legs as linkages

Do legs really need to produce mechanical power, given steady level locomotion requires vertical forces to be supported during horizontal motion, but does not require net input of work?

Torchie the tortoise showing that forces are approximately vertical, and are not directed through hips and shoulders

This PAPER begins to describe how the demand for power from legs can be avoided with ‘sliding’ weight support. For sprawled animals (including most amphibians, lizards, crocodiles and tortoises), vertical-axis joints can support horizontal motions for free. Just think of a door swinging about its hinge: after the push, the door continues to swing freely, with the vertical joint carrying the weight without loss.

Mammals are generally ‘parasagittal’, with their legs under their bodies supporting weight with horizontal-axis joints. But still, the forces are predominantly vertical (at least much more vertical than if they projected through the hip or shoulder joints) meaning that this sliding weight support might again be avoiding mechanical power demand.

Rumple the pet hamster showing approximately vertical forces, especially from the back leg.
Galloping racehorse again showing that measured forces are much more vertical than inline with the leg.

The sliding weight support is economical at the level of the leg: vertical weight support during horizontal motion requires no mechanical power. But how is this achieved? In particular, how is this possible with muscles and tendons also not producing or dissipating mechanical power? THIS PAPER describes a range of linkages in front and back legs that support the sliding with muscles that, when under tension, do not change length; they are effectively ‘tension struts’ like bicycle spokes.

If linkages result in exactly straight-line motion of the foot under the body, then the body experiences no horizontal accelerations and forces are vertical, resulting in extreme sliding. In the forelimb this can be achieved with a series of 4-bar linkages formed by a sequence of muscles (the different triceps heads) coming under load.

Dog forelimb showing the fan of muscles (red) that would result in exactly straightline motion of the foot.
Horse forelimb showing the fan of muscles (red) that would result in exactly straight-line motion of the foot.

In the hindlimb, a series of 6-bar linkages result in exactly straight-line motion of the foot. This matches published EMG measurements indicating sequencing of muscle activation: biceps femoris, vastus, rectus femoris, tensor fasciae latae.

Dog hindlimb animation showing series of 6-bar linkages resulting in straight-line motion of the foot
Horse hindlimb showing sequence of 6-bar linkages resulting in straight-line motion of the foot.

In both forelimb and hindlimb linkages, each muscle comes under tension when it is at its longest length, suggesting that ‘activation’ and ‘loading’ can be driven by reflexes rather than (or as well as) direct top-down controls from the brain.

Various toys and demonstrators are available. See the ‘toys and linkages’ site or email jusherwood@rvc.ac.uk for latest versions

Some anatomy apparent in a skinned fox hindlimb: bf biceps femoris; v vastus; rf rectus femoris; TFL tensor fasciae latae. The four muslces have origins along the pelvis, and insert on to the patella. Fox, dissection and graphic thanks to Richard, George, Delyle, Pete and Alice.

A 13 minute conference presentation (with audio) (Society for Integrative and Comparative Biology, 2023) ‘Legs as linkages: thinking of isometric muscles and tendons as bicycle spokes’.