Simple mechanical models of gait provide insight into the basic mechanics of anatomically intact gait and attempt to explain why anatomically intact gait is an energy efficient task. Two types of mechanical model have been proposed to provide insight into human walking. The six determinants of gait model, defined by Saunders et al., 1953, propose that the vertical and lateral movement of the body’s COM is energetically costly.
The model further suggests that certain joints (e.g. pelvis and knee) coordinate their movements in order to smooth out these COM displacements and hence minimize energy expenditure. However, experimental studies have contradicted at least three of the six determinants (Gard & Childress, 1997; Gard & Childress, 1999 and Kerrigan et al., 2001). For example, by adopting a gait in which an individual actively reduces the vertical COM displacements, the metabolic cost is significantly increased (Gordon et al., 2009), in some cases by as much as 100% when compared with normal gait (Ortega & Farley, 2005). This “model” is now considered invalid (Baker, 2012).
In contrast to the six determinants, the inverted pendulum model by Cavagna et al., 1963 and Cavagna & Margaria, 1966, recognises that the COM undergoes vertical sinusoidal trajectories, while rotating over each stance leg similar to the trajectories observed in an energetically conservative pendulum motion. This is illustrated in Figure 2.4.
Figure 2.4: Illustration of COM trajectories by the inverted pendulum model. Figure adapted from (Li et al., 2010).
With the sinusoidal trajectories of the COM, after foot flat during double support, the COM is at its lowest point and hence has maximum kinetic energy and minimum potential energy. As the progression continues, the COM travels upwards and reaches the highest point at mid-stance during single support, and hence kinetic energy is at its minimum and potential energy at its maximum, i.e. an interchange of kinetic and potential energy takes place during each step. The efficiency of this interchange of energy is thought to be central to the observed high energy efficiency of gait (Massaad et al., 2007). Mochon & Mcmahon, 1980a and Mochon & Mcmahon, 1980b, have shown that the swing leg acts like a non-inverted pendulum. Therefore, during a gait cycle, energy is constantly flowing between the coupled inverted pendulum motion of the stance leg and the pendulum motion of the swing leg.
Although the pendulum motion, and more specifically every pendulum arc (stance or swing), is energetically conservative, however, walking does involve metabolic work. This could be because the energy requirement for the period during which one pendulum arc completes and the next one starts is not yet accounted for. The transition between consecutive pendulum arcs (or steps) is the double support period, and is termed as step- to-step transition. While progressing forward, the COM’s velocity has a downward direction at the end of one arc, and this velocity needs to be re-directed upward (to prescribe the next pendulum arc) in order to continue forward progression. This re- direction of the COM’s velocity during step-to-step transitions requires muscle work, and explains why metabolic energy is required for level walking (Kuo et al., 2005), a concept also supported by Grabowski et al., 2005. Figure 2.5 illustrates the step-to-step transitions and that the leading leg performs negative work on the COM at heel strike, whereby this negative work needs to be replenished by positive work done on the COM by the trailing leg.
Figure 2.5: Inverted pendulum model.(a). Inverted pendulum model showing the single and double supports.(b). Work required to redirect COM velocity during step-to-step transitions. (c). Leading and
trailing leg work to redirect COM velocity. Figure adapted from Kuo et al., 2005.
The most energy efficient way to replenish the negative work undertaken by the leading leg is considered a power burst from the trailing leg just before the heel strike of the leading leg (Houdijk et al., 2009). This can be achieved either by an exclusively active actuation or supplemented by an appropriately timed release of energy that could be stored in elastic elements (typically tendons) during the earlier foot-ground collisions. Storing energy in elastic elements occurs at a number of lower limb joints, whereby Eng & Winter, 1995 and Kuo et al., 2005, have shown that during push-off, the ankle joint contributes more power than the hip or knee.
The relative contribution of the ankle muscle’s positive work or Achilles tendon’s passive return of the stored energy to this push off power has been studied using ultrasound techniques (Fukunaga et al., 2001; Ishikawa et al., 2005 and Lichtwark & Wilson, 2006). These studies have shown that the ankle muscles contribute little positive
work, whereby the majority of the push-off power comes from the strain energy stored in the Achilles tendon. Specifically, during push-off, the Achilles tendon releases its stored strain energy and the ankle plantarflexor muscles contract approximately isometrically. This mechanism is thought to be a major factor in reducing the metabolic cost during gait (Sawicki et al., 2009).
As the ankle joint is believed to play a major role in determining the overall energy efficiency of gait, it is beneficial to look in more detail at its role during gait, as described in the following section.