Eur J Appl Physiol (1985) 54:210--215 European Journal of

Applied Physiology and Occupational Physiology �9 Springer-Verlag 1985

A dynamometer for the measurement of force, velocity, work and power during an explosive leg extension

F. J. Avis 1, A. Hoving 2, and H. M. Toussaint 3

1 Department of Physical Education and Sports, University of Technologie, Delft 2 Technical Construction Centre, University of Technology, Delft 3 Interfaculty of Physical Education, Dept. of Functional Anatomy, Free University, Amsterdam, The Netherlands

Summary. A dynamometer for measurement un- der static and dynamic conditions is presented. At different load levels, force, velocity, work and power can be measured in explosive leg exten- sions. Measurements on 53 subjects at different load levels (0--125.5 kg) were carried out. Peak power ranged from 2611 to 1746 W, force from 1351 to 1899 N, velocity from 1.61 to 0.89 m- s -1 and work from 329 to 605 J. Between trial correla- tion coefficients ranged from 0.72 to 0.95. The dy- namometer is compared with others, and it is con- cluded that data obtained by this dynamometer have a greater practical validity.

Key words: Dynamometer -- Force -- Work -- P o w e r - Legs

(Gregoire et al. 1984). In devices where only monoarticular isotonic or isokinetic measure- ments are made one or both aspects are ne- glected.

With these objections in mind a dynamometer was constructed for measuring the uni- or bila- teral force, velocity, work and power in acceler- ated leg extensions against different loads.

Technical data

Apparatus

The dynamometer enables measurements under static and dynamic conditions.

Introduction

The use of dynamometers has become a widely accepted method in evaluating muscle strength. However, with the majority of dynamometers only static measurements of muscle strength can be made. A disadvantage of these dynamometers is that neither work nor power can be measured, while in many sports these variables are impor- tant prerequisites for good performance. A few devices are described for the measurement of muscle strength, work and power under isotonic, isokinetic (e. g. Cybex) and other conditions (Ariel 1983; Buhrle et al. 1983).

In many athletic activities like jumping, run- ning and rowing the body is accelerated. Further- more the transport of power by biarticular mus- cles plays an important role in these activities

Static condition

Figure 1 shows the main parts of the dynamom- eter during static measurement. The foot rests (A)

D w-

E ~ 1~ 1 U

--B

I

A% zlk

Offprint requests to: F. J. Avis, Sportstichting, Mekelweg 8, Fig. 1. Functional parts of the dynamometer during static 2628 CD Delft, The Netherlands measurements. For further explanation see text

F. J. Avis et al. : A d y n a m o m e t e r for force, work a n d power m e a s u r e m e n t 211

are mounted on a bar to which four strain gauges are attached. Together with an amplifier, an ana- log-digital converter (ADC) and an Apple II mi- crocomputer these parts form the force-registering system.

The bar (B) is part of a yoke is connected to the bearings (C) and is coupled on one side to an angle t ransducer (D).

This construction can be placed in the desired position by sliding it in the indicated directions. There it is fastened with clamps (E). Thus it is possible to measure isometric forces over a range of knee-angles and to adjust the measuring device to the specific dimensions of the different sub- jects.

The subject is s trapped to the seat (F), which is immobilized by two bars (G). Two handgrips (H) enable addit ional fixation of the subject.

Dynamic situation

By removing the bars (G) the dynamometer is ready for dynamic measurements (Fig. 2). The seat is now movable on a rail and mounted to it with 6 ball-bearings (f--0.0025) to minimize fric- tion and to make high stretch velocities possible (Fig. 3). Two cables are attached to the seat. One leads via a pulley-system to an electromagnet (I).

The other is coupled to a counterweight (J) to compensate for the weight of the electromagnet. When the electromagnet is switched on a weight- holder (K) can be coupled to it. On the weight- holder (mass 25.5 kg) different weights (L) (1.125--280.0 kg) can be placed, thus different loads can be applied. To prevent the subject from damaging himself a cushion (M) is placed behind the seat at such a distance that full stretching of the legs is possible. The cushion decelerates the subject after an explosive stretch movement. At that moment the electromagnet can be switched off to prevent the weight pulling back on the sub- ject. The weightholder then drops on the buffer (N).

The displacement of the seat is registered by an incremental encoder (0) (Leine & Linde AB, Sweden, model 58, type 5806/A/15V/400) which is coupled to a non-elastic loop (P) attached to the seat (Fig. 2 and 3).

The angle between the horizontal plane and the direction of the force is registered with an an- gle transducer (D).

Calibration

The force-measuring system can be calibrated us- ing the device depicted in Fig. 4. The construction

~ '" " :D']

�9 r l I II t ,IF,

E

c

H ~P ,,~ " - ~,/I Fig. 2. Func t iona l par ts o f the d y n a m o m - eter du r ing d y n a m i c m e a s u r e m e n t s . For fur ther exp l ana t i on see text

212 F. J. Avis et al.: A dynamometer for force, work and power measurement

. O N ELAST,C LOOP r { - k ' ! . . . . . . . E N C O D E R \ ~ . . . . . II . . . . . .

- - - - ~ - B A L L B E A R I N G S

/ / / / / / / / / / / / / / /

Fig. 3. Attachment of seat to rail with ball- bearings and the coupling of the displace- ment t ransducer to the seat with a non-elastic loop

shown permits the application of a very large range of forces, by using a few calibration weights.

The encoder produced 400 pulses per revolu- tion. Since the circumference of the wheel is 0.1 m, the resolution is 0.25 mm (1/4000).

The angle transducer was calibrated to pro- duce 100 mV per degree.

The force-, angle- and displacement-signals are amplified, digitized by the ADC (12-bits, 150 Hz) and processed by an Apple II microcomput- er. According to the diagram representing the method of calculation (Fig. 5), velocity, power and work are computed.

A further detailed description is available on request (Hoving 1981; Kramer 1982).

Example of measurement

Several interesting research questions can be dealt with by this versatile dynamometer. It can be

WEIGHT ~ F 700

j LEVER ~ 6 F I . . . . . i . . . . . i

BEARINGS

\ \ \ \ \ \ \ \ \ FRAME

Fig. 4. Calibration device for the calibration of the force meas- uring system

ANGLE ~ ( TRANSDUCER t)

DISPLACEMENT

Fig. 5. Diagram of the method of calculation. S is the displace- ment of the seat, F is the force in the horizontal plane, V is the velocity of the seat, P is the power, and W equals work

used, for instance, to determine the influences of training, the differences between one leg and two leg movements, the effect of countermovements, and the influences of feedback or knowledge of results.

As an example of the application of the dyna- mometer in the dynamic situation, force, velocity, work and power was registered during a simple explosive leg extension of both legs in 53 healthy males (age 23.1 years+3.1, length 184.9 cm+5.2, weight 76.3 kg+5.6) (Fig. 6). Informed consent was obtained from all subjects. The movement was started with the knees flexed (70~ An 'all out' effort was made on an accoustic starting sig- nal 2 s after a warning signal. Seven levels of ad- ditional load (between 0 and 125.5 kg) were ap- plied. At each level two measurements were made. Occurrence of fatigue was avoided during the course of the experiment.

Figure 7 gives a typical example of the instan- taneous force, velocity and power curves at loads of 45.5 kg and 105.5 kg. From the curves, force (F)

F. J. Avis et al.: A dynamometer for force, work and power measurement 213

Fig. 6. Stroboscopic photograph of subject performing an ex- plosive leg extension

and velocity (V) were determined 1/75 s before peak power (P) was delivered. The amount of work (W) was computed by integrating the power curve. Means and standard-deviations are given in Table 1. Because the angle transducer was not operational, the force values are overestimated ( + 10%) with respect to the horizontal plane and thus the values of work and power are overesti- mated as well. Pearson's correlation coefficients between trials at each load level are given for the four variables in Table 2.

Discussion

The high correlations (Table 2) show that good re- producibility of measurements can be obtained.

FORCE POWER VELOCITY

. ~ . . - .... / . . \ Pi :" - ,.

/ . "~ ': V

F !1 ' . .

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i ./ q

/ t.

T I M E 1/15 see

"1

250 N

250 W

0.2 M . S E C - !

FORCE POWER VELOCITY

2 5 0 N

I 250 W

0.2 M ,SEC - |

F

I "'i �84 TIME 1 / 1 5 SEC

L.--.a

Fig. 7. Typical examples of the instantaneous force (F), veloc- ity (V), and Power (P) at a load of 45.5 (a) and 105.5 kg (b)

Table 1. Peak power (P), force (F), velocity (V) and work (W) at different load levels. Means (X) and standard-deviations (SD) of the first (1) and second (2) trial are given. (N= 53)

Load P (W) F (N) V ( m - s - 1) W (J) (kg)

X (SD) X (SD) X (SD) X (SD)

0 1 2216 (500) 2 2267 (492)

25.5 1 2574 (474) 2 2611 (484)

45.5 1 2503 (495) 2 2525 (515)

65.5 1 2397 (531) 2 2301 (542)

85.5 1 2131 (497) 2 2104 (496)

105.5 1 1944 (484) 2 1862 (472)

125.5 1 1762 (451) 2 1746 (442)

1351 (255) 1.57 (0.15) 1371 (255) 1.59 (0.15)

1544 (249) 1.61 (0.12) 1564 (237) 1.60 (0.12)

1660 (266) 1.46 (0.12) 1645 (282) 1.49 (0.12)

1727 (285) 1.34 (0.13) 1666 (297) 1.33 (0.13)

1747 (297) 1.17 (0.12) 1709 (298) 1.18 (0.12)

1828 (302) 1.02 (0.11) 1748 (326) 1.01 (0.12)

1899 (337) 0.89 (0.12) 1883 (360) 0.89 (0.11)

329 (65) 340 (66)

447 (68) 453 (66)

477 (67) 492 (74)

523 (80) 522 (84)

547 (82) 553 (83)

582 (87) 580 (100)

605 (113) 604 (111)

214 F.J. Avis et al.: A dynamometer for force, work and power measurement

Table 2. Pearson's correlation coefficients between the two trials (1 and 2) as a test-retest reliability of the measurements. (N=53)

Load P F V W

0 0.88 0.92 0.72 0.84 25.5 0.89 0.84 0.77 0.92 45.5 0.93 0.95 0.72 0.86 65.5 0.94 0.94 0.84 0.93 85.5 0.95 0.93 0.89 0.92

105.5 0.93 0.87 0.87 0.94 125.5 0.93 0.95 0.86 0.95

The mean peak power during the simple stretch movement was 2210 Watt. This is more than twice the peak power reported by Ivy et al. 1981 for isokinetic knee extension with one leg (397.5 Watt). In our view this difference is due to the fact that the present apparatus facilitates the transport of power by polyarticular muscles and lays no artificial constraints on acceleration of the movements. This view is supported by the fair agreement between the power reported here and values for specific explosive movements like jumping (Vergroesen et al. 1982). In comparison with other means of measuring force, velocity, ex- ternal mechanical work and power, such as verti- cal jumps with or without the use of force plat- forms (Asmussen and Bonde-Petersen 1974; As- mussen et al. 1976; Bosco 1981; Bosco et al. 1983; Bosco and Komi 1979; Cavagna et al. 1971; Cav- agna 1975; di Prampero and Mognoni 1981; Vii- tasalo and Bosco 1982), stairclimbing (Margaria et al. 1966; Kalamen 1968) and ergometry (Bar-Or et al. 1980; Ikuta and Ikai 1972) this dynamom- eter has several attractive properties. As force and displacement are directly measured it is not nec- essary to make assumptions concerning, for ex- ample, take off and landing body position, the contribution of other body parts, or the relation- ship between horizontal and vertical velocity, which are open to criticism and to the use of inac- curate integration techniques. Another advantage is the possibility of measuring the indicated varia- bles as functions of a continuum of loads during a simple extension of the legs unaffected by compli- cated (sports-) movement techniques. Very impor- tant is the fact that the excursions of the move- ments can be completely controlled, which is es- sential in the case of research on positive work as a function of eccentric loads, a fact until now overlooked in countermovement and depth jump- ing experiments in which subjects spontaneously chose the extent of flexion preceding the exten- sion. Although Hubley and Wells (1983) state that

"The amplitude of knee flexion was standardized at the start of the upward movement", it remains unclear as to how this was done.

In general, it can be said that data obtained by the dynamometer described have a greater valid- ity for practical applications.

The dynamometer is being used for research, and results dealing with the influences of two training schedules and the effect of countermove- ments will soon be reported (Avis et al. unpub- lished work). At present the apparatus is being used in studying the differences between one and two leg movements combined with EMG registra- tion.

Acknowledgement. The authors wish to express their gratitude to the coworkers of the Centrale Werkplaats and the Centrale Electronische Dienst, University of Technology Delft and W Rijnsburger, Interfaculty of Physical Education, Free Univer- sity, Amsterdam.

The work performed by HM Toussaint is part of his doc- toral examination and was supervised by FJ Avis, GJ van Ingen Schenau, PA Huijing and RD Woittiez.

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Accepted April 30, 1985