Suspending loads decreases load stability but may slightly improve body stability

Here, we seek to determine how compliantly suspended loads could affect the dynamic stability of legged locomotion. We theoretically model the dynamic stability of a human carrying a load using a coupled spring-mass-damper model and an actuated spring-loaded inverted pendulum model, as these models have demonstrated the ability to correctly predict other aspects of locomotion with a load in prior work, such as body forces and energetic cost. We report that minimizing the load suspension natural frequency and damping ratio significantly reduces the stability of the load mass but may slightly improve the body stability of locomotion when compared to a rigidly attached load. These results imply that a highly-compliant load suspension could help stabilize body motion during human, animal, or robot load carriage, but at the cost of a more awkward (less stable) load.     

An actuated dissipative spring-mass walking model: Predicting human-like ground reaction forces and the effects of model parameters

Simple models are widely used to understand the mechanics of human walking. The optimization-based minimal biped model and spring-loaded-inverted-pendulum (SLIP) model are two popular models that can achieve human-like walking patterns. However, ground reaction forces (GRF) from these two models still deviate from experimental data. In this paper, we proposed an actuated dissipative spring-mass model by integrating these two models to realize more human-like GRF patterns. We first explored the function of stiffness, damping, and weights of both energy cost and force cost in the objective function and found that these parameters have distinctly different influences on the optimized gait and GRF profiles. The stiffness and objective weight affect the number and size of peaks in the vertical GRF and stance time. The damping changes the relative size of the peaks but has little influence on stance time. Based on these observations, these parameters were manually tuned at three different speeds to approach experimentally measured vertical GRF and the highest correlation coefficient can reach 0.983. These results indicate that the stiffness, damping, and proper objective functions are all important factors in achieving human-like motion for this simple walking model. These findings can facilitate the understanding of human walking dynamics and may be applied in future biped models.     

Dynamic analysis of load carriage biomechanics during level walking

This paper describes an investigation into the biomechanical effects of load carriage dynamics on human locomotion performance. A whole body, inverse dynamics gait model has been developed which uses only kinematic input data to define the gait cycle. To provide input data, three-dimensional gait measurements have been conducted to capture whole body motion while carrying a backpack. A nonlinear suspension model is employed to describe the backpack dynamics. The model parameters for a particular backpack system can be identified using a dynamic load carriage test-rig. Biomechanical assessments have been conducted based on combined gait and pack simulations. It was found that the backpack suspension stiffness and damping have little effect on human locomotion energetics. However, decreasing suspension stiffness offers important biomechanical advantages. The peak values of vertical pack force, acting on the trunk, and lower limb joint loads are all moderated. This would reduce shoulder strap pressures and the risk of injury when heavy loads are carried.     

Resonance-based oscillations could describe human gait mechanics under various loading conditions

The oscillatory behavior of the center of mass (CoM) and the corresponding ground reaction force (GRF) of human gait for various gait speeds can be accurately described in terms of resonance using a spring–mass bipedal model. Resonance is a mechanical phenomenon that reflects the maximum responsiveness and energetic efficiency of a system. To use resonance to describe human gait, we need to investigate whether resonant mechanics is a common property under multiple walking conditions. Body mass and leg stiffness are determinants of resonance; thus, in this study, we investigated the following questions: (1) whether the estimated leg stiffness increased with inertia, (2) whether a resonance-based CoM oscillation could be sustained during a change in the stiffness, and (3) whether these relationships were consistently observed for different walking speeds. Seven healthy young subjects participated in over-ground walking trials at three different gait speeds with and without a 25-kg backpack. We measured the GRFs and the joint kinematics using three force platforms and a motion capture system. The leg stiffness was incorporated using a stiffness parameter in a compliant bipedal model that best fitted the empirical GRF data. The results showed that the leg stiffness increased with the load such that the resonance-based oscillatory behavior of the CoM was maintained for a given gait speed. The results imply that the resonance-based oscillation of the CoM is a consistent gait property and that resonant mechanics may be useful for modeling human gait.     

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.     

Lower-limb joint work and power are modulated during load carriage based on load configuration and walking speed

Soldiers regularly transport loads weighing >20 kg at slow speeds for long durations. These tasks elicit high energetic costs through increased positive work generated by knee and ankle muscles, which may increase risk of muscular fatigue and decrease combat readiness. This study aimed to determine how modifying where load is borne changes lower-limb joint mechanical work production, and if load magnitude and/or walking speed also affect work production. Twenty Australian soldiers participated, donning a total of 12 body armor variations: six different body armor systems (one standard-issue, two commercially available [cARM1-2], and three prototypes [pARM1-3]), each worn with two different load magnitudes (15 and 30 kg). For each armor variation, participants completed treadmill walking at two speeds (1.51 and 1.83 m/s). Three-dimensional motion capture and force plate data were acquired and used to estimate joint angles and moments from inverse kinematics and dynamics, respectively. Subsequently, hip, knee, and ankle joint work and power were computed and compared between armor types and walking speeds. Positive joint work over the stance phase significantly increased with walking speed and carried load, accompanied by 2.3–2.6% shifts in total positive work production from the ankle to the hip (p < 0.05). Compared to using cARM1 with 15 kg carried load, carrying 30 kg resulted in significantly greater hip contribution to total lower-limb positive work, while knee and ankle work decreased. Substantial increases in hip joint contributions to total lower-limb positive work that occur with increases in walking speed and load magnitude highlight the importance of hip musculature to load carriage walking.     

Body size effects on locomotion and load carriage in the highly polymorphic leaf-cutting ants Atta colombica and Atta cephalotes

Leaf-cutting ants reduce their walking speed under the weightof the leaf fragments they carry, an effect likely to havesome consequence for the foraging performance of a colony.I manipulated loads carried by workers from two Atta speciesto determine how load mass and body size affect walking speed.A comparison of speeds before and after load manipulation indicatesthat change in load mass has a linear effect on velocity. Several different regression models of speed as a function of loadsand body size have similar fit to the data, so a single bestmodel cannot easily be identified. However, there is statisticalevidence that the slope of the linear effect is more pronouncedfor smaller ants, an outcome most consistent with a regression model based on loading ratio, a metric that scales load massrelative to body mass. I then examined the effect of loadingratio on the leaf transport rate (the product of load massand carriage velocity). It has been claimed that this rateis maximized over a range of loading ratios that is the samefor all ants regardless of their size. However, I found thata latent body mass effect persists in the relation of transportrate to loading ratio, even though loading ratio is alreadyscaled relative to body mass. The maxima seem to be reachedonly at artificially elevated loading ratios, so that transportrates with natural fragments tend to be sub-maximal. This conclusionis in agreement with analytical predictions of rate-maximizingload masses derived from the regression models. Thus, loadingratio does not adequately scale load mass relative to bodysize when used in this context (effect on leaf transport rate),and should be used cautiously. Ants are likely to accommodateloads through modulation of both stride length and step frequency,but precisely how this takes place requires future study.     

Energy cost of balance control during walking decreases with external stabilizer stiffness independent of walking speed

Human walking requires active neuromuscular control to ensure stability in the lateral direction, which inflicts a certain metabolic load. The magnitude of this metabolic load has previously been investigated by means of passive external lateral stabilization via spring-like cords. In the present study, we applied this method to test two hypotheses: (1) the effect of external stabilization on energy cost depends on the stiffness of the stabilizing springs, and (2) the energy cost for balance control, and consequently the effect of external stabilization on energy cost, depends on walking speed. Fourteen healthy young adults walked on a motor driven treadmill without stabilization and with stabilization with four different spring stiffnesses (between 760 and 1820 N m⁻¹) at three walking speeds (70%, 100%, and 130% of preferred speed). Energy cost was calculated from breath-by-breath oxygen consumption. Gait parameters (mean and variability of step width and stride length, and variability of trunk accelerations) were calculated from kinematic data. On average external stabilization led to a decrease in energy cost of 6% (p<0.005) as well as a decrease in step width (24%; p<0.001), step width variability (41%; p<0.001) and variability of medio-lateral trunk acceleration (12.5%; p<0.005). Increasing stabilizer stiffness increased the effects on both energy cost and medio-lateral gait parameters up to a stiffness of 1260 N m⁻¹. Contrary to expectations, the effect of stabilization was independent of walking speed (p=0.111). These results show that active lateral stabilization during walking involves an energetic cost, which is independent of walking speed.     

A phenomenological model for estimating metabolic energy consumption in muscle contraction

A phenomenological model for muscle energy consumption was developed and used in conjunction with a simple Hill-type model for muscle contraction. The model was used to address two questions. First, can an empirical model of muscle energetics accurately represent the total energetic behavior of frog muscle in isometric, isotonic, and isokinetic contractions? And second, how does such a model perform in a large-scale, multiple-muscle model of human walking? Four simulations were conducted with frog sartorius muscle under full excitation: an isometric contraction, a set of isotonic contractions with the muscle shortening a constant distance under various applied loads, a set of isotonic contractions with the muscle shortening over various distances under a constant load, and an isokinetic contraction in lengthening. The model calculations were evaluated against results of similar thermal in vitro experiments performed on frog sartorius muscle. The energetics model was then incorporated into a large-scale, multiple-muscle model of the human body for the purpose of predicting energy consumption during normal walking. The total energy estimated by the model accurately reflected the observed experimental behavior of frog muscle for an isometric contraction. The model also accurately reproduced the experimental behavior of frog muscle heat production under isotonic shortening and isokinetic lengthening conditions. The estimated rate of metabolic energy consumption for walking was 29% higher than the value typically obtained from gait measurements.     

Mass-dependence in the predation risk of unequal competitors; some models

Foragers can monitor their survival through the size of body reserves in a starvation/predation risk trade-off. Energy reserves reduce the risk of energetic shortfall, while survival will be maximised at intermediate reserve levels when there is a cost of carrying mass loads. The size of reserves that will maximise survival may not be identical for unequal competitors, when unequal access to resources will affect the costs and benefits of energy reserves. Here, I evaluate the effect of competitive ability (dominance) for the mass-dependence in predation risk and how it is affected by (1) attack rate (attack rate effect), (2) distance to the emergence of an unconcealed predator attack (attack distance effect) and (3) distance to cover (cover distance effect). This general model is illustrated by empirical data for parameters specific for birds. The effect of competitive ability for the mass-dependence in predation risk is ambiguous and depends on how rank is mediated into mass-dependent predation risk. Dominants pay a lower cost in predation risk for mass loads than sub-ordinates when competitive ability entails that they feed closer to cover (cover distance effect) and when the exposure to attacks and attack rate is lower than for sub-ordinates (attack rate effect) . In contrast, a shorter distance to the emergence of an unconcealed attack (attack distance effect) implies a lower increase in predation risk with mass for sub-ordinates. As a consequence of how the cost of mass load varies with conditions there is no unambiguous relationship for how predation risk can be traded off for starvation risk for individuals with different competitive ability.     

External load can alter the energy cost of prolonged exercise

The present study was undertaken to examine the energy cost of prolonged walking while carrying a backpack load. Six trained subjects were tested while walking for 120 min on a treadmill at a speed of 1.25 m.s-1 and 5% elevation with a well fitted backpack load of 25 and 40 kg alternately. Carrying 40 kg elicited a significantly higher (p less than 0.01) energy cost than 25 kg. Furthermore, whereas carrying 25 kg resulted in a constant energy cost, 40 kg yielded a highly significant (p less than 0.05) increase in energy cost over time. The study implies that increase in load causes physical fatigue, once work intensity is higher than 50% maximal work capacity. This is probably due to altered locomotion biomechanics which in turn lead to the increase in energy cost. Finally, the prediction model which estimates energy cost while carrying loads should be used with some caution when applied to heavy loads and long duration of exercise, since it might underestimate the actual energy cost.     

Compliant bipedal model with the center of pressure excursion associated with oscillatory behavior of the center of mass reproduces the human gait dynamics

Although the compliant bipedal model could reproduce qualitative ground reaction force (GRF) of human walking, the model with a fixed pivot showed overestimations in stance leg rotation and the ratio of horizontal to vertical GRF. The human walking data showed a continuous forward progression of the center of pressure (CoP) during the stance phase and the suspension of the CoP near the forefoot before the onset of step transition. To better describe human gait dynamics with a minimal expense of model complexity, we proposed a compliant bipedal model with the accelerated pivot which associated the CoP excursion with the oscillatory behavior of the center of mass (CoM) with the existing simulation parameter and leg stiffness. Owing to the pivot acceleration defined to emulate human CoP profile, the arrival of the CoP at the limit of the stance foot over the single stance duration initiated the step-to-step transition. The proposed model showed an improved match of walking data. As the forward motion of CoM during single stance was partly accounted by forward pivot translation, the previously overestimated rotation of the stance leg was reduced and the corresponding horizontal GRF became closer to human data. The walking solutions of the model ranged over higher speed ranges (~1.7 m/s) than those of the fixed pivoted compliant bipedal model (~1.5 m/s) and exhibited other gait parameters, such as touchdown angle, step length and step frequency, comparable to the experimental observations. The good matches between the model and experimental GRF data imply that the continuous pivot acceleration associated with CoM oscillatory behavior could serve as a useful framework of bipedal model.     

Increased musculoskeletal stiffness during load carriage at increasing walking speeds maintains constant vertical excursion of the body center of mass

The primary objective of this research was to determine changes in body and joint stiffness parameters and kinematics of the knee and body center of mass (COM), that result from wearing a backpack (BP) with a 40% body weight load at increasing speeds of walking. It was hypothesized that there would be speed and load-related increases in stiffness that would prevent significant deviations in the COM trajectory and in lower-extremity joint angles. Three independent biomechanical models employing kinematic data were used to estimate global lower-extremity stiffness, vertical stiffness and knee joint rotational stiffness in the sagittal plane during walking on a treadmill at speeds of 0.6-1.6 ms(-1) in 0.2 ms(-1) increments in BP and no backpack conditions. Kinematic data were collected using an Optotrak, three-dimensional motion analysis system. Knee angles and vertical excursion of the COM during the compression (loading phase) increased as a function of speed but not load. All three estimates of stiffness showed significant increases as a function of both speed and load. Significant interaction effects indicated a convergence of load-related stiffness values at lower speeds. Results suggested that increases in muscle-mediated stiffness are used to maintain a constant vertical excursion of the COM under load across the speeds tested, and thereby limit increases in metabolic cost that would occur if the COM would travel through greater vertical range of motion.     

Predicting human walking gaits with a simple planar model

Models of human walking with moderate complexity have the potential to accurately capture both joint kinematics and whole body energetics, thereby offering more simultaneous information than very simple models and less computational cost than very complex models. This work examines four- and six-link planar biped models with knees and rigid circular feet. The two differ in that the six-link model includes ankle joints. Stable periodic walking gaits are generated for both models using a hybrid zero dynamics-based control approach. To establish a baseline of how well the models can approximate normal human walking, gaits were optimized to match experimental human walking data, ranging in speed from very slow to very fast. The six-link model well matched the experimental step length, speed, and mean absolute power, while the four-link model did not, indicating that ankle work is a critical element in human walking models of this type. Beyond simply matching human data, the six-link model can be used in an optimization framework to predict normal human walking using a torque-squared objective function. The model well predicted experimental step length, joint motions, and mean absolute power over the full range of speeds.     

Forward dynamic simulation of bipedal walking in the Japanese macaque: investigation of causal relationships among limb kinematics, speed, and energetics of bipedal locomotion in a nonhuman primate

Japanese macaques that have been trained for monkey performances exhibit a remarkable ability to walk bipedally. In this study, we dynamically reconstructed bipedal walking of the Japanese macaque to investigate causal relationships among limb kinematics, speed, and energetics, with a view to understanding the mechanisms underlying the evolution of human bipedalism. We constructed a two-dimensional macaque musculoskeletal model consisting of nine rigid links and eight principal muscles. To generate locomotion, we used a trajectory-tracking control law, the reference trajectories of which were obtained experimentally. Using this framework, we evaluated the effects of changes in cycle duration and gait kinematics on locomotor efficiency. The energetic cost of locomotion was estimated based on the calculation of mechanical energy generated by muscles. Our results demonstrated that the mass-specific metabolic cost of transport decreased as speed increased in bipedal walking of the Japanese macaque. Furthermore, the cost of transport in bipedal walking was reduced when vertical displacement of the hip joint was virtually modified in the simulation to be more humanlike. Human vertical fluctuations in the body's center of mass actually contributed to energy savings via an inverted pendulum mechanism.     

Predicting metabolic cost of running with and without backpack loads

In the past, a mathematical equation to predict the metabolic cost of standing or walking (Mw) was developed. However, this equation was limited to speeds less than 2.2 m.s-1 and overestimated the metabolic cost of walking or running at higher speeds. The purpose of this study was, therefore, to develop a mathematical model for the metabolic cost of running (Mr), in order to be able to predict the metabolic cost under a wide range of speeds, external loads and grades. Twelve male subjects were tested on a level treadmill under different combinations of speed and external load. Speed varied between 2.2 to 3.2 m.s-1 using 0.2 m.s-1 intervals and external loads between 0-30 kg with 10 kg intervals. Four of the subjects were also tested at 2 and 4% incline while speed and load remained constant (2.4 m.s-1, 20 kg). The model developed is based on Mw and is proportionately linear with external load (L) carried as follows: Mr = Mw-0.5 (1-0.01L)(Mw -15L-850), (watt) The correlation coefficient between predicted and observed values was 0.99 (P less than 0.01) with SER of 7.7%. The accuracy of the model was validated by its ability to predict the metabolic cost of running under different conditions extracted from the literature. A highly significant correlation (r = 0.95, P less than 0.02, SER = 6.5%) was found between our predicted and the reported values. In conclusion, the new equation permits accurate calculation of energy cost of running under a large range of speeds, external loads and inclines.     

Physiological responses to prolonged treadmill walking with external loads

Limited information is available regarding the physiological responses to prolonged load carriage. This study determined the energy cost of prolonged treadmill walking (fixed distance of 12 km) at speeds of 1.10 m.s-1, 1.35 m.s-1, and 1.60 m.s-1, unloaded (clothing mass 5.2 kg) and with external loads of 31.5 and 49.4 kg. Fifteen male subjects performed nine trials in random order over a 6-week period. Oxygen uptake (VO2) was determined at the end of the first 10 min and every 20 min thereafter. A 10-min rest period was allowed following each 50 min of walking. No changes occurred in VO2 over time in the unloaded condition at any speed. The 31.5 and 49.4 kg loads, however, produced significant increases (ranging from 10 to 18%) at the two fastest and at all three speeds, respectively, even at initial exercise intensities less than 30% VO2max. In addition, the 49.4 kg load elicited a significantly higher (P less than 0.05) VO2 than did the 31.5 kg load at all speeds. The measured values of metabolic cost were also compared to those predicted using the formula of Pandolf et al. In trials where VO2 increased significantly over time, predicted values underestimated the actual metabolic cost during the final minute by 10-16%. It is concluded that energy cost during prolonged load carriage is not constant but increases significantly over time even at low relative exercise intensities. It is further concluded that applying the prediction model which estimates energy expenditure from short-term load carriage efforts to prolonged load carriage can result in significant underestimations of the actual energy cost.     

How close to a pendulum is human upper limb movement during walking?

The aim of this work was to investigate how close to pendulum-like behaviour the periodic motion of the human upper limb (or upper extremity) is, during normal walking at a comfortable speed of locomotion. Twenty-five healthy young persons (males and females) participated in the experiment. Biomechanical testing was undertaken (mass and centre of mass of each segment of the total upper extremity). Participants were walking on a treadmill with a standardised velocity of 1.1 ms(-1) (comfortable speed for all of them). A video analysis system with Silicon software was used to measure the different angles of the arm and forearm. The theoretical period of motion and maximal angular velocity were computed for the centre of mass of the total upper limb from the measured phases of the arm swing and associated positional potential energies. Actual measured periods of motion, in comparison, represented a level of similarity to a lightly damped simple pendulum. Using this assumption, the "damping factor" was calculated from the ratio between theoretical and measured values. A vast majority of people exhibited an actual angular velocity exceeding the expected theoretical angular velocity calculated for a virtual pendulum of similar mass and length characteristics. This may be due to muscle forces that are contributing to the motion of the upper limb during walking rather than simple gravity force acting alone. The observed positional potential energy of the dominant limb was greater than that of the non-dominant limb for the vast majority of participants.     

Energetics of walking and running: insights from simulated reduced-gravity experiments.

On Earth, a person uses about one-half as much energy to walk a mile as to run a mile. On another planet with lower gravity, would walking still be more economical than running? When people carry weights while they walk or run, energetic cost increases in proportion to the added load. It would seem to follow that if gravity were reduced, energetic cost would decrease in proportion to body weight in both gaits. However, we find that under simulated reduced gravity, the rate of energy consumption decreases in proportion to body weight during running but not during walking. When gravity is reduced by 75%, the rate of energy consumption is reduced by 72% during running but only by 33% during walking. Because reducing gravity decreases the energetic cost much more for running than for walking, walking is not the cheapest way to travel a mile at low levels of gravity. These results suggest that the link between the mechanics of locomotion and energetic cost is fundamentally different for walking and for running.     

Energetics of locomotion and load carriage in the nectar feeding ant, Camponotus rufipes

Abstract.  To investigate if there is an energetic constraint influencing a nectar feeding ant's decision to come back to the nest with partial loads, the energetic costs of running and carrying a load in the ant Camponotus rufipes are measured. Metabolic rates of individuals are measured in a running tube respirometer while they are unladen and laden at 25 °C. Workers voluntarily collect a load of 6 µL of a 30% sucrose solution (mass = 6.8 mg), which results in an internal load of about 50% of the ant mass and is close to a full load for ants within this size range. The gross cost of unladen running is 264 J kg⁻¹ m⁻¹, while that of laden running is 225 J kg⁻¹ m⁻¹. The mass used to calculate the cost of laden running includes body mass of ant and load carried. Load carriage cost in C. rufipes foragers is calculated to be about 60% as much as body carriage per unit mass. Internal load carriage in C. rufipes is energetically cheaper compared with external carriage in other ant species. Such low carriage costs make it unlikely that the collection of partial crop loads in C. rufipes foragers is based on a minimization of foraging costs, as suggested for honeybees.