E2 Integrated Elastic System

Topic

In mammals, the tendons of the limbs and the spine act as accumulators and returners of elastic energy. Examples of limb tendons include the Achilles tendon in quadrupeds and humans, the deep digital flexor tendon in equids, and the proximal tendons in kangaroos; all of these store elastic potential energy during the loading phase of a stride and release it during the subsequent propulsive phase, thereby reducing the metabolic cost of locomotion.

In addition to these tendons, the spine in felids plays the same role of accumulating and returning elastic energy: it acts as a spring that flexes and extends with each stride, extending stride length beyond what the limbs alone would allow and storing additional elastic energy during the gallop—energy that the spine returns to the animal in the next phase of the cycle.

The mechanical behavior of these tendons is viscoelastic and non-linear: the curve relating the force borne by the tendon to its elongation initially shows a low-stiffness phase—where previously slack collagen fibers become taut—followed by a linear phase of higher stiffness once the fibers are under tension. Once this linear phase is reached, tendon stiffness becomes the key mechanical parameter determining how much elastic energy the tendon can store and return during each loading cycle.

Not all the elastic energy stored by the tendon during loading is fully returned during propulsion; a fraction of that energy is lost as heat in each cycle—a phenomenon known as hysteresis. In a healthy tendon, this loss per cycle is low, amounting to just four to ten percent of the stored energy. Tendon stiffness, combined with the body mass the tendon supports, defines the natural frequency of the spring-mass system they form together: the stiffer the tendon and the lower the mass it must move, the higher that natural frequency. This natural frequency, in turn, determines the running cadence at which the animal expends the least energy, as running near this frequency allows for the most efficient exchange of elastic energy between the tendon and the body.

Mammals with tendons specialized for elastic energy storage—such as kangaroos, gazelles, and cheetahs—exhibit particularly high tendon stiffness and energy recovery efficiency relative to their body size. This combination of high stiffness and low hysteresis loss enables them to achieve metabolic cost savings in each stride exceeding half the energy they would otherwise require without the contribution of their tendons and spines acting as elastic energy accumulators and returners.

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