Legged terrestrial locomotion results from the coupling of a motor (the muscular system) and a machine (the skeletal lever system of the limbs). The function of the motor is to produce mechanical energy, when muscle shortens and the muscular force performs positive work, and to absorb mechanical energy, when active muscle is forcibly lengthened and the muscular force performs negative work. Primary muscle length changes, similar to the displacement of the pistons in a car engine, are not suitable to sustain locomotion directly. Both during positive and negative work, muscle length changes are applied through tendons to the lever system of the limbs, which interacts appropriately with the different surroundings to promote different kinds of locomotion.
Although the machine (i.e. the skeletal lever system of the limbs) differs widely between animal species according to the diverse kinds of locomotion and surroundings, the motor operating the different machines (i.e. the skeletal muscle) has remained largely the same throughout evolution, maintaining, from frogs to humans, its basic property to resist stretching with a force greater than that developed during shortening, the difference increasing with the velocity of the length change as described by the force–velocity relation of muscle [1
Recent studies have shown that in humans running at low and intermediate speeds [2
], hopping kangaroos and springhares, and running birds, trotting dogs, rams and a monkey [3
], where a stretch–shorten cycle of muscle–tendon units takes place each step during the rebound of the body, the different machines act in accordance with the asymmetric response of their motor, allowing a greater force applied for a shorter duration during stretching after landing, and a lower force applied for a longer duration during shortening before takeoff.
This ‘landing–takeoff asymmetry’ appears to be greater the greater the length change of muscle relative to that of tendon during the stretch–shorten cycle [2
]. If the force were so high and the muscle so stiff as to be kept in a state of isometric contraction, the whole of the length change during stretching would be taken by the elastic structures of tendon, and both duration and force could be equal during stretching and shortening, as in the elastic rebound of a symmetric spring–mass system [5
]. From this point of view, therefore, the landing–takeoff asymmetry is the expression of a less economical bounce. In fact, the mechanical efficiency (i.e. the ratio between positive work production and metabolic energy expenditure) was found to be greater in hopping and at high running speeds in humans when the landing–takeoff asymmetry was reduced or absent [6
On the other hand, of course, the difference between the average forces developed during stretching and during shortening depends not only on the difference in force developed by each active muscle fibre when it is forcibly lengthened or allowed to shorten according to the force–velocity relation of its contractile component, but also on the number of fibres activated by the central nervous system during stretching and shortening. Fewer fibres could be activated during stretching and more fibres could be activated during shortening in such a way as to compensate for the different forces exerted by each fibre in the two conditions, resulting in the same average force during stretching and shortening (i.e. in a symmetric rebound). However, this strategy is usually not followed: when muscle length change contributes to the length change of the whole muscle–tendon unit, the asymmetric rebound seems to be the more convenient procedure to follow.
During running on the level at a constant average speed, the absolute amount of negative work done when muscle–tendon units are stretched during the brake equals that of positive work done when muscle–tendon units shorten during the push. Since work is force times displacement, the greater force developed during the brake implies a displacement of the centre of mass of the body in the sagittal plane that is smaller during negative work than during positive work.
We hypothesize that the machine (i.e. the different lever systems of the limbs operating in the different kinds of bouncing gaits), allows the asymmetric rebound by making the displacement of the centre of mass of the body smaller during negative work than during positive work.
In human running, the adaptation of the machine to this goal is, at least qualitatively, consistent with the asymmetric lever system of the human foot, since the moment arm between heel and ankle operating after landing (brake) is shorter than the moment arm between ankle and toe operating before take-off (push [8
]), even if other joints may contribute to the asymmetric rebound.
In this study, we measured the landing–takeoff asymmetry in backward running (i.e. in an exercise where the normal coupling between motor and machine, phylogenetically adapted to forward running, is voluntarily disrupted). The dissociation between motor and machine in backward running gives an indication of their relative roles in causing the landing–takeoff asymmetry and shows whether (and, if so, how) the stretch–shorten cycle and the mechanical work and power output differ in the two conditions.