Introduction to Sports Biomechanics: Analysing Human Movement ...

INTRODUCTION TO SPORTS BIOMECHANICS
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This imaginary force is known as an ‘inertia’ force. Its introduction allows the use of
the general and very simple equations of static equilibrium for forces (F) and torques
(M): ΣF = 0; ΣM = 0; that is, the vector sum (Σ) of all the forces, including the
imaginary inertia forces, is zero and the vector sum of all the torques, including the
imaginary inertia torques, is also zero (see Appendix 4.2 for a simple graphical method
to calculate vector sums). These vector equations of static equilibrium can be applied to
all force systems that are static or have been made quasi-static through the use of inertia
forces. How the vector equations simplify to the scalar equations used to calculate the
magnitudes of forces and moments of force will depend on how the forces combine to
form the system of forces. Two-dimensional systems of forces are known as planar force
systems and have forces acting in one plane only; three-dimensional force systems are
known as spatial force systems. Force systems can be classified as follows:
Linear (also called collinear) force systems consist of forces with the same line of
action, such as the forces in a tug-of-war rope or the swimmer in Figure 5.6(b). No
torque equilibrium equation is relevant for such systems as all the forces act along
the same line.
Concurrent force systems have the lines of action of the forces passing through a
common point, such as the centre of mass. The collinear system in the previous
paragraph is a special case. The runner in Figure 5.10(a) is an example of a planar
concurrent force system and many spatial ones can also be found in sport and
exercise movements. As all forces pass through the centre of mass, no torque
equilibrium equation is relevant.
Parallel force systems have the lines of action of the forces all parallel; they can be
planar, as in Figure 5.6(a), or spatial. The tendency of the forces to rotate the object
about some point means that the equation of moment equilibrium must be considered.
The simple cases of first-class and third-class levers in the human musculoskeletal
system are examples of planar parallel force systems and are shown in Figures
5.11(a) and (b). The moment equilibrium equation in these examples reduces to the
‘principle of levers’. This states that the product of the magnitudes of the muscle
force and its moment arm, sometimes called the force arm, equals the product of
the resistance and its moment arm, called the resistance arm. Symbolically, using the
notation of Figure 5.11: F m r m = F r r r. The force equilibrium equation leads to F j =
F m + F r and F j = F m − F r for the joint force (F j) in the first-class and third-class levers
of Figures 5.11(a) and (b), respectively. It is worth mentioning here that the example
of a second-class lever often quoted in sports biomechanics textbooks – that of a
person rising onto the toes treating the floor as the fulcrum – is contrived. Few, if
any, such levers exist in the human musculoskeletal system. This is not surprising as
they represent a class of mechanical lever intended to enable a large force to be
moved by a small one, as in a wheelbarrow. The human musculoskeletal system, by
contrast, achieves speed and range of movement but requires relatively large muscle
forces to accomplish this against resistance.
Finally, general force systems may be planar or spatial, have none of the above
simplifications and are the ones normally found in sports biomechanics, such as