Trot-gallop Transition Research Articles

The gaits of primates: center of mass mechanics in walking, cantering and galloping ring-tailed lemurs,Lemur catta

Most primates, including lemurs, have a broad range of locomotor capabilities, yet much of the time, they walk at slow speeds and amble, canter or gallop at intermediate and fast speeds. Although numerous studies have investigated limb function during primate quadrupedalism, how the center of mass (COM) moves is not well understood. Here, we examined COM energy, work and power during walking, cantering and galloping in ring-tailed lemurs, Lemur catta (N=5), over a broad speed range (0.43-2.91 m s(-1)). COM energy recoveries were substantial during walking (35-71%) but lower during canters and gallops (10-51%). COM work, power and collisional losses increased with speed. The positive COM works were 0.625 J kg(-1) m(-1) for walks and 1.661 J kg(-1) m(-1) for canters and gallops, which are in the middle range of published values for terrestrial animals. Although some discontinuities in COM mechanics were evident between walking and cantering, there was no apparent analog to the trot-gallop transition across the intermediate and fast speed range (dimensionless v>0.75, Fr>0.5). A phenomenological model of a lemur cantering and trotting at the same speed shows that canters ensure continuous contact of the body with the substrate while reducing peak vertical COM forces, COM stiffness and COM collisions. We suggest that cantering, rather than trotting, at intermediate speeds may be tied to the arboreal origins of the Order Primates. These data allow us to better understand the mechanics of primate gaits and shed new light on primate locomotor evolution.

Comparison of the morphology of the limbs of juvenile and adult horses (Equus caballus) and their implications on the locomotor biomechanics

We analyzed the morphology and the walk-trot and trot-gallop transition velocities of nine juvenile horses and compared them with their mothers. We also compared the relative stride length and the duty factor of the juveniles with respect to adults at three equivalent trotting speeds (Froude numbers 0.5, 0.75, and 1.0), to determine dynamic similarity. Juveniles had a negative allometry in their leg bones, mainly because of little size changes of the distal portions. The negative allometry of extremities allows juveniles to increase stride length without increasing step frequency, which can be biomechanically advantageous. The Froude number during the walk-trot velocity transition of juveniles was similar to that of adult horses, but walk-trot transition velocity in juveniles was greater than expected for their mass. However, during the change trot-gallop, the trot-gallop velocity transition was conserved, but the Froude number was lower. Thus, juvenile horses did not move in a manner that was dynamically similar to the adult horses. At low speed (walk-trot), the gait approaches the behavior predicted by the inverted pendulum model, but at high speed (trot-gallop) dominates the inertial forces. The trot-gallop gait change would be conducted at speeds that would minimize energy costs of transport owing to collisions and changes in the trajectory of the center of mass.

The adaptation of limb kinematics to increasing walking speeds in freely moving mice 129/Sv and C57BL/6

The kinematics of locomotion was analyzed in two strains of great importance for the creation of mutated mice (C56BL/6 and 129/Sv). Different behavioral situations were used to trigger sequences of movement covering the whole range of velocities in the mice, and the variations of kinematic parameters were analyzed in relation with velocity. Both stride frequency and stride length contributed to the moving speed, but stride frequency was found to be the main contributor to the speed increase. A trot-gallop transition was detected at speed about 70 cm/s, in relation with a sharp shift in limb coordination. The results of this study were consistent with pieces of information previously published concerning the gait analyses of other strains, and provided an integrative view of the basic motor pattern of mice. On the other hand some qualitative differences were found in the movement characteristics of the two strains. The stride frequency showed a higher contribution to speed in 129/Sv than in C57BL/6. In addition, 129/Sv showed a phase shift in the forelimb and hindlimb, and a different position of the foot during the stance time that revealed a different gait and body position during walking. Overall, 129/Sv moved at a slower speed than C57BL/6 in any behavioral situation. This difference was related to a basal lower level of motor activity. The possibility that an alteration in the dopamine circuit was responsible for the different movement pattern in 129/Sv is discussed.

What explains the trot–gallop transition in small mammals?

The transition from trot to gallop in quadruped mammals has been widely hypothesized to be a strategy to minimize the energetic costs of running. This view, however, has been challenged by some experimental evidence suggesting instead that this transition might be triggered by mechanical cues, and would occur when musculoskeletal stresses reach a certain critical value. All previous experiments to test those hypotheses have used relatively large species and their results, therefore, may not be applicable to small mammals. In this study we evaluated the effect of carrying loads on the locomotor energetics and gait transitions of the rodent Octodon degus running on a treadmill. Metabolic rate and cost of transport increased about 30% with a 20% increment in body mass. This increment was higher than expectations based on other mammals, where energy consumption increases in proportion to the added mass, but similar to the response of humans to loads. No abrupt change of energy consumption between gaits was observed and therefore no evidence was found to support the energetic hypothesis. The trot-gallop transition speed did not vary when subjects were experimentally loaded, suggesting that the forces applied to the musculoskeletal system do not trigger gait transition.

What are the relations between mechanics, gait parameters, and energetics in terrestrial locomotion?

Are the different energy-conserving mechanics (i.e., pendulum and spring) used in different gaits reflected in differences in energetics and/or stride parameters? The analysis included published data from several species and new data from horses. When changing from pendulum to spring mechanics, there is a change in the slope of metabolic rate (MR) vs. speed in all species, in birds and quadrupeds there is no step increase, and in humans there are conflicting reports. At the trot-gallop transition, where quadrupeds are hypothesized to change from spring mechanics to some combination of spring and pendulum mechanics, there is a change in slope of MR vs. speed in horses but not in other species. Stride frequency (SF) is a logarithmic function of walking speed in all species, a linear function of trotting/running speed, and nearly independent of speed in galloping. In humans and horses there is a discontinuity in SF at the walk-trot (run) transition but not in birds. The slope of time of contact vs. speed does not change with mechanics in most species, but it does in humans. In horses and humans, there is a discontinuity at the walk-trot (run) transition and data for other species do not permit generalization. Duty factor (DF) in humans is greater than 0.5 in walking (pendulum mechanics) and less than 0.5 when running (spring mechanics). However, this is not true in many species that have DF>0.5 at the lowest speeds where they use spring mechanics. When trotting at low speeds, horses use forelimb DF>0.5 and hind limb DF<0.5. Thus, it is confusing to distinguish between walking and running by DF.

Jointed setae – their role in locomotion and gait transitions in polychaete worms

Many families of polychaete worms have jointed setae in which the joint is external to the body and is not directly controlled by muscles or nerves. We assessed the role of these specialized structures in the hesionid polychaete, Ophiodromus pugettensis, by examining speed, step length, stride distance, stride frequency and gait transitions in worms with and without setal joints. Individual worms were videotaped while they moved over sandy surfaces at a range of speeds. The worms were then anaesthetized and all their compound setae were trimmed either distally or proximally to the setal joints. After two days of recovery the worms were videotaped a second time while they again moved over sandy surfaces at a range of speeds. From the video tapes we analyzed their locomotory performance before and after setal ablation. Animals in which the setae were shortened but in which the joint was left intact showed no consistent change in speed, step length, stride distance, stride frequency or gait transitions. Animals in which the joint had been removed both changed gaits at slower speeds (walking to undulatory walking and undulatory walking to swimming) and showed a significant decrease in maximum swimming speeds and stride distance. A subset of data containing only cases where the worms were moving at the same speed in the same gait before and after setal ablation was analyzed. In these instances, after the removal of the joint, the worms had significantly smaller stride distances and compensated for this by increasing stride frequency. In O. pugettensis, the undulatory walking gait is analogous to the trot–gallop transition in quadrupedal mammals because the animal switches from moving the appendages on a relatively rigid body to using a combination of body flexion and appendage movement to achieve propulsion, however, unlike quadrupedal mammals this transition takes place over a wide range of speeds and at different sites on the body as speed increases. These experiments indicate that jointed setae may be important both in allowing a worm to better control setal contact and traction with the substrate as well as in altering the effectiveness of its swimming stroke.

THE INFLUENCE OF MIDSTANCE VERTICAL GROUND REACTION FORCE ON THE HUMAN WALK-RUN TRANSITION 519

In a study on the trot-gallop transition of horses Farley & Taylor(1991) measured vertical ground reaction forces (VGRF) and found a critical level of force which seemed to be the controlling factor in the transition. The following experiment was planned to assess the roles of midstance VGRF and speed of locomotion in the human walk-run transition. If midstance VGRF has a greater role in the transition than speed, then an addition of weight (15% BW) to a subject should cause the preferred transition speed (PTS) to change while maintaining similar levels of midstance VGRF. Two sets of measurements were conducted on 10 subjects in an attempt to discern these roles. Using a treadmill instrumented to measure VGRF, a subject's PTS was determined by systematically increasing speed from 1 to 3 m/s in 0.2 m/s increments until the subject switched his/her preferred gait to running. Then midstance VGRF was measured while subjects walked and ran at speeds from 0.6 m/s below PTS to 0.6 m/s above PTS. At each speed the midstance VGRF was calculated as a mean over 5-10 strides. These two measurements were repeated under both weighted and unweighted conditions. With speed aligned at the PTS, midstance VGRF was plotted for each condition and averaged across subjects. As speed increased, midstance VGRF for both walking conditions decreased, then increased once above PTS. The variability of midstance VGRF significantly increased above the PTS (p<0.05). For both conditions the mean PTS was similar (2.07 vs. 2.11 m/s) and midstance VGRF at the PTS was only slightly greater under the weighted condition (p=0.67). While speed and midstance VGRF cannot be differentiated in their affect on the walk-run transition, the increase in midstance VGRF variability may indicate a perturbation potentially influencing the transition.

Energy comparison between trot, bound, and gallop using a simple model.

In this paper, the dynamics of quadruped trot, gallop, and bound will be examined using a simple model for the quadruped. The body of the quadruped is modeled as a uniform bar and the legs are modeled by massless springs. It will be shown that symmetry can be used to study the locomotion of this system. Using symmetry, a technique will be developed to obtain periodic solutions for each of the gaits of the quadruped model. These periodic solutions will be computed at various speeds. The energy levels will be compared for each of the gaits. The exchange of energy between its different forms will be shown for different gaits. It will be shown that even without body flexibility, there are significant savings in energy due to gait transition from trot to gallop. The energy levels will be used to predict the trot-gallop transition speed. These results will be compared with the experimental results for horses and dogs.

Locomotion in Dromiciops-Australis (Marsupialia, Microbiotheriidae)

Cinematography was used to record locomotion in two adult male Dromiciops australis. Both animals were run on five horizontal dowels varying in diameter from 6.3 to 39 mm and on a horizontal board 89 mm wide. Film records were analysed to determine locomotor velocity, stride length and gait. Locomotor speed and stride length were not affected by substratum, but gait was. Truly symmetrical gaits were used by both animals across a range of speeds on the narrowest dowel. These were characterised by diagnoal couplets of support and a diagonal sequence of limb activition. During locomotion on the other substrata, gaits characterised by slight asymmetry were generally used. The most common of these was one in which diagonal support couplets predominated and each hindlimb was activated slightly ahead of the contralateral forelimb. At higher speeds on the 39-mm dowel the animals sometimes used the half-bound and transverse gallop. The duration of the locomotor cycle decreased exponentially with increasing speed and seemed not to be influenced by substratum diameter, once speed was taken into account. Stride length increased exponentially with speed and also appeared independent of substratum. With symmetrical gaits, the relative phase lag of forelimbs with respect to their ipsilateral hindlimbs changed with speed so that a moderate walkig trot was replaced either by a fast waling trot or fast diagonal sequence walk and ultimately by a slow diagonal sequence run. Two of the symmetrical gaits used by Dromiciops are similar to those used by arboreal didelphids and phalangeroids and by most primates, but are rarely used by other mammals. These gaits appear especially suited to locomotion on narrow branches, suggesting that this species may utilise such substrata to a significant extent in nature. The asymmetrical gaits used by Dromiciops, the half-bound and transverse gallop, are used by various other quadrupedal marsupials, although not commonly by arboreal didelphids. It is conjectured that the symmetrical marsupials, although not commonly by arboreal didelphids and phalangeroids were present in ancestral marsupials and that the latter forms also used the half-bound or transverse gallop. Absolute speed at the transition from symmetrical to asymmetrical gaits ('trot-gallop transition') exceeded that predicted by allometric equations derived from data for terrestrial placental mammals. Relative speed (as measured by the square root of the Froude number) was also higher at this transition than in placentals.

Exoskeletal Strain: Evidence for a Trot–Gallop Transition in Rapidly Running Ghost Crabs

ABSTRACT 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.

A Mechanical Trigger for the Trot-Gallop Transition in Horses

It is widely thought that animals switch gaits at speeds that minimize energetic cost. Horses naturally switched from a trot to a gallop at a speed where galloping required more energy than trotting, and thus, the gait transition actually increased the energetic cost of running. However, by galloping at this speed, the peak forces on the muscles, tendons, and bones, and presumably the chance of injury, are reduced. When the horses carried weights, they switched from a trot to a gallop at a lower speed but at the same critical level of force. These findings suggest that the trot-gallop transition is triggered when musculoskeletal forces reach a critical level.

Power Output and the Frequency of Oscillatory Work in Mammalian Diaphragm Muscle: the Effects of Animal Size

Bundles of muscle fibres were isolated from the diaphragm of mouse, rat and rabbit. Mean oscillatory power output was determined during phasic stimulation and imposed sinusoidal length changes. Maximum power output was measured over a range of cycle frequencies. The cycle frequency for maximum power output (fopt) decreased with increasing body mass and was described by the equation, fopt = 4.42M-0.16, where M is body mass. A very similar relationship has been reported between body mass and the frequency of the trot-gallop transition in terrestrial, quadrupedal mammals [Heglund et al. (1974), Science 186, 1112-1113), and the significance of this similarity is discussed.

Speed-related changes in hindlimb intersegmental dynamics during the swing phase of cat locomotion

To determine speed-related changes in hindlimb motion that might account for the mutability of bifunctional (hip extensor/knee flexor) muscle activity during the E1 phase of swing, we studied hip and knee joint kinematics and kinetics during swing over a ten-fold increase in locomotor speed (0.35 to 3.5 m/s). Three cats were filmed (100 frames/s) while locomoting on a motorized treadmill; kinematics were analyzed for the entire step cycle and kinetics for the swing phase. During swing, angular excursions at the hip and knee joints were similar for walking and trotting, but hip flexion and extension were significantly less after the transition from trot to gallop, while knee-angle range of motion increased during gallop phases E1, E2, and E3. During swing, knee-extension velocity peaked early in E1 and increased linearly with speed, while hip-flexion velocity peaked late in the flexion (F) phase and also increased linearly, but decreased precipitously at the trot-gallop transition and remained constant as speed of galloping increased. Muscle torque directions during E1, flexor at the knee and extensor at the hip, were consistent with the proposed role of bifunctional posterior thigh muscles to decelerate thigh and leg segments for paw contact. At the knee joint, muscle torque during E1 counteracted a large interactive torque due to leg angular acceleration; the magnitudes of both torques were speed related with maximal values at the fastest speed tested (3.5 m/s). At the hip joint, muscle torque during E1 also counteracted a large interactive torque due to leg angular acceleration; the magnitudes of these two torques were speed related during the walk and trot, and like hip flexion velocity, decreased at the trot-gallop transition. Our data on speed-related changes in hindlimb dynamics suggest that the E1 burst amplitude (and perhaps duration) of posterior thigh muscles will be speed related during the walk and trot. After the trot-gallop transition at about 2.5 m/s, the recruitment of these bifunctional muscles may decline due to the changes in hindlimb dynamics. Because activity of these muscles counteracts interactive torques primarily related to leg angular acceleration, we suggest that motion-related feedback decoding this action may be important for regulating recruitment during E1.

Speed, stride frequency and energy cost per stride: how do they change with body size and gait?

In this study we investigate how speed and stride frequency change with body size. We use this information to define 'equivalent speeds' for animals of different size and to explore the factors underlying the six-fold difference in mass-specific energy cost of locomotion between mouse- and horse-sized animals at these speeds. Speeds and stride frequencies within a trot and a gallop were measured on a treadmill in 16 species of wild and domestic quadrupeds, ranging in body size from 30 g mice to 200 kg horses. We found that the minimum, preferred and maximum sustained speeds within a trot and a gallop all change in the same rather dramatic manner with body size, differing by nine-fold between mice and horses (i.e. all three speeds scale with about the 0.2 power of body mass). Although the absolute speeds differ greatly, the maximum sustainable speed was about 2.6-fold greater than the minimum within a trot, and 2.1-fold greater within a gallop. The frequencies used to sustain the equivalent speeds (with the exception of the minimum trotting speed) scale with about the same factor, the -0.15 power of body mass. Combining this speed and frequency data with previously published data on the energetic cost of locomotion, we find that the mass-specific energetic cost of locomotion is almost directly proportional to the stride frequency used to sustain a constant speed at all the equivalent speeds within a trot and a gallop, except for the minimum trotting speed (where it changes by a factor of two over the size range of animals studied). Thus the energy cost per kilogram per stride at five of the six equivalent speeds is about the same for all animals, independent of body size, but increases with speed: 5.0 J kg-1 stride-1 at the preferred trotting speed; 5.3 J kg-1 stride-1 at the trot-gallop transition speed; 7.5 J kg-1 stride-1 at the preferred galloping speed; and 9.4 J kg-1 stride-1 at the maximum sustained galloping speed. The cost of locomotion is determined primarily by the cost of activating muscles and of generating a unit of force for a unit of time. Our data show that both these costs increase directly with the stride frequency used at equivalent speeds by different-sized animals. The increase in cost per stride with muscles (necessitating higher muscle forces for the same ground reaction force) as stride length increases both in the trot and in the gallop.

Locomotion Energetics of the Ghost Crab: II. Mechanics of the Centre of Mass During Walking and Running

ABSTRACT Terrestrial locomotion involving appendages has evolved independently in vertebrates and arthropods. Differences in the mechanical design of the locomotor apparatus could impose constraints on the energetics of locomotion. The mechanical energy fluctuations of the centre of mass of an arthropod, the ghost crab Ocvpode quadrata (Fabricius), were examined by integrating the ground reaction forces exerted during sideways locomotion. Crabs used a pendulum-type energy exchange mechanism during walking, analogous to an egg rolling end over end, with the same effectiveness as birds and mammals. Moreover, ghost crabs were found to have two running gaits. A switch from a slow to a fast run occurred at the same speed and stride frequency predicted for the trot-gallop transition of a quadrupedal mammal of the same body mass. In addition, the mass-specific mechanical energy developed over a unit distance was independent of speed and was within the limits measured for birds and mammals. Despite the obvious differences in mechanical design between crabs and mammals, energy-conserving mechanisms and the efficiency of locomotion were remarkably similar. These similarities may result from the fact that the muscles that generate forces during terrestrial locomotion have relatively conservative mechanical and energetic properties.

Rat locomotory muscle fiber activity during trotting and galloping.

This study was designed to investigate the hypothesis that the trot-gallop transition in running guadrupeds occurs when active cross-sectional areas of muscles or fiber populations within muscles, reach some critical point as animals increase speed within trotting. Rats (Rattus norvegicus) were used as experimental animals, and glycogen depletion was used to estimate patterns or fiber activity. Our results indicate that 1) the contribution to power output by the front limb muscles was less than that of the hind limb muscles during trotting and galloping; 2) the active cross-sectional area of plantaris muscles peaked immediately prior to the transition in gait; 3) the ankle plantar flexor group of muscles as a whole did not attain a maximum active cross-sectional area during fast trotting; and 4) no major discontinuities in whole muscle or fiber type glycogen depletion rates occurred across the gait change. Although these findings do not prove the hypothesis, they support the concept that the trop-gallop transition follows the attainment of peak active muscle cross-sectional areas as animals increase trotting speed.

Why Change Gaits? Recruitment of Muscles and Muscle Fibers as a Function of Speed and Gait

Muscles shorten, stay the same length and are stretched while they are active during normal modes of terrestrial locomotion. The relative importance of these different types of muscular activity changes as animals change gait. Energy is conserved during a walk by an alternate storage and recovery of gravitational potential energy within each stride, as in an inverted pendulum. In order for this transfer of energy to take place, muscular activity is required to hold the limb rigid while the animal rotates over it. Energy is conserved by a spring mechanism during running, trotting, galloping, and hopping. Energy is stored when active muscles and their tendons are stretched and recovered as they subsequently shorten. The recruitment patterns of motor units as a function of speed therefore, depends on the type of muscular activity as well as the force exerted. Discontinuities in the cross sectional area of active fibers with increasing speed have been observed at the trot-gallop transition. It is suggested that at this point the trunk is recruited as an additional spring enabling more energy to be stored elastically. It is concluded that we must consider what muscles are doing during normal modes of locomotion before we become too involved in designing schemes of motor unit recruitment.

Muscle fiber activity as a function of speed and gait.

These experiments were designed to test the hypothesis that locomotory gait transitions occur when some critical cross-sectional area of active muscle is reached as animals increase speed within a gait. We used glycogen depletion as evidence of muscle fiber activity and selected an experimental animal in which all muscle fibers in the locomotory muscles rely extensively on glycogen as a substrate--the lion. We found a high correlation between biochemically and histochemically determined rates of glycogen depletion (r = 0.906). Rates of glycogen depletion in the biceps femoris and triceps brachii muscles increased logarithmically with speed with no discontinuities at the gait transitions. However, we found large discontinuities both in the total cross-sectional area of muscle that showed depletion and in the rates at which the different types of fibers depleted glycogen at the trot-gallop transition. Our results indicate that 1) gait transition did not occur at a maximum tension level either for a particular type of fiber or the whole muscle, and 2) different configurations of motor units within an individual muscle may be recruited as an animal changes gait.

Using body size to understand the structural design of animals: quadrupedal locomotion.

Many parameters of gait and performance, including stride frequency, stride length, maximum speed, and rate of O2 uptake are experimentally found to be power-law functions of body weight in running quadrupeds. All of these parameters are reasonably easy to measure except maximum speed, where the question arises whether one means top sprinting speed or top speed for sustained running. Moreover, differences in training and motivation make comparisons of top speed difficult. The problem is circumvented by comparing animals running at the transition between trotting and galloping, a physiologically similar speed. Theoretical models are proposed which preserve either geometric similarity, elastic similarity, or static stress similarity between animals of large and small body weights. The model postulating elastic similarity provides the best correlation with published data on body and bone proportions, body surface area, resting metabolic rate, and basal heart and lung frequencies. It also makes the most successful prediction of stride frequency, stride length, limb excursion angles, and the metabolic power required for running at the trot-gallop transition in quadrupeds ranging in size from mice to horses.

Scaling stride frequency and gait to animal size: mice to horses.

The stride frequency at which animals of different size change from one gait to another (walk, trot, gallop) changes in a regular manner with body mass. The speed at the transition from trot to gallop can be used as an equivalent speed for comparing animals of different size. This transition point occurs at lower speeds and higher stride frequencies in smaller animals. Plotting stride frequency at the trot-gallop transition point as a function of body mass in logarithmic coordinates yields a straight line.