Although the rotary–transverse dichotomy is well established in the lexicon of gait analysis, the mechanics of galloping are remarkably independent of this distinction and it is possible to use a horse-like hindlimb-initiated transition or cheetah-like forelimb-initiated transition with either footfall sequence or with a sequence that does not match either. For instance, the North American jackrabbit (Lepus townsendii
) generally gallops using a bound or half bound, where the hindlimbs contact in near unison while the forelimbs can contact together or slightly separated in time and position. However, in spite of using the same footfall pattern, the jackrabbit can employ both the hindlimb-initiated (horse-like) and forelimb-initiated (cheetah-like) gallop. The similarity of the bound and half bound and gallop has been well recognized (Hildebrand 1977
). The cheetah-like, flexed back half bound is used by rabbits and hares during high-speed running when the animals are evading an immediate threat. In this gait, the spine displays a substantial arch as in the cheetah gallop and is the gait commonly identified with the rabbits and hares (b
; Alexander 1988
; Simons 1999
). Although the flexed-back half bound is the common high-speed gait, the jackrabbit also performs an alternative slower speed, stiff backed half bound. This slower gallop-like gait clearly shows the horse-like initiation of the CoM transition via hindlimb contact and subsequent deflection of the CoM path through contacts progressing from rear to front (a
). The fact that the jackrabbit can perform both styles of gallop using a virtually identical footfall pattern demonstrates that the key mechanical determinant of each gait is not the left–right sequence of foot contacts, but rather the role played by the front and rear limbs in the downward-to-upward transition of the CoM.
Figure 6 A comparison of (a) the hindlimb-initiated half bound used at slow speeds (jackrabbit) and (b) the forelimb-initiated half bound used at high speeds (domestic rabbit). The transition mechanics of the hindlimb-initiated half bound are similar to those (more ...)
The horse-like hindlimb-initiated gallop, whether in the horse, dog or jackrabbit (at slower galloping speeds in the latter two species), distributes the transition so that a large portion of the available momentum is not involved in the impulsive contact of the limbs, but remains to contribute to the next stride. Although muscular action and some elastic energy storage and return doubtlessly contribute to the effectiveness of the gait, the gait does not appear to depend fundamentally on this (see, for instance, elastic recovery calculations of Pfau et al. (2006)
for the horse distal limb). The transition of the CoM from downward–forward to upward–forward occurs in a manner grossly analogous to a stone skipping on the surface of water. Although the stone appears to bounce along the surface, it does so inelastically (the water is unable to store and return elastic strain energy). The ‘bounce’ occurs with the same geometry of the strut model in , except in this case the ‘strut’ is simply the line of action between the surface and the CoM of the stone. Provided the angle of deflection is within a boundary that allows sufficient kinetic energy to remain perpendicular to this line of action following contact, the stone will become airborne again (Rosellini et al. 2005
). In the horse gallop, the bounce also need not be elastic. But unlike the vertical impulse produced on the stone, the transition of the hindlimb-initiated gallop is performed by multiple legs, allowing for a relatively smooth transition by distributing the individual contacts. Also unlike the stone, which dissipates energy with each skip, the legs perform work in each stride to maintain total mechanical energy in spite of some inevitable loss as a result of foot contact.
The configuration of the strut model of the cheetah-like gallop (b
) indicates that it should result in large momentum losses due to the direction of the momentum vector relative to the ground contact points (i.e. a substantial component of the momentum vector is oriented parallel to the limb strut, so should be ‘lost’ to the collision). Alexander (1988)
suggested that the front limb contact and flexion of the back following the extended flight in this type of gallop allow storage of strain potential energy in the spine and associated tissues that could then be transferred to the rear for hindlimb take-off following the collected flight phase. This may be the fundamental explanation of the highly arched back in this gait, which has coincident advantages of extending stride length and having the highest forward speed during the ballistic portion of the gait cycle. Such energy storage and return requires that net deceleration occurs on the forelimbs and net acceleration in the hindlimbs. This is consistent with the currently available evidence (Bryant et al. 1987
; Walter & Carrier 2007
), but no ground reaction force measurements are available from truly high-speed galloping in cheetahs or fast running dogs such as greyhounds. If there is no net difference in acceleration from the forelimb and hindlimb then transfer of energy through elastic structures in the back would not be possible. High-speed video of greyhounds at their highest running speeds suggests that if energy storage and return exists (i.e. if there is a speed change from forelimb to hindlimb contacts), it may not be very great (J. R. Usherwood 2008, personal communication).
Although the high-speed dog/cheetah gallop employs four contacts, the transition process and relationship of the CoM to the contact point of the limb struts is reminiscent of that of bipedal humans in running (b
). Similar to the interpretation of the cheetah gallop above, human running has also been considered dependent on elastic energy storage and return and is routinely modelled as a classic spring–mass system (Cavagna et al. 1977
; Blickhan 1989
; Dalleau et al. 1998
). Although strain energy storage and return certainly plays a substantial role in the action and efficiency of the human leg in running, the gait may not be fundamentally dependent on this. In running, the downward to upward CoM transition occurs while the contact limb changes its effective length (distance between ground contact and CoM). This length change provides an opportunity to manage the momentum loss of the transition. By changing limb length, the CoM transition is smoothed in the same way sequential limb contacts reduce momentum losses in the horse-like gallop. A single limb that changes length in a manner that minimizes impulse along its axis could have much the same effect as a large number of limbs, each of a different length, acting in a sequence (Ruina et al. 2005
). To exploit this strategy, the limb muscles must follow the same force–length relation as a passive spring–mass system, so this form of transition ‘management’ has been termed ‘pseudo-elasticity’ (Ruina et al. 2005
). Although the passive strain energy storage and return and pseudo-elastic momentum retention have the same action (a linear force–extension relation) and effect (kinetic energy saving), the mechanism responsible for the retention of energy is fundamentally different, where one stores and returns available energy while the other avoids energy loss in the first place. These two mechanisms for conserving energy are not mutually exclusive, so both are probably employed during running in bipeds and quadrupeds.
To some degree it is inconvenient that the predictions of the spring–mass and pseudo-elastic models of transition dynamics are identical, since this makes the design of an experiment that distinguishes the potential contribution of each factor exceedingly difficult in human running. However, if the bipedal run and high-speed canine gallop are indeed functionally parallel, the canine gallop may offer a unique opportunity to evaluate the relative contribution of these two mechanisms for increasing running efficiency. The complexity of the elastic storage system in the galloping canine, which potentially involves not only energy storage in the muscles and tendons surrounding the spine but also energy transfer between the limbs, provides an opportunity to selectively evaluate the contribution of each component to the recovery of energy. Likewise, because the forelimb-initiated transition involves coordination of two sets of limbs and the trunk to manage the CoM position relative to the limb strut contact point, this may provide an opportunity to evaluate the role of specific components in determining the pseudo-elastic transition that are unavailable in the bipedal human model.