The mechanics of jumping by a dog (Canis familiaris)

A force platform has been used to obtain records of the forces exerted on the ground by an Alsatian dog, during take-off for running long jumps and standing scale jumps. The records have been analysed in conjunction with cinematograph film, taken simultaneously, and anatomical data. Stresses in the principal muscles of the hind limb, and in the triceps, have been calculated and the values obtained are compared with the stresses found by other investigators in isometric experiments with excised mammal muscles. Stresses in certain tendons and bones have been calculated, and the values obtained are compared with published values for the strength of tendon and bone. Evidence is presented that the gastrocnemius and plantaris muscles behave, in take-off for a jump, essentially as passive elastic bodies. Most of the elastic energy is probably stored in their tendons. A tendency for distal limb muscles to be pinnate, with much shorter fibres than proximal limb muscles, is noted and discussed.     

Influence of muscle activity on the forces in the femur: An in vivo study

Experiments were performed on two patients with custom-made instrumented massive proximal femoral prostheses implanted after tumour resection. In vivo axial forces transmitted along the prostheses were telemetered during level walking, single- and double-leg stance, and isometric exercises of the hip muscles. These activities varied the lever arms available to the external loads: minimum for double-leg stance and maximum for hip isometric exercises. Kinematic, force plate, EMG and telemetered force data were recorded simultaneously. The force magnification ration (FMR; the ratio of the telemetered axial force to the external force) was calculated. The FMRs ranged from 1.3 (during double-leg stance) to 29.8 (during abductors test), indicating that a major part of the axial force in the long bones is a response to muscle activity, the strength of which depends on the lever arms available to the external loads. From these results, it was shown that the bulk of the bending moment along limbs is transmitted by a combination of tensile forces in muscles and compressive forces in bones, so moments transmitted by the bones are smaller than the limb moments. It was concluded that appropriate simulation of muscle forces is important in experimental or theoretical studies of load transmission along bones.     

Estimating the muscle forces generated in the human lower extremity when walking: a physiological solution

A model capable of estimating individual muscle activity during human lower extremity activity has been developed. This model was implemented and applied to normal gait. Both 3D cinematography and force platform records were collected to define the kinematics of the lower limb segments and the ground reaction forces. From these data the lengths, velocities, and moment arms of the muscles and the net muscle moments were calculated. These data were then used to estimate the output from a set of pattern generators which specified the neural input to and hence the force generated in each muscle. Results were obtained which demonstrate that it is feasible to construct a hierarchical physiological model which will estimate individual muscle forces. This statement must be tempered somewhat in that better anatomical and neurophysiological data must be made available and that this model, and all others attempting to estimate individual muscle forces, must be rigorously tested before being applied in a research, sports, or clinical setting.     

Elastic properties of the forefoot of the Donkey, Equus asinus

The elastic properties of the forefeet of Donkeys, and of tendons removed from the feet, have been investigated in dynamic tests at a frequency chosen to simulate running. The elastic properties of the foot are explained in terms of the properties of individual tendons and check ligaments. The elastic strain energy stored in the foot, during a trotting step, is calculated to be only a little less than the optimum quantity which would minimize the work required of the muscles in this gait. Frictional and viscous energy losses were fairly small in the experiments on feet, and would probably be smaller in the intact animal.     

Mechanics of running of the ostrich (Struthio camelus)

Ostriches have been filmed running fast in their natural habitat. A female ostrich has been dissected and the principal bones, muscles and tendons in a leg have been measured. It is calculated that stresses up to 240 kN m⁻² and 40 MN m⁻², respectively, act in the digital flexor muscles and their tendons during running. Tensile and compressive stresses up to about 70MNm⁻² and 110 MNm⁻² act in the tibiotarsus. A large proportion of the energy which would otherwise be required for running is probably saved by elastic storage in tendons. Comparisons are made with the legs of flying birds and of antelopes.     

Relative shortening velocity in locomotor muscles: turkey ankle extensors operate at low V/V(max)

The force-velocity properties of skeletal muscle have an important influence on locomotor performance. All skeletal muscles produce less force the faster they shorten and typically develop maximal power at velocities of approximately 30% of maximum shortening velocity (V(max)). We used direct measurements of muscle mechanical function in two ankle extensor muscles of wild turkeys to test the hypothesis that during level running muscles operate at velocities that favor force rather than power. Sonomicrometer measurements of muscle length, tendon strain-gauge measurements of muscle force, and bipolar electromyographs were taken as animals ran over a range of speeds and inclines. These measurements were integrated with previously measured values of muscle V(max) for these muscles to calculate relative shortening velocity (V/V(max)). At all speeds for level running the V/V(max) values of the lateral gastrocnemius and the peroneus longus were low (<0.05), corresponding to the region of the force-velocity relationship where the muscles were capable of producing 90% of peak isometric force but only 35% of peak isotonic power. V/V(max) increased in response to the demand for mechanical power with increases in running incline and decreased to negative values to absorb energy during downhill running. Measurements of integrated electromyograph activity indicated that the volume of muscle required to produce a given force increased from level to uphill running. This observation is consistent with the idea that V/V(max) is an important determinant of locomotor cost because it affects the volume of muscle that must be recruited to support body weight.     

Stresses exerted in the hindlimb muscles of common chimpanzees (Pan troglodytes) during bipedal locomotion

Recent studies have indicated that chimpanzee bipedality is mechanically inefficient and dynamically unlike that of humans, thus undermining the chimpanzee analogy for mechanical aspects of the early evolution of hominid bipedalism. This paper continues this theme by measuring the forces and stresses engendered by the muscles during bipedal locomotion, for an untrained chimpanzee and for data from chimpanzees which have been encouraged to walk bipedally, presented in the literature. Peak stresses in the triceps surae were lower for the untrained chimpanzee than for the trained subjects because during the late stance phase, when peak ankle moments occur, the centre of pressure of the ground reaction force on the foot of the untrained chimpanzee stayed close to the ankle joint. In contrast, for the trained subjects it moved closer to the toes, as in human bipedalism. Quadriceps and hip extensor stresses are approximately 30% larger for the untrained chimpanzee than for the trained subjects, because the trained chimpanzees walked with a more erect posture. These results may reflect the way in which muscles can develop in response to training, since research on humans has shown that muscle physiological cross-sectional area increases as a result of exercise, resulting in smaller stresses for a given muscle force. During a slow walk, untrained chimpanzees were found to exert far greater muscle stresses than humans do when running at moderate speed, particularly in the muscles that extend the hip, because of the bent-hip, bent-knee posture.     

Joint moments and contact forces in the foot during walking

The net force and moment of a joint have been widely used to understand joint disease in the foot. Meanwhile, it does not reflect the physiological forces on muscles and contact surfaces. The objective of the study is to estimate active moments by muscles, passive moments by connective tissues and joint contact forces in the foot joints during walking. Joint kinematics and external forces of ten healthy subjects (all males, 24.7 ± 1.2 years) were acquired during walking. The data were entered into the five-segment musculoskeletal foot model to calculate muscle forces and joint contact forces of the foot joints using an inverse dynamics-based optimization. Joint reaction forces and active, passive and net moments of each joint were calculated from muscle and ligament forces. The maximum joint reaction forces were 8.72, 4.31, 2.65, and 3.41 body weight (BW) for the ankle, Chopart’s, Lisfranc and metatarsophalangeal joints, respectively. Active and passive moments along with net moments were also obtained. The maximum net moments were 8.6, 8.4, 5.4 and 0.8%BW∙HT, respectively. While the trend of net moment was very similar between the four joints, the magnitudes and directions of the active and passive moments varied between joints. The active and passive moments during walking could reveal the roles of muscles and ligaments in each of the foot joints, which was not obvious in the net moment. This method may help narrow down the source of joint problems if applied to clinical studies.     

Mechanical stresses in fast locomotion of buffalo (Syncews coffer) and elephant (Loxodonta africana)

Films of buffalo and elephant running, and detailed measurements on dissected legs, have been used to estimate the maximum stresses which occur in locomotion, in certain muscles, tendons and bones. These stresses are similar to stresses previously determined for some other, smaller mammals.     

Individual muscle force parameters and fiber operating ranges for elbow flexion-extension and forearm pronation-supination

We have quantified individual muscle force and moment contributions to net joint moments and estimated the operating ranges of the individual muscle fibers over the full range of motion for elbow flexion/extension and forearm pronation/supination. A three dimensional computer graphics model was developed in order to estimate individual muscle contributions in each degree of freedom over the full range of motion generated by 17 muscles crossing the elbow and forearm. Optimal fiber length, tendon slack length, and muscle specific tension values were adjusted within the literature range from cadaver studies such that the net isometric joint moments of the model approximated experimental joint moments within one standard deviation. Analysis of the model revealed that the muscles operate on varying portions of the ascending limb, plateau region, and descending limb of the force-length curve. This model can be used to further understand isometric force and moment contributions of individual muscles to net joint moments of the arm and forearm and can serve as a comprehensive reference for the forces and moments generated by 17 major muscles crossing the elbow and wrist.     

Force platforms as ergometers.

Walking and running on the level involves external mechanical work, even when speed averaged over a complete stride remains constant. This work must be performed by the muscles to accelerate and/or raise the center of mass of the body during parts of the stride, replacing energy which is lost as the body slows and/or falls during other parts of the stride. External work can be measured with fair approximation by means of a force plate, which records the horizontal and vertical components of the resultant force applied by the body to the ground over a complete stride. The horizontal force and the vertical force minus the body weight are integrated electronically to determine the instantaneous velocity in each plane. These velocities are squared and multiplied by one-half the mass to yield the instantaneous kinetic energy. The change in potential energy is calculated by integrating vertical velocity as a function of time to yield vertical displacement and multiplying this by body weight. The total mechanical energy as a function of time is obtained by adding the instantaneous kinetic and potential energies. The positive external mechanical work is obtained by adding the increments in total mechanical energy over an integral number of strides.     

Structural Mechanics of DNA Wrapping in the Nucleosome

Experimental X-ray crystal structures and a database of calculated structural parameters of DNA octamers were used in combination to analyse the mechanics of DNA bending in the nucleosome core complex. The 1kx5 X-ray crystal structure of the nucleosome core complex was used to determine the relationship between local structure at the base-step level and the global superhelical conformation observed for nucleosome-bound DNA. The superhelix is characterised by a large curvature (597°) in one plane and very little curvature (10°) in the orthogonal plane. Analysis of the curvature at the level of 10-step segments shows that there is a uniform curvature of 30° per helical turn throughout most of the structure but that there are two sharper kinks of 50° at ± 2 helical turns from the central dyad base pair. The curvature is due almost entirely to the base-step parameter roll. There are large periodic variations in roll, which are in phase with the helical twist and account for 500° of the total curvature. Although variations in the other base-step parameters perturb the local path of the DNA, they make minimal contributions to the total curvature. This implies that DNA bending in the nucleosome is achieved using the roll-slide-twist degree of freedom previously identified as the major degree of freedom in naked DNA oligomers. The energetics of bending into a nucleosome-bound conformation were therefore analysed using a database of structural parameters that we have previously developed for naked DNA oligomers. The minimum energy roll, the roll flexibility force constant and the maximum and minimum accessible roll values were obtained for each base step in the relevant octanucleotide context to account for the effects of conformational coupling that vary with sequence context. The distribution of base-step roll values and corresponding strain energy required to bend DNA into the nucleosome-bound conformation defined by the 1kx5 structure were obtained by applying a constant bending moment. When a single bending moment was applied to the entire sequence, the local details of the calculated structure did not match the experiment. However, when local 10-step bending moments were applied separately, the calculated structure showed excellent agreement with experiment. This implies that the protein applies variable bending forces along the DNA to maintain the superhelical path required for nucleosome wrapping. In particular, the 50° kinks are constraints imposed by the protein rather than a feature of the 1kx5 DNA sequence. The kinks coincide with a relatively flexible region of the sequence, and this is probably a prerequisite for high-affinity nucleosome binding, but the bending strain energy is significantly higher at these points than for the rest of the sequence. In the most rigid regions of the sequence, a higher strain energy is also required to achieve the standard 30° curvature per helical turn. We conclude that matching of the DNA sequence to the local roll periodicity required to achieve bending, together with the increased flexibility required at the kinks, determines the sequence selectivity of DNA wrapping in the nucleosome.     

Elastic energy savings and active energy cost in a simple model of running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic “Spring-mass” computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s^-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.     

Elastic properties of the hind foot of the Donkey, Equus asinus

The elastic properties of the hind feet of Donkeys, and of tendons removed from the feet, have been investigated by methods similar to those used in a previous study of the forefoot. The elastic strain energy stored in the foot, during a trotting step, is calculated to be approximately the optimum which would minimize the work required of the muscles in this gait.     

Mechanically simulated muscle forces strongly stabilize intact and injured upper cervical spine specimens

Although muscles are assumed to be capable of stabilizing the spinal column in vivo, they have only rarely been simulated in vitro. Their effect might be of particular importance in unstable segments. The present study therefore tests the hypothesis that mechanically simulated muscle forces stabilize intact and injured cervical spine specimens. In the first step, six human occipito-cervical spine specimens were loaded intact in a spine tester with pure moments in lateral bending (+/- 1.5 N m), flexion-extension (+/- 1.5 N m) and axial rotation (+/- 0.5 N m). In the second step, identical flexibility tests were carried out during constant traction of three mechanically simulated muscle pairs: splenius capitits (5 N), semispinalis capitis (5 N) and longus colli (15 N). Both steps were repeated after unilateral and bilateral transection of the alar ligaments. The muscle forces strongly stabilized C0-C2 in all loading and injury states. This was most obvious in axial rotation, where a reduction of range of motion (ROM) and neutral zone to <50% (without muscles=100%) was observed. With increasing injury the normalized ROM (intact condition=100%) increased with and without muscles approximately to the same extend. With bilateral injury this increase was 125-132% in lateral bending, 112%-119% in flexion-extension and 103-116% in axial rotation. Mechanically simulated cervical spine muscles strongly stabilized intact and injured cervical spine specimens. Nevertheless, it could be shown that in vitro flexibility tests without muscle force simulation do not necessarily lead to an overestimation of spinal instability if the results are normalized to the intact state.     

Relationship between mechanomyogram signals and changes in force of human forefinger flexor muscles during voluntary contraction

In previous studies on mechanomyogram (MMG) signals no analysis of these signals accompanying force generation has been performed. Therefore, we have recorded MMG signals (previously referred to as muscle sound or acoustomyographic signals) during voluntary contractions of forefinger flexor muscles in 31 young subjects. These subjects made contractions to produce force records of triangular or trapeziform shape. The peak target force amounted to 10, 20 or 40 N which represented less than 40% of maximal voluntary contraction. The MMG signals during the transient phases of force generation at three different rates were analysed. The MMG intensity level calculated for MMG records and the peak-to-peak amplitude of MMG signals correlated with both the velocity of force increase and the contraction force. The occurrence of the strongest MMG signals corresponded to changes in contractile force. Therefore, it is suggested that measurements of these parameters could be a useful tool in studies of changes in contractile force. Accepted: 11 March 1998     

Optimum stiffness for leg bones

A limb bone will be lighter if it is made thinner. However, thinner bones are more flexible (for given length and shape of cross-section) so their muscles must shorten more to move the distal end of the bone against a resisting force. To shorten more, a muscle needs longer muscle fibres and so must be heavier. Thus a particular thickness for the bone will enable the combined mass of bone plus muscle to be minimized. Peak stresses due to bending moments, in bones that were optimized according to this criterion, would be about ±70 MPa. Stresses of about this magnitude have been found in leg bones of various mammals, in strenuous activities such as running and jumping. However, similar stresses might be predicted on grounds of strength requirements, to give adequate factors of safety.     

Multi-functionality of the cat medical gastrocnemius during locomotion

The functional role of biarticular muscles was investigated based on direct force measurement in the cat medial gastrocnemius (MG) and analysis of hindlimb kinematics and kinetics for the stance phase of level, uphill, and downhill walking. Four primary functional roles of biarticular muscles have been proposed in the past. These functional roles have typically been discussed independently of each other, and biarticular muscles have rarely been assigned more than one functional roles for different phases of the work cycle. The purpose of this study was to elucidate the functional role of the biarticular cat MG during locomotion. It was found that MG forces were primarily associated with the moment requirements at the ankle for most of the stance phase, but also helped to satisfy the moments at the knee in the initial phase of stance. In the second half of stance, MG transferred mechanical energy from the knee to the ankle from the knee to the ankle, while simultaneously producing a substantial amount of mechanical work. Based on these results, we hypothesize that MG's primary function is that of an ankle extensor. However, because of the coupling of the ankle extensor moment with a knee flexor moment in the initial, and a knee extensor moment in the final phase of stance, MG satisfies two joint moments in early stance, and transfers mechanical energy from the knee to the ankle in late stance. We conclude that cat MG has multiple functional roles during the stance phase of locomotion, and speculate that such multi-functionality also exists in other bi- and multi-articular muscles.     

Field measurement of the dynamics of the bull kelp Durvillaeaantarctica (Chamisso) Heriot

Seaweed habitats and morphological development are strongly affected by wave forces. Novel measurements were made of the force dynamics of the large intertidal macroalga Durvillaeaantarctica under the influence of wave action. Synchronized video, a pressure sensor and a resistance wave gauge provided data describing the wave field. The response of seaweeds to waves was gauged using instrumentation mounted directly on the seaweed, including accelerometers and displacement and force transducers. These field measurements were used to estimate forces and bending moments acting at the holdfast, where failure is most likely to occur. For waves of the order of 0.5 m high, we measured maximum forces on the stipe of around 300 N and blade accelerations that exceeded 30 m s⁻². During large wave events, inferred bending moments at the base of the stipe reached average values of around 140 N m. There was a decoupling between the blade response and the force experienced at the stipe base. Furthermore, changes in water depth throughout the tidal cycle had a systematic effect on blade accelerations and moments at the holdfast.