Morphological conservation of limb natural pendular period in the domestic dog (Canis familiaris): Implications for locomotor energetics

For better understanding of the links between limb morphology and the metabolic cost of locomotion, we have characterized the relationships between limb length and shape and other functionally important variables in the straightened forelimbs and hindlimbs of a sample of 12 domestic dogs (Canis familiaris). Intra-animal comparisons show that forelimbs and hindlimbs are very similar (not significantly different) in natural pendular period (NPP), center-of-mass, and radius of gyration, even though they differ distinctly in mass, length, moment-of-inertia, and other limb proportions. The conservation of limb NPP, despite pronounced dissimilarity in other limb characteristics, appears to be the result of systematic differences in shape, forelimbs tending to be cylindrical and hindlimbs conical. Estimating limb NPP for other species from data in the literature on segment inertia and total limb length, we present evidence that the similarity between forelimbs and hindlimbs in NPP is generally true for mammals across a large size range. Limbs swinging with or near their natural pendular periods will maximize within-limb pendular exchange of potential and kinetic energy. As all four limbs of moderate- and large-size animals swing with the same period during walking, maximal advantage can be derived from the pendular exchange of energy only if forelimbs and hindlimbs are very similar in NPP. We hypothesize that an important constraint in the evolution of limb length and shape is the locomotor economy derived from forelimbs and hindlimbs of similar natural pendular period. J. Morphol. 234:183–196, 1997. © 1997 Wiley-Liss, Inc.     

Effects of arm swing on mechanical parameters of human gait

The aim of this study was to investigate the influence of the upper limb swing on human gait. Measurements were performed on 52 subjects by using the Elite system with two cameras and a Kistler force platform. The recording of trajectories of characteristic body points on the subjects and the measurement of ground reaction forces have been performed at normal walking and at walking with emphasised rhythmic upper limb swing. The trajectory of the whole body mass centre, central dynamic moments of inertia and ground reaction forces have been calculated for every subject and mean curves of the entire group have been determined for walking with the natural and the emphasised upper limb swing. The determined mean values of normalised mechanical parameters have been compared and differences between the gait with the natural and the emphasised upper limb swing have been described.     

Assessment of the mass,length, center of mass,and principal moment of inertia of body segments in adult males of the brown anole (Anolis sagrei) and green,or carolina,anole (Anolis carolinensis)

This study provides a morphometric data set of body segments that are biomechanically relevant for locomotion in two ecomorphs of adult male anoles, namely, the trunk‐ground Anolis sagrei and the trunk‐crown Anolis carolinensis. For each species, 10 segments were characterized, and for each segment, length, mass, location of the center of mass, and radius of gyration were measured or calculated, respectively. The radii of gyration were computed from the moments of inertia by using the double swing pendulum method. The trunk‐ground A. sagrei has relatively longer and stockier hindlimbs and forelimbs with smaller body than A. carolinensis. These differences between the two ecomorphs demonstrated a clear relationship between morphology and performance, particularly in the context of predator avoidance behavior, such as running or jumping in A. sagrei and crypsis in A. carolinensis. Our results provide new perspectives on the mechanism of adaptive radiation as the limbs of the two species appear to scale via linear factors and, therefore, may also provide explanations for the mechanism of evolutionary changes of structures within an ecological context. J. Morphol., 2012. © 2012 Wiley Periodicals, Inc.     

Quadrupedal locomotion in squirrel monkeys (Cebidae: Saimiri sciureus): a cineradiographic study of limb kinematics and related substrate reaction forces

Quadrupedal locomotion of squirrel monkeys on small-diameter support was analyzed kinematically and kinetically to specify the timing between limb movements and substrate reaction forces. Limb kinematics was studied cineradiographically, and substrate reaction forces were synchronously recorded. Squirrel monkeys resemble most other quadrupedal primates in that they utilize a diagonal sequence/diagonal couplets gait when walking on small branches. This gait pattern and the ratio between limb length and trunk length influence limb kinematics. Proximal pivots of forelimbs and hindlimbs are on the same horizontal plane, thus giving both limbs the same functional length. However, the hindlimbs are anatomically longer than the forelimbs. Therefore, hindlimb joints must be more strongly flexed during the step cycle compared to the forelimb joints. Because the timing of ipsilateral limb movements prevents an increasing amount of forelimb retraction, the forelimb must be more protracted during the initial stance phase. At this posture, gravity acts with long moment arms at proximal forelimb joints. Squirrel monkeys support most of their weight on their hindlimbs. The timing of limb movements and substrate reaction forces shows that the shift of support to the hindlimbs is mainly done to reduce the compressive load on the forelimb. The hypothesis of the posterior weight shift as a dynamic strategy to reduce load on forelimbs, proposed by Reynolds ([1985]) Am. J. Phys. Anthropol. 67:335-349; [1985] Am. J. Phys. Anthropol. 67:351-362), is supported by the high correlation of ratios between forelimb and hindlimb peak vertical forces and the range of motion of shoulder joint and scapula in primates.     

The dynamics of quadrupedal locomotion

This paper presents a dynamical analysis of quadrupedal locomotion, with specific reference to an adult Nubian goat. Measurements of ground reaction forces and limb motion are used to assess variations in intersegmental forces, joint moments, and instantaneous power for three discernible gaits: walking, running, and jumping. In each case, inertial effects of the torso are shown to dominate to the extent that lower-extremity contributions may be considered negligible. Footforces generated by the forelimbs exceed those exerted by the hindlimbs; and, in general, ground reactions increase with speed. The shoulder and hip dominate mechanical energy production during walking, while the knee plays a more significant role in running. In both cases, however, the elbow absorbs energy, and by so doing functions primarily as a damping (control) element. As opposed to either walking or running, jumping requires total horizontal retardation of the body's center of mass. In this instance, generating the necessary vertical thrust amounts to energy absorption at all joints of the lower extremities.     

The jump as a fast mode of locomotion in arboreal and terrestrial biotopes

The jump is always used for locomotion. For its execution in arboreal and terrestrial biotopes the requirements are of somewhat different nature. In an arboreal biotope the jump is characterized by a rapid progression through discontinuous substrates and the ability to take off from a small area and a secure landing on a spot. This requires well coordinated movements in all phases of the jump. On the ground, the jump is less frequent and often used for crossing obstacles or gaps. In primates both variants can be observed. In order to relate the details of locomotor behaviour to a certain environment, the biomechanics of jumping are analyzed in five primate species: The three mainly arboreal prosimian species Galago moholi, the smallest and most specialized leaper of all, Galago garnettii, a medium-sized bushbaby with some capacities for jumping, and Lemur catta also with some abilities to jump. The two simian species, Macaca fuscata and Homo sapiens, are usually terrestrial and have good jumping capacities, although not in terms of quantity. The investigation is based on high-speed motion analyses (100-500 frames/second) and the synchronized records of a force-plate from which all subjects had to jump off. On the basis of the results two kinds of jumping can be distinguished: standing and running jumps. The three prosimian species perform standing jumps. Dorsiflexion of their tails compensates ventrally oriented rotational moments of the trunk during body extension at take-off. The upward arm swing yields an overall increase in take-off velocity without additional muscular force exerted by the legs. The main difference among the species are the high relative forces in the small Galago moholi (up to 13 times body weight) as compared to the larger G. garnettii (8.5 times body weight) and the even larger Lemur catta (4.5 times body weight). In Homo sapiens the standing jump is characterized by an extensive arm swing backward, which is then followed by a forward and upward movement. The velocity at take-off is much smaller if compared to the prosimians. The running jump in Macaca fuscata is always preceded by at least one gallop cycle. The body assumes a ball shape at the beginning of the actual take-off. This is advantageous for rotating the body into a position in which the trunk axis is in line with the direction of movement. The tail of the Japanese macaque is too short to compensate the trunk's lift exerted on the hip region by the extending hindlimbs.(ABSTRACT TRUNCATED AT 400 WORDS)     

Brief communication: Three‐dimensional motion analysis of hindlimb during brachiation in a white‐handed gibbon (Hylobates lar)

In brachiating gibbons, it is thought that there is little movement in the hindlimb joints and that lateral body movement is quite limited. These hypotheses are based on naked‐eye observations, and no quantitative motion analyses of the hindlimbs have been reported. This study quantitatively describes the three‐dimensional movements of the lower trunk and distal thigh during continuous‐contact brachiation in a white‐handed gibbon (Hylobates lar) to evaluate the roles of the trunk and hindlimb. The results revealed that the lower trunk moved both laterally and vertically. The lateral movement of the lower trunk resulted from the lateral inclination of the trunk by gravity. The vertical movement of the trunk was converted into forward velocity, indicating an exchange between potential and kinetic energy. We also observed flexion and extension of the hip, although the excursion was within a small range. In addition, the lateral movement of the hindlimb in thedirection opposite to that of trunk movement helped to reduce the lateral sway of the body. These results suggest that during continuous‐contact brachiation a gibbon uses hip flexion and extension motions to increase the kinetic energy in the swing. In addition, fine motions of the hip may restrict the lateral sway of the center of body mass. Am J Phys Anthropol 142:650–654, 2010. © 2010 Wiley‐Liss, Inc.     

Influences of limb proportions and body size on locomotor kinematics in terrestrial primates and fossil hominins

During locomotion, mammalian limb postures are influenced by many factors including the animal's limb length and body mass. Polk (2002) compared the gait of similar-sized cercopithecine monkeys that differed limb proportions and found that longer-limbed monkeys usually adopt more extended joint postures than shorter-limbed monkeys in order to moderate their joint moments. Studies of primates as well as non-primate mammals that vary in body mass have demonstrated that larger animals use more extended limb postures than smaller animals. Such extended postures in larger animals increase the extensor muscle mechanical advantage and allow postures to be maintained with relatively less muscular effort (Polk, 2002; Biewener 1989). The results of these previous studies are used here to address two anthropological questions. The first concerns the postural effects of body mass and limb proportion differences between australopithecines and members of the genus Homo. That is, H. erectus and later hominins all have larger body mass and longer legs than australopithecines, and these anatomical differences suggest that Homo probably used more extended postures and probably required relatively less muscular force to resist gravity than the smaller and shorter-limbed australopithecines. The second question investigates how animals with similar size but different limb proportions differ in locomotor performance. The effects of limb proportions on gait are relevant to inferring postural and locomotor differences between Neanderthals and modern Homo sapiens which differ in their crural indices and relative limb length. This study demonstrates that primates with relatively long limbs achieve higher walking speeds while using lower stride frequencies and lower angular excursions than shorter-limbed monkeys, and these kinematic differences may allow longer-limbed taxa to locomote more efficiently than shorter-limbed species of similar mass. Such differences may also have characterized the gait of Homo sapiens in comparison to Neanderthals, but more experimental data on humans that vary in limb proportions are necessary in order to evaluate this question more thoroughly.     

On birds: scale effects in the neognath hindlimb and differences in the gross morphology of wings and hindlimbs

Scale effects on whole limb morphology (i.e. bones together with in situ overlying muscles) are well understood for the neognath forelimb. However, scale effects on neognath gross hindlimb morphology remain largely unexplored. To broaden our understanding of avian whole limb morphology, I investigated the scaling of hindlimb inertial properties in neognath birds, testing empirical scaling relationships against the model of geometric similarity. Inertial property data – mass, moment of inertia, centre of mass distance, and radius of gyration – were collected from 22 neognath species representing a wide range of locomotor specializations. When scaled against body mass, hindlimb inertial properties scale with positive allometry. Thus, in terms of morphology, larger bodied neognaths possess hindlimbs requiring disproportionately more energy to accelerate and decelerate relative to body mass than smaller bodied birds. When scaled against limb length, hindlimb inertial properties scale according to isometry. In the subclade Land Birds (sensu Hackett et al.), hindlimb inertial properties largely scale according to positive allometry. The contrasting results of positive allometry vs. isometry in neognaths are due to how hindlimb length scales against body mass. Negative allometry of hindlimb inertial properties, which would reduce terrestrial locomotion costs, would probably make the hindlimb susceptible to mechanical failure or too diminutive for its many ecological functions. Comparing the scaling relationships of wings and hindlimbs highlights how locomotor costs influence the scaling of limb inertial properties. © 2013 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 110 , 14–31.     

The effect of direct measurement versus cadaver estimates of anthropometry in the calculation of joint moments during above-knee prosthetic gait in pediatrics

Joint reaction forces, moments and powers are important in interpreting gait mechanics and compensatory strategies used by patients walking with above-knee prostheses. Segmental anthropometrics, required to calculate joint moments, are often estimated using data from cadaver studies. However, these values may not be accurate for patients following amputation as prostheses are composed of non-biologic material. The purpose of this study was to compare joint moments using anthropometrics calculated from cadaver studies versus direct measurements of the residual limb and prosthesis for children with an above-knee amputation. Gait data were collected for four subjects with above-knee prostheses walking at preferred and fast speeds. Joint moments were computed using anthropometrics from cadaver studies and direct measurements for each subject. The difference between these two methods primarily affected the inertia couple (Ialpha term) and the inertial effect due to gravity, which comprised a greater percentage of the total joint moment during swing as compared to stance. Peak hip and knee flexor and extensor moments during swing were significantly greater when calculated using cadaver data (p<0.05). These differences were greater while walking fast as compared to slow speeds. A significant difference was not found between these two methods for peak hip and knee moments during stance. A significant difference was found for peak ankle joint moments during stance, but the magnitude was not clinically important. These results support the use of direct measurements of anthropometry when examining above-knee prosthetic gait, particularly during swing.     

An investigation of the interactions between lower-limb bone morphology,limb inertial properties and limb dynamics

Bone mass and size clearly affect the safety and survival of wild animals as well as human beings, however, little is known about the interactions between bone size and movement dynamics. A modeling approach was used to investigate the hypothesis that increased bone cortical area causes increased limb moments of inertia, decreased lower-limb movement maximum velocities, and increased energy requirements to sustain submaximum lower-limb locomotion movements. Custom software and digital data of a human leg were used to simulate femur, tibia, and fibula cortical bone area increases of 0%, 22%, 50%, and 80%. Limb segment masses, center of mass locations, and moments of inertia in the sagittal plane were calculated for each bone condition. Movement simulations of unloaded running and cycling motions were performed. Linear regression analyses were used to determine the magnitude of the effect cortical area has on limb moment of inertia, velocity, and the internal work required to move the limbs at a given velocity. The thigh and shank moment of inertia increased linearly up to 1.5% and 6.9%, respectively for an 80% increase in cortical area resulting in 1.3% and 2.0% decreases in maximum unloaded cycling and running velocities, respectively, and in 3.0% and 2.9% increases in internal work for the cycling and running motions, respectively. These results support the hypothesis and though small changes in movement speed and energy demands were observed, such changes may have played an important role in animal survival as bones evolved and became less robust.     

Scale Effects between Body Size and Limb Design in Quadrupedal Mammals

Recently the metabolic cost of swinging the limbs has been found to be much greater than previously thought, raising the possibility that limb rotational inertia influences the energetics of locomotion. Larger mammals have a lower mass-specific cost of transport than smaller mammals. The scaling of the mass-specific cost of transport is partly explained by decreasing stride frequency with increasing body size; however, it is unknown if limb rotational inertia also influences the mass-specific cost of transport. Limb length and inertial properties – limb mass, center of mass (COM) position, moment of inertia, radius of gyration, and natural frequency – were measured in 44 species of terrestrial mammals, spanning eight taxonomic orders. Limb length increases disproportionately with body mass via positive allometry (length ∝ body mass^0.40); the positive allometry of limb length may help explain the scaling of the metabolic cost of transport. When scaled against body mass, forelimb inertial properties, apart from mass, scale with positive allometry. Fore- and hindlimb mass scale according to geometric similarity (limb mass ∝ body mass^1.0), as do the remaining hindlimb inertial properties. The positive allometry of limb length is largely the result of absolute differences in limb inertial properties between mammalian subgroups. Though likely detrimental to locomotor costs in large mammals, scale effects in limb inertial properties appear to be concomitant with scale effects in sensorimotor control and locomotor ability in terrestrial mammals. Across mammals, the forelimb''s potential for angular acceleration scales according to geometric similarity, whereas the hindlimb''s potential for angular acceleration scales with positive allometry.     

Effects of the Racket Polar Moment of Inertia on Dominant Upper Limb Joint Moments during Tennis Serve

This study examined the effect of the polar moment of inertia of a tennis racket on upper limb loading in the serve. Eight amateur competition tennis players performed two sets of 10 serves using two rackets identical in mass, position of center of mass and moments of inertia other than the polar moment of inertia (0.00152 vs 0.00197 kg.m²). An eight-camera motion analysis system collected the 3D trajectories of 16 markers, located on the thorax, upper limbs and racket, from which shoulder, elbow and wrist net joint moments and powers were computed using inverse dynamics. During the cocking phase, increased racket polar moment of inertia was associated with significant increases in the peak shoulder extension and abduction moments, as well the peak elbow extension, valgus and supination moments. During the forward swing phase, peak wrist extension and radial deviation moments significantly increased with polar moment of inertia. During the follow-through phase, the peak shoulder adduction, elbow pronation and wrist external rotation moments displayed a significant inverse relationship with polar moment of inertia. During the forward swing, the magnitudes of negative joint power at the elbow and wrist were significantly larger when players served using the racket with a higher polar moment of inertia. Although a larger polar of inertia allows players to better tolerate off-center impacts, it also appears to place additional loads on the upper extremity when serving and may therefore increase injury risk in tennis players.     

Modulation of limb dynamics in the swing phase of locomotion

A method was presented for quantifying cat (Felis catus) hind limb dynamics during swing phase of locomotion using a two-link rigid body model of leg and paw, which highlighted the dynamic interactions between segments. Comprehensive determination was made of cat segment parameters necessary for dynamic analysis, and regression equations were formulated to predict the inertial parameters of any comparable cat. Modulations in muscle and non-muscle components of knee and ankle joint moments were examined at two treadmill speeds using three gaits: (a) pace-like walk and trot-like walk, at 1.0 ms-1, and (b) gallop, at 2.1 ms-1. Results showed that muscle and segment interactive moments significantly effected limb trajectories during swing. Some moment components were greater in galloping than in walking, but net joint maxima were not significantly different between speeds. Moment magnitudes typically were greater for pace-like walking than for trot-like walking at the same speed. Generally, across gaits, the net and muscle moments were in phase with the direction of distal joint motion, and these same moments were out of phase with proximal joint motion. Intersegmental dynamics were not modulated exclusively by speed of locomotion, but interactive moments were also influenced significantly by gait mode.     

Proportions and function of the limbs of glyptodonts

Vizcaíno, S.F., Blanco, R.E., Bender, J.B. & Milne, N. 2010: Proportions and function of the limbs of glyptodonts. Lethaia, Vol. 44, pp. 93–101. This study examines the limb bone proportions and strength of glyptodonts (Xenarthra, Cingulata). Two methods are used to estimate the body mass and location of the centre of gravity of the articulated specimens. These estimates, together with measurements of the femur and humerus, are used to calculate strength indicators (SI). The other long bones of the limbs are used to calculate limb proportion indices that give an indication of digging ability, speed, and limb dominance in armadillos, the glyptodonts’ living closest relatives. The results show that regardless of how the body mass and centre of gravity are calculated, the majority of the glyptodont’s weight is borne by the hindlimbs. The SI calculations show that femora are sturdy enough to bear these loads. The fact that the femora have higher SI than the humerii indicates that sometimes the hindlimbs are required to bear an even greater proportion of the body weight, possibly when rising to a bipedal posture or pivoting on their hindlimbs to deliver a blow with their armoured tail. The analysis of limb proportions indicates that both the hindlimb and the forelimb have proportions that correlate strongly with body mass. This outcome supports the other results, but also shows that forelimbs must be also involved in manoeuvring the glyptodont body. □Glyptodonts, Mammalia, Xenarthra, limbs, strength indicators.     

Energetic benefits and adaptations in mammalian limbs: Scale effects and selective pressures

Differences in limb size and shape are fundamental to mammalian morphological diversity; however, their relevance to locomotor costs has long been subject to debate. In particular, it remains unknown if scale effects in whole limb morphology could partially underlie decreasing mass‐specific locomotor costs with increasing limb length. Whole fore‐ and hindlimb inertial properties reflecting limb size and shape—moment of inertia (MOI), mass, mass distribution, and natural frequency—were regressed against limb length for 44 species of quadrupedal mammals. Limb mass, MOI, and center of mass position are negatively allometric, having a strong potential for lowering mass‐specific locomotor costs in large terrestrial mammals. Negative allometry of limb MOI results in a 40% reduction in MOI relative to isometry's prediction for our largest sampled taxa. However, fitting regression residuals to adaptive diversification models reveals that codiversification of limb mass, limb length, and body mass likely results from selection for differing locomotor modes of running, climbing, digging, and swimming. The observed allometric scaling does not result from selection for energetically beneficial whole limb morphology with increasing size. Instead, our data suggest that it is a consequence of differing morphological adaptations and body size distributions among quadrupedal mammals, highlighting the role of differing limb functions in mammalian evolution.     

Changes in segment inertia proportions between 4 and 20 years

Growth between 4 and 20 yr produces an increase in body mass and a redistribution of that mass throughout the body. It is the purpose of this investigation to describe changes in the segment mass, radius to the mass centre and radius of gyration for a sample of males, 4-20 yr and the potential effects of these changes on joint reaction forces and moments. The data were collected annually over 9 yr in a mixed longitudinal study completed in 1985. Elliptical zones 2 cm wide were used to model the 16 segments of the body. From these and reported segment densities, mass, the coordinates of the mass centre and the principal moments of inertia were determined for the segments and the body. The parameters reported are the inertia parameters suitable for a sagittal planar analysis with the head and neck considered one segment and values given for other fused segments. The accuracy of the method was judged against the total body mass, and other accuracy estimates from the literature were examined. The parameters are presented as proportions of total mass or segment length. It is clear from the polynomial regressions that there is a substantial redistribution of the mass between segments and this is consistent with the principles of cephalo-caudal and distal-to-proximal development. The proportions for radius and radius of gyration indicate that mass redistribution within segments is comparatively small. The parameters for a 6 yr-old were compared to the parameters expected at 18, 24 and 54 yr and substantial differences noted.(ABSTRACT TRUNCATED AT 250 WORDS)     

Measurement of body segment mass,center of gravity,and determination of moments of inertia by double pendulum in Lemur fulvus

The collection of data on physical parameters of body segments is a preliminary critical step in studying the biomechanics of locomotion. Little data on nonhuman body segment parameters has been published. The lack of standardization of techniques for data collection and presentation has made the comparative use of these data difficult and at times impossible. This study offers an approach for collecting data on center of gravity and moments of inertia for standardized body segments. The double swing pendulum approach is proposed as a solution for difficulties previously encountered in calculating moments of inertia for body segments. A format for prompting a computer to perform these calculations is offered, and the resulting segment mass data for Lemur fulvus is presented.     

Segment interactions within the swing leg during unloaded and loaded running

In this study, designed to determine the effect of lower extremity inertia manipulation on joint kinetics and segment energetics during the swing phase, 15 male distance runners were filmed as they performed treadmill running (3.35 m s-1) under five load conditions: no added load and loads of 0.25 kg and 0.50 kg added to each thigh or each foot. Results of this study demonstrated that the energetics of the lower extremity movements during the swing phase of the running cycle were dominated by mechanical energy transfers between adjacent segments attributed to the joint reaction forces, which acted to redistribute mechanical energy within the system. These contributions were considerably greater than those of the net joint moments, which primarily reflected muscular generation and dissipation of mechanical energy. Lower extremity loading caused little change in the movement pattern of the swing leg. However, increases in the joint reaction forces and net moments and in the amount of work done and the energy transfer attributed to the reaction forces and moments were observed, but were limited to the joints proximal to the location of the added load. These results were consistent with the increased aerobic demand associated with increases in lower extremity inertia that have been reported elsewhere and also have implications for the manner in which the neuromuscular system controls the motion of the legs during running.