METROLOGICAL CHARACTETIZATION OF A

CYCLE-ERGOMETER

Bocciolone Marco, Comolli Lorenzo

Department of Mechanical Engineering, Politecnico di Milano, Via La Masa 34, 20156 Milano, Italy

Molteni Franco

Valduce Hospital, Villa Beretta Rehabilitation Center, Via N.Sauro 17, Costamasnaga (LC), Italy

Keywords: Cycle-ergometer, wireless data transmission, mechanical measurements, data analysis, rehabilitation.

Abstract: A cycle-ergometer has been instrumented with suitable strain gauges to obtain metrological qualified

measurements of the left and right leg torque. A wireless device has been used to transmit in real-time the

gathered signals to the acquisition PC. Advantages are to give to doctors and physiotherapists a diagnostic

tool, to analyze the cycling pattern of the patients and to monitor the improvements during rehabilitation.

The real-time measures are also suitable input data for the Functional Electrical Stimulation (FES). All the

analysis was conducted with a particular attention to spinal cord injured patients, who are characterized by

highly asymmetric cycling: yet, this measurement setup, by independent measurement of right and left

torques, can be used successfully also in this particular situation. An explanation of the measuring principles

and a set of first results are given, that show the potentiality of the setup.

1 INTRODUCTION

The present work is aimed at the metrological

characterization of a commercial cycle-ergometer,

used in clinical and private field, for the

rehabilitation of people who need a motor therapy.

The device shows on a display the mean value of

clinical parameters: subject’s motor power, angular

velocity, energy, right and left leg unbalance. Those

values are computed using electrical quantities from

the motor and the unbalance supposes that one of the

legs is not opposing a relevant resistance to the

motion. These average measurements proved to be

quite accurate on healty subjects, but problems could

arise in the unbalance measurement expecially with

strongly asymmetric spinal cord injured patients.

Indeed, in the standard device, the unbalance is

computed by splitting the revolution in half; but in

asymmetric patients one of the legs typically has a

bigger resistance during flexure respect to extension

(e.g. due to spasticity, contracture or joint

limitation), that could lead to systematic errors. The

proposed measurement of indipendent left and right

torques would solve the problem. An introduction to

the devices can be found in (Comolli et al., 2005).

Moreover the average data on the display are not

saved. To give specialists a better idea of the

rehabilitation of a patient, a recording and tracking

of the data should be done, together with an

a-posteriori appropriate data analysis to quantify the

improvements of the treatment.

Another advantage of having a real time

measurement setup is to provide a proper input to a

Functional Electrical Stimulation (FES) system such

as that in (Ferrante et al., 2005 and 2006).

2 CYCLE-ERGOMETER

INSTRUMENTATION

The employed cycle-ergometer provides the mean

value of the above parameters by using measurement

techniques and data processing that, in particular

working situations (typically asymmetries), could

give unreliable information. In order to overcome

those limitations and to have instantaneous

information, an independent measurement system

has been designed and developed, using mechanical

Marco B., Lorenzo C. and Franco M. (2008).

METROLOGICAL CHARACTETIZATION OF A CYCLE-ERGOMETER.

In Proceedings of the First International Conference on Biomedical Electronics and Devices, pages 23-28

DOI: 10.5220/0001052500230028

 SciTePress

sensors. Such system provides the following

quantities:

• bending moments (M

) and radial forces

) of right and left cranks: through two

Wheatstone full-bridges each made up of

electrical resistance strain gauges;

• angular crank position (

θ): through

optical encoders (Gföhler et al., 2001;

Mimmi, Pennacchi & Frosini, 2004) drawn

with white and black sectors on the main

wheel (see Appendix for additional

solutions).

Strain gauges are sensors suitable for superficial

strain measurements. To measure the bending

moments and radial forces, the gauges must be

positioned in the appropriate position and direction

on the crank, and must be connected on a

Wheatstone full-bridge electrical circuit (made of 4

strain gauges) so that the voltage output is made

proportional only to the selected quantity. An

analysis of the strains present on the crank, subject

to a generic force on the pedal axis, and the

application of the basic laws of the theory of

elasticity, will lead to the conclusion that for the

measurement of the bending moment the sensors

must be positioned near the crank axis, where the

strain is larger, two on the upper and two on the

lower surfaces, with the sensing direction along the

crank longer dimension. The radial forces can be

measured with two opposite strain gauges with the

sensing direction along the crank longer dimension

in a position corresponding to the smaller section;

but to complete the Wheatstone bridge, two more

strain gauges are necessary and they will be

positioned transverse to the former so that they will

sense transverse strain.

The positions on the Wheatstone bridge of each

group of 4 strain gauges are selected such that

compensation of radial forces and bending moments

are achieved respectively in the bridges apt to

measure the bending moment and radial force.

Moreover temperature compensation is achieved

automatically by means of auto-compensated strain

gauges for the crank material (steel) and also thanks

to the full-bridge properties. In this specific

application, the locations of strain gauges are shown

in Figure 4, with the numbers corresponding to

specific positions on the Wheatstone bridge,

according to the conventions of Figure 12. A

detailed description of the applied methods can be

found in Doebelin, 2003, Hoffmann, 1989 and

Cigada, Comolli and Manzoni, 2006.

The strain gauge bridges are conditioned through

a four-channel wireless device, which allows to

transmit the signal from the rotating shaft to the

acquisition system. This solution was selected after

also considering slip rings and capacitive coupling

(Mimmi et al., 2004), both of which required too

much additional space.

The selected components are very compact: the

wireless device is mounted on the left side crank

inside a metal protection box (

Figure 1); the

connections between the sensors located on the right

and left side of the device are realized by means of a

multi-core cable passing through the crank axis

(Figure 2). The power supply is given by an internal

hi-capacity rechargeable battery that provides up to

9 h working time. The transmitted data are then

converted in analog signals and acquired with a

traditional DAQ board.

Figure 1: The strain gauge wireless acquisition device is

inside the blue box, mounted on the left crank.

Figure 2:The right crank with the strain gauges wires

passes through the axis to be connected to the wireless

device that is on the other crank.

BIODEVICES 2008 - International Conference on Biomedical Electronics and Devices

Figure 3: Scheme of the measuring chain and feedback on

the patient.

3 MEASURED QUANTITIES

The measurement setup was designed and developed

in order to identify the torque T as a combination of

the bending moment M

and the radial force F

(Figure 4).

Known all the dimensions of the crank, the

torques T are given by:

()

dbe

LrLbL

RrRbR

−

−=

−

−=

(1)

where b, d, e are the dimensions shown in Figure 4,

and L and R pedex are respectively referred as the

left and right leg.

The instantaneous total power P

tot

can be

computed, known the angular velocity

measured

by the encoder, as:

()

⋅+=

LRtot

TTP

(2)

Moreover the mean energy per revolution can be

computed as:

∫

⋅=

)(

totm

dttPE

(3)

where t is the time and t

and t

are the instants of

start and end of a revolution.

The unbalance U, a very significant quantity for

asymmetric patients, can be computed as:

totm

LmRm

−

(4)

where a positive value of U mean an unbalance

toward the right leg that is more powerful.

Another useful quantity is the jerk J, i.e. the rate

of change of angular acceleration, which shows the

fluidity of the motion (Schot, 1978 and Teulings et

al., 1997). Absolute jerk is defined as the third

derivative of angular position, while a more

interesting parameter is J

std

, the standard deviation of

jerk computed per revolution:

()

∫

−

std

dtJJ

&&&

(5)

where

J is the mean jerk in one revolution.

Figure 4: Scheme of the positioning of strain gauges on

the right crank. For the strain gauges numbering

conventions, see Figure 12.

4 FIRST RESULTS

The identification of the motor strategy of a patient

and the comparison with healthy subjects (or with

the same patient before rehabilitation) is

fundamental to diagnose a pathology and verify the

progress. The modified cycle-ergometer gives to the

doctors and physiotherapist many information: in the

following some examples.

Figure 5 shows a spinal cord injured patient

cycling with the help of FES. Such a patient can

cycle also without FES because the cycle-ergometer

is motorized and maintains a minimum speed. But

the muscles of the insane leg would never make any

work and may loose mass. FES permits also the use

Wireless strain gauges

device:

• 2 bridges for M

• 2 bridges for F

Receiver and

analog output

Acquisition PC

and FES device

controller

PCI

radio

2.4 GHz

Cycle-ergometer

encoder

signals

(

BNC

)

Acquisition board

USB

FES

controller

Patient

BNC

pedal axis

crank axis

b,R

bending moment

strain gauges

1+3

2+4

b-d

t,R

r,R

radial force

strain gauges

1+2

3+4 opposite

METROLOGICAL CHARACTETIZATION OF A CYCLE ERGOMETER

of those muscles and therefore let them grow in size,

even if the patient cannot control them.

Figure 5: A spinal cord injured patient cycling with the

help of FES.

Figures 6-9 show an example of data that can be

retrieved from the measuring system. A healthy

subject was asked to cycle in different conditions,

such as active (time 0-15 s), passive (15-40 s), active

(40-58 s, various powers), only right leg (58-68 s)

and only left leg (68-82 s).

Figure 6 shows the angular position and the three

derivatives that are necessary to compute all the

subsequent quantities.

Figure 6: Angle and derivatives from cycling data of a

healthy subject in different operating conditions.

In Figure 7 the standard deviation of jerk per

revolution was computed; this quantity has relevant

information: particularly the higher jerk is obtained

when only one leg is used, this is due to the higher

speed variations. Values up to 20 rev/s

are normal

for healthy subjects during normal cycling with a

high cycling resistance, while small values such as

2 rev/s

can be obtained with small resistance (not

shown).

Figure 7: standard deviation of jerk per revolution: the

biggest values are at right when only one leg was used.

The raw measurements would lead to instantaneous

torque and power plots (not shown), with left, right

and total components. Those information are

interesting but highly difficult to analyze. A better

solution has been found in re-phasing and averaging

the torque values from some adjacent revolutions.

Some examples will be shown ahead.

Average power and energy per revolution are

shown in Figure 8, and give a good idea of the

cycling conditions.

Figure 9 shows the percent unbalance and the

total energy produced by the patient from the start of

the test. Here also very small unbalance will build

up and will be easily visible at the end of the test.

Figure 8: Average power and energy per revolution.

Figure 9: Unbalance and total energy from the start of the

test.

A better way to evaluate the torque produced by the

patient is to re-phase the torque signals and compute

the median value in a number of revolutions. The

median torque (along with percentiles) shows a

BIODEVICES 2008 - International Conference on Biomedical Electronics and Devices

better waveform of the cycling and allows a better

comparison between healthy and non healthy

subjects and between the same patient before and

after the rehabilitation. Figure 10 shows the torque

from a healthy subject, while in Figure 11 the same

subject was asked to use only the right leg. The zero

crank angle is set at the maximum flexion of the left

hip.

Figure 10: Median torque from a healthy subject actively

cycling: (a) the left (dashed) and right (solid) components,

(b) total torque that show nearly symmetric peaks. In

dotted line the 5

-95

percentiles.

Figure 11: Same as the previous figure but related to an

healthy subject, asked to cycle only with the right leg; the

curves show highly asymmetric peaks.

The situation of a healthy subject asked to cycle only

with the right leg simulates only one of the many

possible cases of pathologic patients, where one of

the legs is very weak but not completely passive.

Indeed a healthy subject is unable to perform a true

passive pedaling, as shown in Figure 11(a), where

the left leg curve (dashed) is nearly flat in the

angular range 270-360°, indicating that the weight of

the leg is unconsciously partially compensated.

5 CONCLUSIONS

The paper deals with the design and the realization

of a measurement system able to measure relevant

quantities of the cycling, such as the torque (left,

right and total), power, energy, unbalance and jerk.

The experimental tests involved both healthy

subjects and spinal cord injured patients. Examples

of the obtained measurements had been shown

extensively in the figures. The results obtained up to

now allowed the doctors and physiotherapists to

have at their disposal additional and metrological

qualified information, useful for diagnostic purposes

and for checking the effects of the rehabilitation.

ACKNOWLEDGEMENTS

This work was supported by the Fondazione Cariplo

in the framework of the research program

HINT@Lecco. Authors would like to acknowledge

Mauro Rossini (Villa Beretta Rehabilitation Center)

for his helpful discussion.

REFERENCES

Comolli, L., Cantatore, A., Zappa, E., Bocciolone, M.,

Molteni, F., 2005. HINT@LECCO project:

metrological characterization of a cycle-ergometer,. In

SIAMOC 05, 6th Congress of the Italian Society of

Movement Analysis in Clinics.

Ferrante, S., Pedrocchi, A., Gioia, M., Ferrigno, G.,

Molteni, F., 2005. HINT@LECCO project: FES

cycling optimization and first clinical experiments of

on patients. In SIAMOC 05, 6th Congress of the

Italian Society of Movement Analysis in Clinics.

Ferrante, S., Pedrocchi, A., Ferrigno, G., Molteni, F.,

2006. Experimental campaign of FES cycling on

hemiplegics: first results. In SIAMOC 06, 7th

Congress of the Italian Society of Movement Analysis

in Clinics.

Gföhler, M., Angeli, T., Eberharter, T., Lugner, P., Mayr,

W., Hofer, C., 2001. Test Bed with Force-Measuring

Crank for Static and Dynamic Investigations on

Cycling by Means of Functional Electrical

Stimulation. IEEE Transactions On Neural Systems

And Rehabilitation Engineering, Vol. 9, No. 2, June

2001, pp. 169-180.

Mimmi, G., Pennacchi, P., Frosini, L., 2004.

Biomechanical Analysis of Pedalling for

Rehabilitation Purposes: Experimental Results on Two

Pathological Subjects and Comparison with

Non-pathological Findings. Computer Methods in

Biomechanics and Biomedical Engineering, Vol. 7,

No. 6, Dec. 2004, pp. 229-345.

(a)

(b)

(a)

(b)

METROLOGICAL CHARACTETIZATION OF A CYCLE ERGOMETER

Doebelin, E.O., 2003. Measurement Systems, McGraw-

Hill, 5

edition.

Hoffmann, K., 1989. An introduction to measurements

using strain gauges, Hottinger Baldwin Messtechnik

GmbH, 1

edition.

Cigada, A., Comolli, L., Manzoni, S., 2006. Estensimetria

Elettrica, CittàStudi Edizioni, 1

edition.

Schot, S.H., 1978. Jerk: The time rate of change of

acceleration, American Journal of Physics, Nov. 1978,

Vol. 46, Iu. 11, pp. 1090-1094.

Teulings, H.L., Contreras-Vidal, J.L., Stelmach, G.E.,

Adler, C.H., 1997. Parkinsonism Reduces

Coordination of Fingers, Wrist and Arm in Fine Motor

Control, Experimental Neurology, Vol 146, pp. 159-

170.

APPENDIX

For the crank angle measurement, a traditional

encoder solution was chosen using a photo-reflective

sensor coupled with a yet-present encoder drawn on

the main cycle-ergometer wheel. Another two

solutions have been also investigated.

The first solution was an inclinometer able to

measure the bending of a beam with a small mass at

the extreme, by means of strain gauges. The

inclinometer has been positioned on the crank and

have a nearly cosinusoidal output dependent on the

angular position. The measured bending moment is

proportional to the tangential acceleration a

of the

mass, which can be computed as:

ρθθ

+= cosga

(6)

where g is the acceleration of gravity and ρ is the

distance of the mass from the crank axis (see Figure

12). After the realization of an inclinometer with a

small ρ value (Figure 13), the measurements showed

that the angular acceleration term can be neglected

and so the signal is actually a cosinusoid.

Another consideration is about the thickness of

the beam that should not be too thin, this because a

high natural frequency is desirable; but also not too

thick because the bending must be measurable. The

output signal was gathered with the same strain

gauge wireless device used for moments and forces

measurements, then it is filtered and analyzed to find

the unknown angle. To solve the two solutions

ambiguity of the arccosine function, the first

derivative was considered: a negative value indicate

that the solution is in the first or second quadrant.

Another studied solution takes advantage of a

cam positioned on the crank axis (Figure 12); the

distance of the cam to a fixed point on the

cycle-ergometer was measured by means of a laser

triangulation transducer. The resulting signal is

nearly cosinusoidal and can be analyzed in the same

way of the inclinometer one. In fact the signal is of

this kind:

()

θθθ

sincos

eRer −+−=

(7)

where r is the distance from the crank axis of a point

on the cam surface that cannot rotate with it, e

is the

cam eccentricity and R is the cam radius. With the

proper selection of the dimensions, the cosinusoid

approximation can give as low as ±5° errors, as in

the realized cam.

All the described measurement solutions were

successfully used and proved to be of interest when

no simpler alternatives are possible.

Figure 12: Scheme of the inclinometer and the cam

mounted on the crank.

Figure 13: The adopted inclinometer.

)

Cran

Pedal

axis

F = mg

2+4

strain

gauges

1+3

Inclinometer

1 2

Strain gauges

Wheatstone bridge

conventions

Laser triangulation

distance sensor

Laser

beam

Cran

axis Cam cente

BIODEVICES 2008 - International Conference on Biomedical Electronics and Devices