scholarly journals Energetically optimal running requires torques about the centre of mass

2012 ◽  
Vol 9 (73) ◽  
pp. 2011-2015 ◽  
Author(s):  
James R. Usherwood ◽  
Tatjana Y. Hubel
Keyword(s):  
Large Body ◽  
The Body ◽  
Moment Of Inertia ◽  
Mechanical Work ◽  
Vertical Force ◽  
Centre Of Mass ◽  
Pitch Moment ◽  
Tail Structure ◽  
Reaction Forces ◽  
Long Head

Bipedal animals experience ground reaction forces (GRFs) that pass close to the centre of mass (CoM) throughout stance, first decelerating the body, then re-accelerating it during the second half of stance. This results in fluctuations in kinetic energy, requiring mechanical work from the muscles. However, here we show analytically that, in extreme cases (with a very large body pitch moment of inertia), continuous alignment of the GRF through the CoM requires greater mechanical work than a maintained vertical force; we show numerically that GRFs passing between CoM and vertical throughout stance are energetically favourable under realistic conditions; and demonstrate that the magnitude, if not the precise form, of actual CoM-torque profiles in running is broadly consistent with simple mechanical work minimization for humans with appropriate pitch moment of inertia. While the potential energetic savings of CoM-torque support strategies are small (a few per cent) over the range of human running, their importance increases dramatically at high speeds and stance angles. Fast, compliant runners or hoppers would benefit considerably from GRFs more vertical than the zero-CoM-torque strategy, especially with bodies of high pitch moment of inertia—suggesting a novel advantage to kangaroos of their peculiar long-head/long-tail structure.

The influence of boot longitudinal flexural stiffness on external mechanical work and running economy during skate roller-skiing: A case study

2019 ◽  
Vol 233 (4) ◽  
pp. 548-558
Author(s):  
Jurij Hladnik ◽  
Matej Supej ◽  
Janez Vodičar ◽  
Boris Jerman
Keyword(s):  
Rolling Resistance ◽  
Forward Direction ◽  
Running Economy ◽  
Mechanical Work ◽  
Flexural Stiffness ◽  
Centre Of Mass ◽  
Reaction Forces ◽  
The Impact ◽  
Derivatives Of

This case study examines the impact of boot longitudinal flexural stiffness on the total external mechanical work of a skier’s centre of mass per distance travelled in the forward direction ([Formula: see text] EX (J/m)) and on running economy during skate roller-skiing under submaximal steady-state conditions. Moreover, it analyses time derivatives of total W EX, of W EX performed by the roller-skis and poles, respectively, and of the directly useful mechanical work (the sum of the work to overcome centre of mass’ gravity and rolling resistance) within a typical roller-skiing cycle. Multiple roller-skiing trials (G3 technique) were performed by one subject on an inclined treadmill with boots of soft, intermediate, and stiff flexural stiffness. The orientation and magnitude of the roller-ski and pole ground reaction forces, body kinematics, VO2, and lactic acid concentration were monitored. The stiff boots had 13.4% ( p < 0.01) lower [Formula: see text] EX compared to the intermediate boots, and 20.7% ( p < 0.001) lower [Formula: see text] EX compared to the soft boots. Regarding running economy, the soft boots had 2.2% ( p < 0.05) higher VO2 compared to the intermediate boots, but the same VO2 compared to the stiff boots. In conclusion, the soft boots had significantly higher [Formula: see text] EX and running economy, while stiff boots had significantly lower [Formula: see text] EX and intermediate boots significantly lower running economy. Moreover, [Formula: see text] EX appears to be a better indicator of the boot flexural stiffness impact on energy efficiency than running economy.

scholarly journals Limb work and joint work minimization reveal an energetic benefit to the elbows-back, knees-forward limb design in parasagittal quadrupeds

2020 ◽  
Vol 287 (1940) ◽  
pp. 20201517
Author(s):  
James R. Usherwood ◽  
Michael C. Granatosky
Keyword(s):  
Distal Segment ◽  
Mechanical Work ◽  
Vertical Force ◽  
Centre Of Mass ◽  
Joint Work ◽  
Joint Power ◽  
Work Demand ◽  
Shoulder Joints ◽  
Force Profile ◽  
Physiological Demands

Quadrupedal animal locomotion is energetically costly. We explore two forms of mechanical work that may be relevant in imposing these physiological demands. Limb work, due to the forces and velocities between the stance foot and the centre of mass, could theoretically be zero given vertical limb forces and horizontal centre of mass path. To prevent pitching, skewed vertical force profiles would then be required, with forelimb forces high in late stance and hindlimb forces high in early stance. By contrast, joint work—the positive mechanical work performed by the limb joints—would be reduced with forces directed through the hip or shoulder joints. Measured quadruped kinetics show features consistent with compromised reduction of both forms of work, suggesting some degree of, but not perfect, inter-joint energy transfer. The elbows-back, knees-forward design reduces the joint work demand of a low limb-work, skewed, vertical force profile. This geometry allows periods of high force to be supported when the distal segment is near vertical, imposing low moments about the elbow or knee, while the shoulder or hip avoids high joint power despite high moments because the proximal segment barely rotates—translation over this period is due to rotation of the distal segment.

scholarly journals Race Walking Ground Reaction Forces at Increasing Speeds: A Comparison with Walking and Running

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 873
Author(s):  
Gaspare Pavei ◽  
Dario Cazzola ◽  
Antonio La Torre ◽  
Alberto E. Minetti
Keyword(s):  
High Speed ◽  
Three Dimensional ◽  
The Body ◽  
Ground Reaction Forces ◽  
Centre Of Mass ◽  
Walking Gait ◽  
Wide Range ◽  
Reaction Forces ◽  
Race Walking ◽  
Walking Speeds

Race walking has been theoretically described as a walking gait in which no flight time is allowed and high travelling speed, comparable to running (3.6–4.2 m s−1), is achieved. The aim of this study was to mechanically understand such a “hybrid gait” by analysing the ground reaction forces (GRFs) generated in a wide range of race walking speeds, while comparing them to running and walking. Fifteen athletes race-walked on an instrumented walkway (4 m) and three-dimensional GRFs were recorded at 1000 Hz. Subjects were asked to performed three self-selected speeds corresponding to a low, medium and high speed. Peak forces increased with speeds and medio-lateral and braking peaks were higher than in walking and running, whereas the vertical peaks were higher than walking but lower than running. Vertical GRF traces showed two characteristic patterns: one resembling the “M-shape” of walking and the second characterised by a first peak and a subsequent plateau. These different patterns were not related to the athletes’ performance level. The analysis of the body centre of mass trajectory, which reaches its vertical minimum at mid-stance, showed that race walking should be considered a bouncing gait regardless of the presence or absence of a flight phase.

CFD Verification and Validation Study for a Captive Bullet Entry in Calm Water

2017 ◽  
Author(s):  
António Maximiano ◽  
Guilherme Vaz ◽  
Jule Scharnke
Keyword(s):  
Free Surface ◽  
The Body ◽  
Load Test ◽  
Verification And Validation ◽  
Vertical Force ◽  
Time Step ◽  
Pitch Moment ◽  
The Impact ◽  
Modelling Error ◽  
Quantities Of Interest

As a step towards complex impact loads cases, e.g. lifeboat drop tests or ship/platform slamming in waves, a verification and validation (V&V) study is carried out with an open-usage community based CFD code ReFRESCO for a simple impact load test case: a captive axisymmetric generic lifeboat shape (bullet) that penetrates the water surface at a constant velocity and angle of attack. The quantities of interest are the body fixed longitudinal force FX, vertical force FZ, and pitch moment MYY. The influence of the iterative convergence level, domain size and free surface modelling are investigated. Seven different grids and four time steps were used to assess the grid and time step sensitivity, in a total of 28 calculations. For the tested grids and time steps it was found that the results are more sensitive to the grid resolution than to the time step. The pressure distribution on the hull is correlated with the trends observed in the loads, and the relation between between relative and static pressure is found to be important for the calculated loads. An experimental test campaign was previously carried out by MARIN, and its results are used to validate the simulations performed. A very good match between experiments and simulations is found. A V&V study is performed for the quantities of interest at nine different time instants covering the impact phase. The numerical uncertainties are obtained from a solution verification procedure [1]. The experimental uncertainties are estimated, and a validation exercise carried out according to the ASME standards [2]. The outcome of the validation exercise is an estimated 95 % confidence interval for the modelling error, δM. For FX the modelling error is below 15 N, for 8 out of 9 time instants. For FZ the modelling error is below 14 N, except at the time instants where, due to vibrations in the experimental setup, a larger value (up to 23 N) is found. For MYY the modelling error is under 5N m. These results provide confidence in ReFRESCO for the simulation of free surface impact flows.

CFD Analysis of a Captive Bullet Entry in Calm Water With and Without Turbulence

2019 ◽  
Author(s):  
René Bettencourt Rauffus ◽  
António Maximiano ◽  
Luís Eça ◽  
Guilherme Vaz
Keyword(s):  
Experimental Data ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Computational Cost ◽  
Longitudinal Force ◽  
The Body ◽  
Test Case ◽  
Vertical Force ◽  
Pitch Moment ◽  
The Difference

Abstract Simulations are carried out for a simplified lifeboat drop test case, which consists of a captive axisymmetric generic lifeboat shape (bullet), that penetrates the water surface at a constant velocity and angle of attack. The quantities of interest are the body fixed longitudinal force FX, vertical force FZ, and pitch moment MYY.This case was previously used in a verification and validation exercise [1]. Here, a step forward in complexity is taken, as the previous numerical model is now supplemented with the eddy-viscosity based turbulence model k–ω SST. Both approaches are then used to simulate two different cases: Case 1 with minimal wake effects; and Case 3 with flow separation and significant wake. The results are compared with the experimental data. The numerical uncertainty is estimated for both models. It is seen that for Case 1 the difference between both models is mostly within the comparison uncertainty, except for the longitudinal force FX, where the turbulent flow predicts a larger force, improving the comparison with the experiments. The loads predicted with turbulent flow stayed mostly within 6 % of the laminar flow. For Case 3 small differences between both models are found during/after the wake collapse stage. However, this difference is often within the comparison uncertainty. A reasonable agreement is found with the experimental data, except for FZ after the bow wake collapse. The turbulent flow improves slightly on the laminar approach regarding the agreement with the experiments, however it can be argued if this difference justifies the increased computational cost of the turbulence model.

Force platforms as ergometers

1975 ◽  
Vol 39 (1) ◽  
pp. 174-179 ◽  
Author(s):  
G. A. Cavagna
Keyword(s):  
Body Weight ◽  
Mechanical Energy ◽  
Center Of Mass ◽  
Force Plate ◽  
Vertical Displacement ◽  
The Body ◽  
Mechanical Work ◽  
Vertical Force ◽  
External Work ◽  
Total Mechanical Energy

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.

scholarly journals Mechanical determinants of the minimum energy cost of gradient running in humans.

1994 ◽  
Vol 195 (1) ◽  
pp. 211-225 ◽  
Author(s):  
A E Minetti ◽  
L P Ardigò ◽  
F Saibene
Keyword(s):  
Human Subjects ◽  
Minimum Energy ◽  
Metabolic Cost ◽  
The Body ◽  
Mechanical Work ◽  
Stride Frequency ◽  
Centre Of Mass ◽  
Negative Part ◽  
External Work ◽  
Level Running

The metabolic cost and the mechanical work of running at different speeds and gradients were measured on five human subjects. The mechanical work was partitioned into the internal work (Wint) due to the speed changes of body segments with respect to the body centre of mass and the external work (Wext) due to the position and speed changes of the body centre of mass in the environment. Wext was further divided into a positive part (W+ext) and a negative part (W-ext), associated with the energy increases and decreases, respectively, over the stride period. For all constant speeds, the most economical gradient was -10.6 +/-0.5% (S.D., N = 5) with a metabolic cost of 146.8 +/- 3.8 ml O2 kg-1 km-1. At each gradient, there was a unique W+ext/W-ext ratio (which was 1 in level running), irrespective of speed, with a tendency for W-ext and W+ext to disappear above a gradient of +30% and below a gradient of -30%, respectively. Wint was constant within each speed from a gradient of -15% to level running. This was the result of a nearly constant stride frequency at all negative gradients. The constancy of Wint within this gradient range implies that Wint has no role in determining the optimum gradient. The metabolic cost C was predicted from the mechanical experimental data according to the following equation: [formula: see text] where eff- (0.80), eff+ (0.18) and effi (0.30) are the efficiencies of W-ext, W+ext and Wint, respectively, and el- and el+ represent the amounts of stored and released elastic energy, which are assumed to be 55J step-1. The predicted C versus gradient curve coincides with the curve obtained from metabolic measurements. We conclude that W+ext/W-ext partitioning and the eff+/eff- ratio, i.e. the different efficiency of the muscles during acceleration and braking, explain the metabolic optimum gradient for running of about -10%.

Compensatory Changes in Ground Reaction Forces in Small and Large Breed Dogs with Unilateral Hindlimb Lameness in Comparison to Healthy Dogs

2021 ◽  
Author(s):  
Patrick Wagmeister ◽  
Stephanie Steigmeier-Raith ◽  
Sven Reese ◽  
Andrea Meyer-Lindenberg
Keyword(s):  
Cruciate Ligament ◽  
Weight Bearing ◽  
The Body ◽  
Ground Reaction Forces ◽  
Vertical Force ◽  
Cranial Cruciate Ligament ◽  
Significant Difference ◽  
Reaction Forces ◽  
Labrador Retrievers ◽  
Hindlimb Lameness

Abstract Objective The aim of this study was to investigate whether small- to medium-sized dogs with a naturally occurring unilateral hindlimb lameness show the same compensatory changes in ground reaction forces as large-breed dogs and how the changes are displayed compared with healthy small- to medium-sized dogs. Study Design Small- to medium-sized dogs (n = 15) and large-breed dogs (n = 16) with unilateral rupture of the cranial cruciate ligament were examined. The kinetic parameters peak vertical force and vertical impulse of the two groups were compared with each other and compared with healthy Beagles (n = 15) and with healthy Labrador Retrievers (n = 17), respectively. Results The healthy Beagle group showed a significantly higher weight loading on the forelimbs compared with the healthy Labrador group. The affected groups in comparison with the corresponding healthy groups showed a higher load on the non-affected body half and a significant lower weight bearing on the affected limb. Comparing the two affected groups, no significant difference could be found. Conclusion Despite a substantially different initial situation regarding weight distribution of the examined small- to medium-sized dogs and large dogs, a unilateral hindlimb lameness leads to the same compensatory changes (cranial and lateral shift of the body mass centre).

Leg design in hexapedal runners

1991 ◽  
Vol 158 (1) ◽  
pp. 369-390 ◽  
Author(s):  
R. J. Full ◽  
R. Blickhan ◽  
L. H. Ting
Keyword(s):  
Ground Reaction Force ◽  
Mechanical Energy ◽  
Reaction Force ◽  
The Body ◽  
Whole Body ◽  
Ground Reaction Forces ◽  
Vertical Force ◽  
Muscle Forces ◽  
Body Dynamics ◽  
Reaction Forces

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

The relationship between mechanical work and energy expenditure of locomotion in horses

1999 ◽  
Vol 202 (17) ◽  
pp. 2329-2338 ◽  
Author(s):  
A.E. Minetti ◽  
L.P. Ardigò ◽  
E. Reinach ◽  
F. Saibene
Keyword(s):  
Energy Expenditure ◽  
Elastic Energy ◽  
Three Dimensional ◽  
Indirect Evidence ◽  
The Body ◽  
Mechanical Work ◽  
Metabolic Energy ◽  
Centre Of Mass ◽  
External Work ◽  
Metabolic Energy Expenditure

Three-dimensional motion capture and metabolic assessment were performed on four standardbred horses while walking, trotting and galloping on a motorized treadmill at different speeds. The mechanical work was partitioned into the internal work (W(INT)), due to the speed changes of body segments with respect to the body centre of mass, and the external work (W(EXT)), due to the position and speed changes of the body centre of mass with respect to the environment. The estimated total mechanical work (W(TOT)=W(INT)+W(EXT)) increased with speed, while metabolic work (C) remained rather constant. As a consequence, the ‘apparent efficiency’ (eff(APP)=W(TOT)/C) increased from 10 % (walking) to over 100 % (galloping), setting the highest value to date for terrestrial locomotion. The contribution of elastic structures in the horse's limbs was evaluated by calculating the elastic energy stored and released during a single bounce (W(EL,BOUNCE)), which was approximately 1.23 J kg(−)(1) for trotting and up to 6 J kg(−)(1) for galloping. When taking into account the elastic energy stored by the spine bending and released as W(INT), as suggested in the literature for galloping, W(EL,BOUNCE) was reduced by 0.88 J kg(−)(1). Indirect evidence indicates that force, in addition to mechanical work, is also a determinant of the metabolic energy expenditure in horse locomotion.

Sign in / Sign up

Export Citation Format

Share Document