A two-segment model based on Alexander (1990; Phil. Trans. R. Soc. Lond. B 329, 3–10) was used to investigate the action of knee extensor muscles during long jumps. A more realistic representation of the muscle and tendon properties than implemented previously was necessary to demonstrate the advantages of eccentric force enhancement and non-linear tendon properties. During the take-off phase of the long jump, highly stretched leg extensor muscles are able to generate the required vertical momentum. Thereby, serially arranged elastic structures may increase the duration of muscle lengthening and dissipative operation, resulting in an enhanced force generation of the muscle-tendon complex. To obtain maximum performance, athletes run at maximum speed and have a net loss in mechanical energy during the take-off phase. The positive work done by the concentrically operating muscle is clearly less than the work done by the surrounding system on the muscle during the eccentric phase. Jumping performance was insensitive to changes in tendon compliance and muscle speed, but was greatly influenced by muscle strength and eccentric force enhancement. In agreement with a variety of experimental jumping performances, the optimal jumping technique (angle of attack) was insensitive to the approach speed and to muscle properties (muscle mass, the ratio of muscle fibre to tendon cross-sectional area, relative length of fibres and tendon). The muscle properties also restrict the predicted range of the angle of the velocity vector at take-off.

Stability is fundamental to the performance of terrestrial locomotion. Running cockroaches met the criteria for static stability over a wide range of speeds, yet several locomotor variables changed in a way that revealed an increase in the importance of dynamic stability as speed increased. Duty factors (the fraction of time that a leg spends on the ground relative to the stride period) decreased to 0.5 and below with an increase in speed. The duration of double support (i.e. when both tripods, or all six legs, were on the ground) decreased significantly with an increase in speed. All legs had similar touch-down phases in the tripod, but the shortest leg, the front one, lifted off before the middle and the rear leg, so that only two legs of the tripod were in contact with the ground at the highest speeds. Per cent stability margin (the shortest distance from the center of gravity to the boundaries of support, normalized to the maximum possible stability margin) decreased with increasing speed from 60% at 10 cms-1 to values less than zero at speeds faster than 50 cms-1, indicating instances of static instability at fast speeds. The center of mass moved rearward or posteriorly with respect to the base of support as speed increased. Moments about the center of mass, as shown by the center of pressure (the equivalent of a single 'effective' leg), were variable, but were balanced by opposing moments over a stride. Thus, hexapods can exploit the advantages of both static and dynamic stability. Static or quasi-static assumptions alone were insufficient to explain straight-ahead, constant-speed locomotion and may hinder discovery of behaviors that are dynamic, where kinetic energy and momentum can act as a bridge from one step to the next.

The elongated body theory has been widely used for calculations of the hydrodynamic propulsive performance of swimming fish. In the biological literature, terms containing the slope of the amplitude function at the tail end have been neglected in the calculations of thrust and efficiency, and a slope of zero has been assumed. However, some fishes, such as saithe and trout, have non-zero values of the slope near the tail end and, when this term is taken into account, the efficiency may be reduced by as much as 20 % and approaches the result given by the three-dimensional waving plate theory. The inclusion of the slope in the efficiency considerations results in an optimum ratio of the swimming speed to the wave speed that is clearly less than 1. It is suggested that the slope terms should be included in the estimation of propulsive performance for fish swimming with variable amplitude.

Equivalent gaits may be present in pedestrians that differ greatly in leg number, leg design and skeletal type. Previous studies on ghost crabs found that the transition from a slow to a fast run may resemble the change from a trot to a gallop in quadrupedal mammals. One indication of the trot-gallop gait change in quadrupedal mammals is a distinct alteration in bone strain. To test the hypothesis that ghost crabs (Ocypode quadrata) change from a trot to a gallop, we measured in vivo strains of the meropodite of the second trailing leg with miniature strain gauges. Exoskeletal strains changed significantly (increased fivefold) during treadmill locomotion at the proposed trot-gallop transition. Maximum strains attained during galloping and jumping (1000×10-6-3000×10-6) were similar to the values reported for mammals. Comparison of the maximum load possible on the leg segment (caused by muscular tension) with the strength of the segment under axial loading revealed a safety factor of 2.7, which is similar to values measured for jumping and running mammals. Equivalent gaits may result from similarities in the operation of pedestrian locomotory systems.

Many-legged animals, such as crabs and cockroaches, utilize whole-body mechanics similar to that observed for running bipeds and trotting quadrupedal mammals. Despite the diversity in morphology, two legs in a quadrupedal mammal, three legs in an insect and four legs in a crab can function in the same way as one leg of a biped during ground contact. To explain how diverse leg designs can result in common whole-body dynamics, we used a miniature force platform to measure the ground reaction forces produced by individual legs of the cockroach Blaberus discoidalis. Hexapedal runners were not like quadrupeds with an additional set of legs. In trotting quadrupedal mammals each leg develops a similar ground reaction force pattern that sums to produce the whole-body pattern. At a constant average velocity, each leg pair of the cockroach was characterized by a unique ground reaction force pattern. The first leg decelerated the center of mass in the horizontal direction, whereas the third leg was used to accelerate the body. The second leg did both, much like legs in bipedal runners and quadrupedal trotters. Vertical force peaks for each leg were equal in magnitude. In general, peak ground reaction force vectors minimized joint moments and muscle forces by being oriented towards the coxal joints, which articulate with the body. Locomotion with a sprawled posture does not necessarily result in large moments around joints. Calculations on B. discoidalis showed that deviations from the minimum moments may be explained by considering the minimization of the summed muscle forces in more than one leg. Production of horizontal forces that account for most of the mechanical energy generated during locomotion can actually reduce total muscle force by directing the ground reaction forces through the leg joints. Whole-body dynamics common to two-, four-, six- and eight-legged runners is produced in six-legged runners by three pairs of legs that differ in orientation with respect to the body, generate unique ground reaction force patterns, but combine to function in the same way as one leg of a biped.

Mechanical stresses (force/cross-sectional area) acting in muscles, tendons and bones of the hindlimbs of kangaroo rats (Dipodomys spectabilis) were calculated during steady-speed hops and vertical jumps. Stresses were determined from both high-speed cine films (light and X-ray) and force plate recordings, as well as from in vivo tendon force recordings. Stresses in each hindlimb support element during hopping (1.6-3.1 m s-1) were generally only 33% of those acting during jumping (greater than or equal to 40 cm height): ankle extensor muscles, 80 +/− 12 (S.D.) versus 297 +/− 42 kPa; ankle extensor tendons, 7.9 +/− 1.5 versus 32.7 +/− 4.8 MPa; tibia, −29 +/− 5 versus −110 +/− 25 MPa (all values are for hopping versus jumping). The magnitude of stress in each structure during these locomotor activities was similarly matched to the strength of each element, so that a consistent safety factor to failure is achieved for the hindlimb as a whole (1.5-2.0). The large stresses during jumping were correlated with a three-fold increase in ground reaction forces exerted on the ground compared with the fastest steady hopping speeds. We conclude that, for its size, the kangaroo rat has disproportionately large hindlimb muscles, tendons and bones to withstand the large forces associated with rapid acceleration to avoid predation, which limits their ability to store and recover elastic strain energy. Middle ear morphology and behavioural observations of kangaroo rats jumping vertically to avoid predation by owls and rattlesnakes support this view.

Terrestrial animals have ‘preferred speeds’ within each gait, that are used much more frequently than others for moving along the ground. Energy costs reach minimal values at these speeds within each gait. In this study we asked whether these speeds are mechanically equivalent among different animals (i.e. speeds where the same levels of peak muscle stress occur). If so, this would help in establishing a link between the energetics and the mechanics of the active muscles at these speeds, providing a first step in understanding why energy costs are minimal. We also asked whether peak muscle stress reaches a similar fraction of the maximal isometric stress at these speeds. If so, this would suggest that muscles are structured so that a similar reserve capacity remains, with a similar safety factor for avoidance of injury in response to prolonged repetitive loading. We compared two species that use quite different locomotory methods at their preferred speeds: white rats that gallop and kangaroo rats that hop. We measured peak stress in the ankle extensor muscles of these two species, as they moved at their preferred speeds, using a force platform/cine analysis technique. We also measured the maximum isometric force that this muscle group could develop in situ in the same individuals. We found the ankle extensors of white rats and kangaroo rats developed virtually identical levels of peak stress at their preferred speeds (70 +/− 6 kPa and 69 +/− 6 kPa, respectively, mean +/− S.E.), despite a fourfold difference in peak ground reaction force per unit body mass exerted on each limb. The values of peak isometric stress in situ were also virtually identical (206 +/− 17 kPa and 200 +/− 9 kPa, respectively). Our finding that the peak muscle stress is about one-third of maximum isometric stress at the preferred speeds is consistent with the idea that these are mechanically equivalent speeds, where the same fraction of available muscle fibres is recruited. Finding nearly identical values in two species that move in such different ways (galloping vs hopping), and have such large differences in ground reaction force exerted by each limb, suggests this may be true more generally for terrestrial vertebrates.

The muscle forces and stresses occurring during normal locomotor activity in kangaroo rats are compared with the peak isometric force developed by the same muscles in situ. Two methods were used simultaneously to determine the stresses (force/cross-sectional area) acting in the ankle extensors during steady-speed hopping and during jumps when animals were startled: a direct measurement using a force buckle surgically implanted around a tendon; and an indirect measurement using a force platform/cine analysis technique. We obtained essentially the same values with the two techniques. We found that at slow speeds (0.7 m s-1) the ankle extensor muscles of kangaroo rats exerted 20% of the maximum isometric force developed when the muscles were stimulated via the tibial nerve. This increased to 53% at higher speeds (1.9 m s-1). At the animals's preferred hopping speed (1.5 m s-1), peak force was approximately 40% of maximum isometric force. In jumps when animals were startled, peak forces as high as 175% of the maximal elicited isometric force were recorded. These high forces always occurred when the muscles were being stretched. It appears that kangaroo rats utilize nearly the entire range of muscle force possible during normal locomotor events (i.e. up to 175% of maximum isometric force when muscles are stretched).