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# Force treadmill for measuring vertical and horizontal ground reaction forces

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We constructed a force treadmill to measure the vertical, horizontal and lateral components of the ground-reaction forces (Fz, Fy, Fx, respectively) and the ground-reaction force moments (Mz, My, Mx), respectively exerted by walking and running humans. The chassis of a custom-built, lightweight (90 kg), mechanically stiff treadmill was supported along its length by a large commercial force platform. The natural frequencies of vibration were >178 Hz for Fz and >87 Hz for Fy, i.e., well above the signal content of these ground-reaction forces. Mechanical tests and comparisons with data obtained from a force platform runway indicated that the force treadmill recorded Fz, Fy, Mx and My ground-reaction forces and moments accurately. Although the lowest natural frequency of vibration was 88 Hz for Fx, the signal-to-noise ratios for Fx and Mz were unacceptable. This device greatly decreases the time and laboratory space required for locomotion experiments and clinical evaluations. The modular design allows for independent use of both treadmill and force platform.
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and horizontal ground reaction forces
RODGER KRAM, TIMOTHY M. GRIFFIN, J. MAXWELL DONELAN, AND YOUNG HUI CHANG
Department of Integrative Biology, University of California, Berkeley, California 94720-3140
Kram, Rodger, Timothy M. Griffin, J. Maxwell
Donelan, and Young Hui Chang. Force treadmill for
measuring vertical and horizontal ground reaction forces. J.
Appl. Physiol. 85(2): 764769, 1998.—We constructed a force
treadmill to measure the vertical, horizontal and lateral
components of the ground-reaction forces (F
z
,F
y
,F
x
, respec-
tively) and the ground-reaction force moments (M
z
,M
y
,M
x
),
respectively exerted by walking and running humans. The
chassis of a custom-built, lightweight (90 kg), mechanically
stiff treadmill was supported along its length by a large
commercial force platform. The natural frequencies of vibra-
tion were .178 Hz for F
z
and .87 Hz for F
y
, i.e., well above
the signal content of these ground-reaction forces. Mechani-
cal tests and comparisons with data obtained from a force
platform runway indicated that the force treadmill recorded
F
z
,F
y,
M
x
and M
y
ground-reaction forces and moments
accurately. Although the lowest natural frequency of vibra-
tion was 88 Hz for F
x
, the signal-to-noise ratios for F
x
and M
z
were unacceptable. This device greatly decreases the time
and laboratory space required for locomotion experiments
and clinical evaluations. The modular design allows for
independent use ofboth treadmill and force platform.
biomechanics; locomotion; force platform
OUR GOAL was to construct an improved force treadmill
(FTM) for measuring the forces and moments exerted
on the ground by walking and running humans. Previ-
to reduce substantially data-collection time for locomo-
tion experiments, to allow for feedback to subjects
and/or patients, and to enable experiments to be con-
ducted that are not otherwise possible (9, 1113, 16).
However,previous designs couldsatisfactorilymeasure
only the vertical force component. We sought to build a
FTM that can record all three components of the
ground-reaction force: vertical (F
z
), horizontal (F
y
), and
lateral (F
x
), as well as the moments (M
z
,M
y
, and M
x
).
These measurements are necessary for measuring the
mechanical work performed on the center of mass, for
determining the point of force application, and for
calculating joint moments.
Various combinations of force platforms or force
transducers with treadmills have been constructed in
the past, but each of the designs had limitations.
Several laboratories have mounted a force platform
around a ground-mounted force platform (8, 10). These
devices could record the vertical ground-reaction force
and the moments around the lateral and anterior-
posterior axes with excellent ﬁdelity, but they could not
measureF
y
,F
x
,orM
z
.Otherinvestigatorshave mounted
a treadmill on top of multiple force sensors (4, 14, 18,
20, 22). Although these designs could measure F
y
in
z
,M
x
, and M
y
, they have done so with
unsatisfactoryﬁdelity.Frequency-responsecharacteris-
tics and signal-to-noise ratios were beyond limits nor-
mally considered acceptable. For example, the natural
frequencies of F
z
for all these designs have all been ,45
Hz. These previous attempts were hampered by three
ness,and vibrations inducedby the motororrollers. We
have developed a FTM that is a hybrid of these two
basic designs.
METHODS
A1-in. (2.5 cm)-thick aluminum plate was ﬁrmly affixed to
the laboratory ﬂoor with epoxy glue, bolts, and concrete
anchors. We mounted a large 71 3 24 in. (180 3 60 cm)
commercial strain-gauged multicomponent force platform
(AMTI), Watertown, MA] to the aluminum plate. The tread-
mill chassis was bolted to threaded metal inserts in the top
surface of the force platform. The main chassis of the tread-
millwasbuiltfrom4-in.(10-cm)6061aluminum I-beams that
were connected by eight cross-members made of 2-in. (5-cm)
0.25-in. (6-mm)-thick 6061 aluminum plate with a thin Teﬂon
sheet to reduce belt-bed friction.
Therollerswere custom-made on a lathe from a single piece
ofsteel toachieveexcellent balanceandthus tominimizeinduced
vibrations(F. & G. WilliamsMachine and Tool,Hatboro, PA). The
rollers hada diameter of 3in. (8cm) and aface width of 14in. (35
bymoving thenondrive rolleralongthe horizontallong axisofthe
chassis.A2-hp(1,500-W) variable-speedalternating-current elec-
tric motor (Leeson Electric, Grafton, WI) was mounted on the
mainchassis.Atimingpulleyon themotor shaftwas connectedto
a larger pulley on the drive roller by means of a standard rubber
timing belt. With the use of two different timing-pulley combina-
tions, treadmill speeds of0.5–7.0 m/swere easilyachieved.
In addition, a ﬂywheel mounted on the drive roller shaft
helped to maintain a nearly constant belt speed during
operation. We have found that a very large timing pulley
works adequately asa ﬂywheel, althougha custom-machined
balanced ﬂywheel would be preferable. For safety, the drive
pulleys and ﬂywheel were covered with a plywood box that
did not touch any of the drive parts or the force platform. For
safety in mounting and dismounting, handrails were at-
8750-7587/98 $5.00 Copyright r 1998 the American Physiological Society764 http://www.jap.org tached to the surrounding laboratory ﬂoor. We monitored the speed with a tachometer that detected the revolution rate of the drive roller. Theoverall design is shown in Fig. 1. It is important to recognize that the entire treadmill (motor, drive pulleys, rollers, chassis, and so forth) was supported by the force platform. This was an essential design feature. If the motor were not mounted on the force platform, we would have had to measure the forces and torques imparted by the motor on the force platform. The chassis was supported in a distributed manner along its entire length. Some previous FTM designs have been ‘‘simplysupported’’(3) at four points by force transducers; thus they were much less stiff, particularly in the vertical direction. The total mass of our treadmill was 90 kg. A rough breakdown of the major components of this mass was as follows (in kg): I-beam chassis, 20; treadmill bed, 3; motor, 17; ﬂywheel, 19; and two rollers, 14 each. High-frequency response is desirable in any force-transducing system. The natural frequency of vibration for any object can be increased by decreasing the mass. The most obvious treadmill components that could be lightened are the ﬂywheel and therollers.An ideal ﬂywheel wouldhave its mass concentrated on the rim to maximize the inertia-to- mass ratio. Rollers made of aluminum rather than steel would save nearly 20 kg. Titanium components would provide further mass reduction but at considerably greater expense. One advan- tageofourdesignwasthatthetreadmillcouldbereadilyremoved from the force platform, so that both pieces of equipment could be used independently for other experiments. RESULTS We performeda battery of static and dynamic teststo evaluate the ﬁdelity ofthe FTM. Linearity. We found it convenient to ‘tare’’ the force platform in the vertical direction; that is, we balanced the ampliﬁer bridge circuit to give zero voltage output when the treadmill was mounted on the force platform. To ensure that this did not cause any distortion of the signal, we performed a static-force calibration with the treadmill mounted on the force platform. When we applied known loads, the output voltage response was linear to within 0.2% over a range of applied forces up to 2,300 N (R 2 . 0.99). Point of force application. To verify that the position of force application did not affect the vertical-force output, we applied the same static load (700 N) at different locations. As expected from the manufactur- er’sspeciﬁcations, the recorded voltage output from the ampliﬁers varied ,0.7% from the mean, regardless of the location of force application. To determine the accuracy with which we could locate the point of force application, we placed a known static load at various known positions along the length and width of the treadmill (6). The position of static-force application could be resolved to within 0.5 cm for the y-axis and 0.6 cm along the x-axis. To calculate joint moments or torques during locomo- tion, it is necessary to locate the point of force applica- tion dynamically.AMTI force platforms provide a direct measure of the moment around the mediolateral axis. However, the moment is referenced to an axis that is midway along the length of the platform and slightly below the top surface of the force platform. In the manual, this distance below the top surface is referred to as the origin; for our particular platform, the dis- tance was 0.053 m. The treadmill elevated the point of force application by a distance 0.107 m above the surface of the force platform. As a result, both the vertical-force component (F z ) and the horizontal shear force (F y ) exerted by the subject contributed to the measured M x . If the point of force application occurs at distance a along the length of the force platform from the M x axis, then the equationfor the moment is M x 5 (F z ·a) 1 [F y ·(0.107 1 0.053)] By recording M x ,F z , and F y , it was simple to calculate a and thus locate thepoint of force application. Using the following procedure, we veriﬁed that we could locate dynamically the point of force application. First, weaffixed a smalldot of reﬂective tape onthe end of a sturdy wooden stick. With the treadmill belt in motion, a person standing on the side of the FTM pressed on the treadmill belt with the stick, applying a varying force with both vertical and horizontal compo- nents. The end of the stick naturally moved backward with the treadmill belt.As the force was applied via the stick, we recorded the force signals and simultaneously recorded videotape at 200 ﬁelds/s, synchronized with theforce-datacollection. Severaladditionalsmallreﬂec- tive dots identiﬁed the midpoint along the length of the platform and also provided a scale. Using the above equation, we calculated the point of force application. We also analyzedthe videotape with a Peak 5 digitizing system. The video and force-platform data methods consistently identiﬁed nearly the same point of force application. Above a vertical-force threshold of 50 N, the two methods had a difference of ,1 cm. The results from a sample calibrationtrial are shown in Fig. 2. Fig. 1. Schematic view of force-tread- mill (FTM) design. Handrailsand gear- box cover are omitted from this draw- ing. 765FORCE TREADMILL Natural frequency. Before proceeding to dynamic locomotion trials, we determined the unloaded natural frequencies of the FTM for F z ,F y , and F x . Using a woodenmallet, we gavethe treadmill asharp rap inthe appropriate direction and collected the force signal at 1 kHzbyusing aMacintoshQuadra 650,NationalInstru- ments analog-to-digital board, and LabView4 software. To calculate the natural frequencies, we simply noted the time elapsed for 10 cycles of the ensuing ‘‘ringing’ observed in the force traces. We found that the natural frequencies were .178 Hz for F z , .87 Hz for F y , and .88 Hz for F x . The force platform without the treadmill had higher natural frequencies, as speciﬁed by the manufacturer (350 Hz for F z , and 300 Hz for F y and F x ). The addition of the treadmill mass and the compliance ofthe treadmill clearlydecreased theresonant frequen- cies. Given that the natural frequency of the force platform alone in the vertical direction is 350 Hz, the added mass of the treadmill would theoretically reduce the overall resonant frequency to ,200 Hz. The actual natural frequency was 178 Hz; this indicated that the treadmill chassis was very stiff indeed. The more substantial drop in the natural frequencies in the horizontal directions appeared to be caused by the mass of the motor and the compliance in the mounting of the motor. However, the natural frequencies of the FTM were more than adequate for accurate recording of the ground-reaction forcesof human locomotion. Vibration and electrical noise. When the motor of the FTM was not turned on, we recorded little noise (,63 N for F z , ,61 N for F y and F x ). When the motor was turned on (with no subject on the treadmill), we re- corded noise amplitudes of 680 N on the F z and 660 N on the F y and F x signals. However, a fast Fourier transform (FFT) spectral power analysis of these sig- nals revealed that 99% of this noise was at frequencies .46 Hz (see Fig. 3). The mediolateral forces applied by walkingor runninghumans typicallyhave peakmagni- tudes of only 510% of body weight (BWt; e.g., 70 N); thus the signal-to-noise ratio for F x was poor. A large fraction of the vibration noise was due to ﬂywheel imbalance. If measuring F x were of particular interest, it may be technically feasible to do so with a precision- balanced ﬂywheel. Frequency content of ground-reaction force signals. To determine the frequency content of the ground- reaction force signals in a situation that is free of externalvibrations, we hada subject walk(1.5m/s) and run (3 m/s) over a conventional ground-mounted force platform (model LG6–4–2000, AMTI). We measured speed with a series of photocell beams placed along the runway. Five acceptable trials (average speed within 60.05 m/s) were saved for both walking and running. We considered these data to be virtually noise free. We then performed a FFT spectral power analysis of these force records. For walking,99% of the integrated power content of both the F y and F z signals was ,9 Hz. These values were similar to those reported previously (1). For running,99% of theintegrated power content ofthe F z signal was at frequencies ,10 Hz and .98% of the FFT power of the F y signal was at frequencies ,17 Hz. These spectral analyses are shown in Fig. 3. These analyses helped us choose appropriate ﬁltering cut-off frequencies for processing our FTM data. We used a Fig. 2. Accuracyof the point of force-application determination. With treadmill running, weapplied atime-varying force to the moving belt surfaceby using a sturdywooden stick. Wedetermined the positionof the end of the stick by digitizing a high-speed video recording and by using the force-platform signals, as described in METHODS. Above a vertical force threshold of 50 N, the 2 methods gave results within 0.01 m of each other. The mean difference betweenthe 2 methods was 0.002 6 0.006 (SD) m. The two signals were highly correlated; R 2 . 0.99. Fig. 3. Fast Fourier transform (FFT) power-spectrum analysis for ground-reaction force data and FTM vibration noise. Verticalground- reaction force (F z ) data were obtained (at 1 kHz) during overground runningat3m/s.We considered those data to be essentially noise free and representative of the true signal. FTM noise signals were obtained (also at 1 kHz) while operating the treadmill at 3 m/s with no subject running. Data were then transformed into the frequency domain by using a FFT; 99% of the signal power was ,10 Hz, while 99% of the noise power was .46 Hz.Thus low-pass digital ﬁltering of FTM data, with a cut-off frequency of 25 Hz, eliminated the noise without affecting the signal. 766 FORCE TREADMILL fourth-order low-pass Butterworth nonrecursive ﬁlter passedin bothdirections toeffectzero-phase shiftand a 3-dB cutoff of 25 Hz. We found that this eliminated 99% of the noise while retaining all of the important compo- nents of the signal. Overall system tests. Next we performed some simple dynamic tests of the FTM to determine the overall accuracy of the system. The same subject walked and ran on the FTM at 1.5 and 3 m/s, respectively, while we collected F z and F y at 1 kHz. We ﬁltered these data as described above. Over an integral number of strides, the average vertical force must be equal to BWt, and if the subject is maintaining the speed, the braking and propulsive ground-reaction impulses (force integrated over time) must be equal. We measured the average verticalforce exertedover 10successive, completesteps to be within 1% of BWt. We also compared the inte- grated horizontal-force signals for the ﬁrst and second halves of the stance phase for the running trials. Averaged for 10 steps, the measured braking impulse was within 1% of the propulsive impulse. The roller tachometer indicated that the treadmill speed was quite constant. With a subject walking at 1.25 m/s, the speed ﬂuctuated by ,0.02m/s; for running at 3.0 m/s, ﬂuctuations were ,0.04 m/s. FTM vs. overground measurements. We compared the FTM signals with the established methodology of a traditional runway-mounted force platform. We had a single subject run at 3 m/s on the FTM and across our force-platform runway. A comparison of the average values (from 10 steps) for various force magnitudes from the FTM vs. overground revealed only small differences caused by normal variation. The average peak vertical force (F z ) values were 1.78 vs. 1.83 3 BWt for the impact peak and 2.47 vs. 2.44 3 BWt for the active peak. The average peak braking (F y ) forces were 20.30 vs. 20.35 3 BWt, and the average propulsive peaks were 0.21 vs. 0.20 3 BWt. A comparison of a typical running stride for the FTM vs. overground force-platform records is shown in Fig. 4. The signals obtained with the FTM were quite similar to those obtained overground. Because some stride-to-stride variability occurs, the traces were not identical. All of thesevalues concurred with thosein the literature(21). DISCUSSION From a purely mechanical perspective, steady-speed walkingor runningonan adequatemotorized treadmill is identical to overground walking and running; the only difference is the frame of reference for each situation (23). Locomotion on a treadmill with inad- equate power or momentum (i.e., no ﬂywheel) does indeed differ from overground locomotion. However, on a treadmill with an adequate motor and ﬂywheel, where the belt speeddoes not vary, the kinematics (21), ground-reaction forces (19), and metabolic cost (2) of locomotion are nearly indistinguishable from over- ground locomotion. As detailed above, our motor and ﬂywheel appear to be adequate in maintaining a con- stant tread speed. Fig. 4. Comparison of vertical (F z ; top) and horizontal (F y ; bottom) ground-reaction force signals obtained from FTM (solid line) and a force-platform runway (dashed line) for same subject when running at 3 m/s. FTM data were low-pass ﬁltered at 25 Hz. Fig. 5. Sample FTM data for subject walking at 1.25 m/s. Signals were low-pass ﬁltered at 25 Hz. Dashed line, body weight. 767FORCE TREADMILL FTMs provide many advantages over conventional runway-mounted forceplatforms. Our new FTM design now extends these advantages to many more studies of locomotion because we can measure the vertical and horizontal components of ground-reaction force and their moments. FTMs allow ground-reaction force data to be collected far more rapidly than do traditional runway studies (19). Furthermore, a large number of successive steps can be averaged to determine more representative values, thereby increasing statistical power. To adequately study running mechanics with a ground-mounted force platform system, a long labora- tory or hallway space must be available. With a FTM, high-speed running studies can be conducted in very small laboratories. The modular design of the FTM allows the force platform and treadmill to be used independently of each other. That is an important point, because each itemhas considerable expense. In addition to time and space savings, a FTM allows for experiments and treatments not possible with con- ventional runway-mounted force platforms. For ex- ample, with a FTM, it is possible to study the biome- chanics of gait transitions (13), adjustments to perturbations of stability (5), and locomotion in simu- lated reduced gravity (16) or even microgravity (9). Furthermore, a FTM allows for simultaneous collection of biomechanical and other data (for example, rate of oxygen consumption or electromyography) without the use of telemetry. Dingwell et al. (11) have found that a FTM can provide useful feedback of vertical ground- reaction forces during rehabilitation of clinical patients who have amputations below the knee. In our own research, we ﬁnd that the FTM is very useful as an ergometer that allows us to measure the mechanical work performed on the center of mass during locomo- tion (7). This is possible because the FTM records the summed ground-reaction force fromboth feet. In Fig. 5, we show a typical force recording from the FTM for the same subject walking at 1.25 m/s. When humans walk, both feet are on the ground for at least part of the stride cycle. For some purposes, it is necessary to know the force under each individual foot. Davis and Cavanagh (8) and Dingwell et al. (11) have developed clever algorithms to separate the individual foot vertical forces for use with a FTM. These calcula- tions rely on the location and velocity of the center of pressure to determine the time of single and double support. The same algorithms can be used with the present FTM design. Unfortunately, an equivalent algorithm cannot separate the horizontal forces for the individual feet in walking. This is because, during the double-support period, it is not possible to locate the pointof force application (center of pressure) forthe individual feet along the y-axis of the treadmill. Note that it is possible to locate very accurately the point of force application, and thus joint moments, during run- ningand the single-support phaseof walking. TheFTM designof Belliet al.(4)uses twoparallel treadmills,one for each foot. This allows for separate measurement of the individual foot horizontal forces, but it requires the subject to walk with an unnaturally wide stance. Thus aperfectlyacceptable methodofmeasuring thehorizon- tal forces exerted by the individual feet during the double-support phase of walking for repeated strides remains elusive. In conclusion, the FTM described here can facilitate many types of biomechanical studies of human locomo- tion. Our device can accurately record the vertical (F z ) and horizontal (F y ) ground-reaction forces as well as the moments M x and M y . Induced vibrations prevented satisfactory measurements of F x and M z with the present device. This device can greatly decrease the timeand laboratory spacerequired forstandard experi- ments and clinical evaluations. The authors appreciate the design and machining assistance of Bruce Cannon. This project was supported by the University of California, Berke- ley, Committee on Research and National Institute of Arthritis and Musculoskeletal and Skin Diseases Grant R29AR-44688-01. Address for reprint requests: R. Kram, Dept. of Integrative Biology, Univ. of California, Berkeley, 3060 VLSB, Berkeley, CA 94720-3140 (E-mail:rkram@socrates.berkeley.edu). Received 15 December 1997; accepted in ﬁnal form 21April 1998. REFERENCES 1. Antonsson, E. K., and R. W. Mann. The frequency content of gait. J. Biomech. 18: 3947, 1985. 2. Bassett, D. R., M. D. Giese, F. J. Nagle, A. Ward, D. M. Raab, and B. Balke. Aerobic requirements of overground versus treadmill running. Med. Sci. Sports Exerc. 17: 477481, 1985. 3. Beer, F. P., and E. R. Johnston. Vector Mechanics for Engi- neers. NewYork: McGraw-Hill, 1977. 4. Belli, A., P. Bui, A. Berger, and J. Lacour. A treadmill for measurement of ground reaction forces during walking (Ab- stract). 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Mechanics of running under simulated low gravity. J.Appl. Physiol. 71: 863870, 1991. 17. Horstmann, G. A., F. Huethe, and V. Dietz. Special treadmill for the investigation of standing and walking in research and in clinical medicine. Biomed. Tech. (Berl.) 32: 250254, 1987. 18. Jansen, E. C., D. Vittas, S. Hellberg, and J. Hansen. Normal gait of young and old men and women. Acta Orthop. Scand. 53: 193196, 1982. 19. Kram, R., and A. J. Powell. A treadmill-mounted force plat- form. J. Appl. Physiol. 67: 16921698, 1989. 20. Martin, M. A., M. Gagnon, and M. R. Pierrynowski. Ground reaction forces and frontal plane hip, knee, and ankle angles duringrunning on atreadmill (Abstract). In:XIth Congress ofthe International Society of Biomechanics, edited by G. de Groot. Amsterdam: Free University Press, 1988, p. 201. 21. Nigg, B. M., R. W. De Boer, and V. Fisher. A kinematic comparison of overground and treadmill running. Med. Sci. Sports Exerc. 27: 98105, 1995. 22. Ohmichi, H. Application of a treadmill/force plate system to the kinematics of pathological gait (Abstract). In: XIIIth Interna- tional Congress of the International Society of Biomechanics, edited by R. N. Marshall. Perth,Australia: University of Western Australia, 1991, p. 453454. 23. Van Ingen Schenau, G. J. Some fundamental aspects of the biomechanics of overground versus treadmill locomotion. Med. Sci. Sports Exerc. 12: 257261, 1980. 769FORCE TREADMILL ... While force plates are a great tool to measure the forces exerted onto the floor during a step, their major drawback is that they can only capture one step due to their stationary nature and small size. Solutions to this problem are either wearable sensor solutions [10,11] or force plates with moving substrate [12]. By incorporating force sensors into a treadmill, continuous data can be captured. ... ... Due to their higher natural frequency, the higher stiffness enables piezo sensors to measure extremely fast signals above 1 kHz. A simpler solution is to place a recreational treadmill on top of factory-made force plates [12,21]. While the effort in design and production is small, store-bought treadmills with plywood surfaces can not provide the stiffness and rigidity needed to measure forces with high temporal solutions. ... ... To calibrate the instrumented treadmill, several different methods have been reported. A straightforward way is to use calibrated dead weights to compare the sensor output [12,14,17,19]. While this method is simple to implement and norm conform, it only allows calibration in the vertical direction. ... Preprint Full-text available Ground reaction force sensing is one of the key components of gait analysis in legged locomotion research. To measure continuous force data during locomotion, we present a novel compound instrumented treadmill design. The treadmill is 1.7m long, with a natural frequency of 170Hz and an adjustable range that can be used for humans and small robots alike. Here, we present the treadmill's design methodology and characterize it in its natural frequency, noise behavior and real-life performance. Additionally, we apply an ISO 376 norm conform calibration procedure for all spatial force directions and center of pressure position. We achieve a force accuracy of$\leq$5.6N for the ground reaction forces and$\leq$13mm in center of pressure position. ... Before session 1, the subjects completed a health screening form and then provided informed consent. During all three sessions, we measured height and body mass, and thereafter, the subjects warmed up by running on a custom-built forceinstrumented treadmill (18) for 3 min at 12 km/h followed by 3 min at 14 km/h. The subjects then ran six 5-min trials with 5-min recovery in-between. ... ... Beves and Ferguson (13) used CFD modeling and an unspecified air density to estimate the force acting on Kipchoge running solo at 5.86 m/s as 6.6 N. We did not adjust their value but note that their simulated depiction of Kipchoge was unrealistically corpulent. Schickhofer and Hanson (15) used CFD to simulate aerodynamic drag forces acting on a generic elite female runner (1.65 m and 55 kg) at four running velocities (15,18,21, and 36 km/h). Running solo at 18 km/h (5 m/s;$2:20 marathon pace) at ambient temperature of 20 C they calculated 4.85 N of drag force. ...
Article
The benefits of drafting for elite marathon runners are intuitive, but the quantitative energetic and time savings are still unclear due to the different methods used for converting aerodynamic drag force reductions to gross metabolic power savings. Further, we lack a mechanistic understanding of the relationship between aerodynamic drag forces and ground reaction forces (GRF) over a range of running velocities. Here, we quantified how small horizontal impeding forces affect gross metabolic power and GRF over a range of velocities in competitive runners. In three sessions, 12 runners completed six 5-min trials with 5 min of recovery in-between. We tested one velocity per session (12, 14 and 16 km/h), at three horizontal impeding force conditions (0, 4 and 8 N) applied at the waist of the runners. On average, gross metabolic power increased by 6.13% per 1% body weight of horizontal impeding force but the increases varied considerably between individuals (4.17-8.14%). With greater horizontal impeding force, braking GRF impulses decreased while propulsive GRF impulses increased but the impulses were not related to individual changes in gross metabolic power. Combining our findings with those of previous aerodynamics studies, we estimate that for a solo runner (52 kg) at 2-hour marathon pace, overcoming aerodynamic drag force (1.39% BW) comprises 7.8% of their gross metabolic power and drafting can save between 3 min 42 s and 5 min 29 s.
... Of the three force components (i.e., medio-lateral, anterior-posterior and vertical), vertical peak compression force is most important, accounting for more than 80% of the total in walking [21,22]. Figure 1 shows that the maximum joint compression force is aligned with the tibia and approximates the timing of peak adduction moment [23,24], indicating that total compression force within the joint contributes significantly to the adduction moment. ...
... Table 1. Summary of knee biomechanical parameters and potential application of active knee orthosis [18,[22][23][24][25][26][27][28]. ...
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Knee osteoarthritis (OA) is a degenerative condition that critically affects locomotor ability and quality of life and, the condition is particularly prevalent in the senior population. The current review presents a gait biomechanics conceptual framework for designing active knee orthoses to prevent and remediate knee OA. Constant excessive loading diminishes knee joint articular cartilage and, therefore, measures to reduce kinetic stresses due to the fact of adduction moments and joint compression are an essential target for OA prevention. A powered orthosis enables torque generation to support knee joint motions and machine-learning-driven “smart systems” can optimise the magnitude and timing of joint actuator forces. Although further research is required, recent findings raise the possibility of exoskeleton-supported, non-surgical OA interventions, increasing the treatment options for this prevalent, painful and seriously debilitating disease. Combined with advances in regenerative medicine, such as stem cell implantation and manipulation of messenger ribonucleic acid (m-RNA) transcription, active knee orthoses can be designed to incorporate electro-magnetic stimulators to promote articular cartilage resynthesis.
... 3회의 성공적인 데이터가 200 Hz의 샘플링률(sampling rate)로 수집되었 으며 실험에 사용된 장비는 <Table 2>와 같다. 마커 데이터 수집 후, 원자료(raw data)는 4차 저역 통과 버터워스 필터(4th order low-pass Butterworth filter)를 통해 13Hz의 분별 점(cut-off frequency)으로 스무딩되었으며, 해당 분별점은 Power spectral density의 99%를 목표로 하여 결정되었다(Kram et al., 1998). 분석을 위한 보행주기(gait cycle)는 한걸음주기(stride)로 정 의하였으며, 분석하고자 하는 발의 초기접지부터 동일한 발의 다음 초 기접지까지를 0-100%로 정규화(normalization)하였다. ...
Article
PURPOSE This study aimed to identify movement pattern differences in the running of youth soccer players with and without lateral ankle sprain (LAS) histories. METHODS A total of 12 participants were recruited and assigned to the LAS group or the control group. All participants were assessed for anthropometric data, and they filled in the subjective ankle function questionnaires. Then, reflective markers were attached to their bodies, and they were instructed to run at the preferred speed on the 9-m runway thrice. 3D joint angles for ankle, knee, and hip joints were exported, and their mean values and 95% confidence intervals were calculated. Ensemble curve analysis was conducted to compare running kinematics between the groups. RESULTS The LAS group exhibited fewer dorsiflexion angles and more inversion angles compared to the control group. Excluding the dorsiflexion deficits and more inverted ankles, there were no significant differences between the groups. CONCLUSIONS Although the ankle kinematic patterns found in this paper are not considered LAS risk factors, it will be able to identify precise LAS risk factors with prospective design (e.g., lower extremity movement patterns) as well as intrinsic risk factors.
... Ground reaction forces were collected independently for each limb as subjects walked on the dual-belt instrumented treadmill (Kram et al. 1998) with embedded force platforms (1080 Hz, Advanced Mechanical Technology Incorporated, Watertown, MA, USA). Simultaneous kinematics data were captured using a six-camera motion analysis system (120 Hz, VICON Motion Systems, Oxford, UK). ...
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Lower-limb amputation limits inherent motor abundance in the locomotor system and impairs walking mechanics. Able-bodied walkers vary ankle torque to adjust step-to-step leg force production as measured by resultant ground reaction forces. Simultaneously, knee torque covaries with ankle torque to act as a brake, resulting in consistent peak leg power output measured by external mechanical power generated on the center of mass. Our objective was to test how leg force control during gait is affected by joint torque variance structure in the amputated limb. Within the framework of the uncontrolled manifold analysis, we measured the Index of Motor Abundance (IMA) to quantify joint torque variance structure of amputated legs and its effect on leg force, where IMA > 0 indicates a stabilizing structure. We further evaluated the extent to which IMA in amputated legs used individual (INV) and coordinated (COV) joint control strategies. Amputated legs produced IMA and INV values similar to intact legs, indicating that torque deviations of the prosthetic ankle can modulate leg force at the end of stance phase. However, we observed much lower COV values in the amputated leg relative to intact legs indicating that biological knee joint torque of the amputated leg does not covary with prosthetic ankle torque. This observation suggests inter-joint coordination during gait is significantly limited as a result of transtibial amputation and may help explain the higher rate of falls and impaired balance recovery in this population, pointing to a greater need to focus on inter-joint coordination within the amputated limb.
... Further, results obtained on a cushioned treadmill are specific to that treadmill and not applicable to road racing. Force-measuring treadmills all have rigid beds but I understand that they are expensive, unless you make your own (Kram et al., 1998). Treadmills from the 1970s almost all had rigid beds but they are now exceedingly rare and difficult to maintain/repair. ...
Article
Recently developed shoes that are highly-cushioned and have a curved stiff plate embedded in the midsole are “ergogenic” in that they reduce the rate of metabolic energy required to run at a defined speed. These energy savings are not due to low mass but rather to their foam midsoles which are unusually compliant and resilient. The function of the plate has not yet been elucidated, but evidence is clear that the plate itself does not act as a spring or a teeter-totter. The plate may act synergistically with the foam to create an area-elastic structure, akin to a gymnastics floor. Future studies of ergogenic shoes should: focus on muscle function using EMG and ultrasound, explore footstrike pattern effects, only utilize stiff treadmills, and seek to define a consistent baseline shoe condition for comparison.
... Experiments at large spatiotemporal scales are usually realized by treadmills to keep the animal (including a human) stationary relative to the laboratory (Bélanger et al., 1996;Buchner et al., 1994;Darken et al., 1997;Full, 1987;Herreid and Full, 1984;Jayakumar et al., 2019;Kram et al., 1998;Leblond et al., 2003;Stolze et al., 1997;Watson and Ritzmann, 1997b,a;Weinstein and Full, 1999). However, only small obstacles can be directly mounted on such treadmills (Voloshina et al., 2013); larger obstacles have to be dropped onto the treadmill during locomotion (Park et al., 2015;Snijders et al., 2010;Van Hedel et al., 2002). ...
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A challenge to understanding locomotion in complex 3-D terrain with large obstacles is to create tools for controlled, systematic experiments. Recent terrain arenas allow observations at small spatiotemporal scales (∼10 body length or cycles). Here, we create a terrain treadmill to enable high-resolution observation of animal locomotion through large obstacles over large spatiotemporal scales. An animal moves through modular obstacles on an inner sphere, while a rigidly-attached, concentric, transparent outer sphere rotates with the opposite velocity via closed-loop feedback to keep the animal atop. During sustained locomotion, a discoid cockroach moved through pillar obstacles for up to 25 minutes (2500 cycles) over 67 m (1500 body lengths). Over 12 trials totaling∼1 hour, the animal was maintained within a radius of 1 body length (4.5 cm) on top of the sphere 90% of the time. The high-resolution observation enables study of diverse locomotor behaviors and quantification of animal-obstacle interaction.
... Two force platforms (TF-40120-CL and TF-40120-CR; Tec Gihan, Kyoto, Japan) integrated into the instrumented treadmill collected all components of GRF data (sampling at 1 kHz). The GRFs were further filtered by a fourth-order zero-lag low-pass Butterworth filter with a cut-off frequency at 25 Hz, according to the findings of a previous study [38]. Additionally, a 40-N threshold was applied for further vertical GRF analysis [39][40][41][42] to determine foot contact timing. ...
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Abstract Background Individuals with unilateral transfemoral amputation are prone to developing health conditions such as knee osteoarthritis, caused by additional loading on the intact limb. Such individuals who can run again may be at higher risk due to higher ground reaction forces (GRFs) as well as asymmetric gait patterns. The two aims of this study were to investigate manipulating step frequency as a method to reduce GRFs and its effect on asymmetric gait patterns in individuals with unilateral transfemoral amputation while running. Methods This is a cross-sectional study. Nine experienced track and field athletes with unilateral transfemoral amputation were recruited for this study. After calculation of each participant’s preferred step frequency, each individual ran on an instrumented treadmill for 20 s at nine different metronome frequencies ranging from − 20% to + 20% of the preferred frequency in increments of 5% with the help of a metronome. From the data collected, spatiotemporal parameters, three components of peak GRFs, and the components of GRF impulses were computed. The asymmetry ratio of all parameters was also calculated. Statistical analyses of all data were conducted with appropriate tools based on normality analysis to investigate the main effects of step frequency. For parameters with significant main effects, linear regression analyses were further conducted for each limb. Results Significant main effects of step frequency were found in multiple parameters (P
... The mediolateral, anteroposterior, and vertical components of the ground reaction force (GRF) were recorded using two under belt force platforms (TF-40120-CL and TF-40120-CR; Tec Gihan, Kyoto, Japan) at a sampling frequency of 1,000 Hz. The GRF data were filtered using a fourth-order zero-lag low-pass Butterworth filter, with a cutoff frequency of 25 Hz (Kram et al., 1998;Clark and Weyand, 2014). To measure the contact of the foot on the treadmill belt, the touchdown and toe-off were identified from the filtered vertical GRF data with a threshold of 25 N (Werkhausen et al., 2019). ...
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Carbon-fiber running-specific prostheses have enabled individuals with lower extremity amputation to run by providing a spring-like leg function in their affected limb. When individuals without amputation run at a constant speed on level ground, the net external mechanical work is zero at each step to maintain a symmetrical bouncing gait. Although the spring-like “bouncing step” using running-specific prostheses is considered a prerequisite for running, little is known about the underlying mechanisms for unilateral transfemoral amputees. The aim of this study was to investigate external mechanical work at different running speeds for unilateral transfemoral amputees wearing running-specific prostheses. Eight unilateral transfemoral amputees ran on a force-instrumented treadmill at a range of speeds (30, 40, 50, 60, 70, and 80% of the average speed of their 100-m personal records). We calculated the mechanical energy of the body center of mass (COM) by conducting a time-integration of the ground reaction forces in the sagittal plane. Then, the net external mechanical work was calculated as the difference between the mechanical energy at the initial and end of the stance phase. We found that the net external work in the affected limb tended to be greater than that in the unaffected limb across the six running speeds. Moreover, the net external work of the affected limb was found to be positive, while that of the unaffected limb was negative across the range of speeds. These results suggest that the COM of unilateral transfemoral amputees would be accelerated in the affected limb’s step and decelerated in the unaffected limb’s step at each bouncing step across different constant speeds. Therefore, unilateral transfemoral amputees with passive prostheses maintain their bouncing steps using a limb-specific strategy during running.
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This paper presents the design, analysis, and fabrication of a capacitive-based three-axis force sensor as the building block of a wearable sensing system to directly measure all the components of three-dimensional (3D) ground reaction forces (3D GRFs) during walking. The proposed sensor is low-cost and easy to fabricate with high accuracy, which promotes its accessibility and usability for gait analysis in clinical and research settings. The sensor is comprised of only three parallel capacitors that enable three-axial force measurement while significantly reducing the complexity of fabrication and maintenance prevalent in three-axis force sensors. Comprehensive experiments were conducted to rigorously quantify different aspects of the sensor's performance. The static and dynamic errors along the three axes are less than 2.28%, which is well within the acceptable range for the intended application. The force sensor can decouple three-axial forces with a cross-sensitivity of less than 2%. The developed sensor also demonstrates desirable repeatability and hysteresis behaviors with almost no drift over long periods of usage.
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Muscle, bone, and tendon forces; the movement of the center of mass, and the spring properties of the body during terrestrial locomotion can be measured using ground-mounted force platforms. These measurements have been extremely time consuming because of the difficulty in obtaining repeatable constant speed trials (particularly with animals). We have overcome this difficulty by mounting a force platform directly under the belt of a motorized treadmill. With this arrangement, vertical force can be recorded from an unlimited number of successive ground contacts in a much shorter time. With this treadmill-mounted force platform it is possible to accurately make the following measurements over the full range of steady speeds and under various perturbations of normal gait: 1) vertical ground reaction force over the course of the contact phase; 2) peak forces in bone, muscle, and tendon; 3) the vertical displacement of the center of mass; and 4) contact time for the limbs. In our treadmill-force platform design, belt forces and frictional forces cause no measurable cross-talk problem. Natural frequency (160 Hz), nonlinearity (less than 5%), and position independence (less than 2%) are all quite acceptable. Motor-caused vibrations are greater than 150 Hz and thus can be easily filtered.
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Using a linear mass-spring model of the body and leg (T. A. McMahon and G. C. Cheng. J. Biomech. 23: 65-78, 1990), we present experimental observations of human running under simulated low gravity and an analysis of these experiments. The purpose of the study was to investigate how the spring properties of the leg are adjusted to different levels of gravity. We hypothesized that leg spring stiffness would not change under simulated low-gravity conditions. To simulate low gravity, a nearly constant vertical force was applied to human subjects via a bicycle seat. The force was obtained by stretching long steel springs via a hand-operated winch. Subjects ran on a motorized treadmill that had been modified to include a force platform under the tread. Four subjects ran at one speed (3.0 m/s) under conditions of normal gravity and six simulated fractions of normal gravity from 0.2 to 0.7 G. For comparison, subjects also ran under normal gravity at five speeds from 2.0 to 6.0 m/s. Two basic principles emerged from all comparisons: both the stiffness of the leg, considered as a linear spring, and the vertical excursion of the center of mass during the flight phase did not change with forward speed or gravity. With these results as inputs, the mathematical model is able to account correctly for many of the changes in dynamic parameters that do take place, including the increasing vertical stiffness with speed at normal gravity and the decreasing peak force observed under conditions simulating low gravity.
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Typescript (photocopy). Thesis (M.S.)--Oregon State University, 1996. Includes bibliographical references (leaves 123-125).
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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.