appreciate the genius of Scott Kelso and be inspired by his
approach.
APPENDIX 3.1 FURTHER EXPLORATION OF ANGLE–TIME PATTERNS
Here, we find that the points on the angle–time series at which interesting things
happened in Figures 3.9 and 3.10 have names. At points A to E in Figure 3.22, the
gradient of the tangent to the curve is zero as the tangent is horizontal. The rate of
change of angle with respect to time at these points is therefore zero; that is, the angular
velocity is zero. The point at which this happens is called a ‘stationary point’, which
may be any one of three types; two of these are evident at A and B in Figure 3.22. These
two points are known as ‘turning points’. These are stationary points at which the
gradient of the angle curve – the angular velocity – changes sign from positive to
negative or vice versa. The third point of this type is far more rarely encountered. Points
F to I in Figure 3.22 are known as ‘points of inflexion’, as they are points where the
pattern changes its direction of curvature – from positive to negative or vice versa. We
return to these later.