Force Measuring Crank for Determination of the Pedal Forces during FES-Cycling
M. Gföhler1, T. Angeli1, T. Eberharter2, P. Lugner2, M. Bijak3
1
Institute of Machine Elements, Vienna University of Technology, Vienna/Austria.
2
Department of Mechanics, Vienna University of Technology, Vienna/Austria.
3
Department of Biomedical Engineering and Physics, Vienna University Medical School, Vienna/Austria
Introduction
The objective of this study was the development of a special force measuring crank, which allows
measurements of the applied forces to the pedal while cycling and the resulting drive torque. Common
cycle ergometers and training systems measure the applied drive torque for calculation of the drive power.
For FES-cycling it is intended to monitor all three components of the force applied to the pedal. At least
the two force components in the parasagittal pedaling plane are needed to calculate optimal stimulation
patterns. 3-dimensional force recording helps to remain within a safe operation margin to prevent from
excessive forces and possible joint, tendon, and bone damage, e.g. in case of severe spastic contractions or
sudden mechanical resistance.
Hull and Davis (1981) developed a force measuring pedal for measuring the two components of the
pedal force in the parasagittal pedaling plane; the influence of the side force is compensated by
counter-moments generated by a special mechanical construction inside the pedal. This force-measuring
pedal is sub optimal for measurements with paraplegic subjects because these are unable to direct the
force in the parasagittal plane and very often strong side-forces occur which are too big to be compensated
for by the intrinsic counter-moments and result in measurement errors. Other disadvantages are the weight
of the force measurement pedal and its size, especially the relatively big distance between pedal axis and
foot sole.
Methods
The pedal force is mechanically transferred to the crank. The force measuring crank (see Fig. 1) was
constructed for measuring the force and moment transfer to the crank axis by means of strain gauges. For
an appropriate monitoring of the strain gauges, a sensitive measurement zone was created by reducing the
cross section of the crank to 4 bars for a length of 50 mm (see Fig. 1, point D). The mechanical load in
point D (see also Fig. 3) is defined by the forces (FDr, FDy, FDt) and moments (MDr, MDy, MDt) in three
orthogonal directions. The tensile strain gauges measure the radial force FDr and the moment MDy. Shear
strain gauges are used to measure the side force FDy. The influences of the torques MDr and MDt are
compensated by the arrangement of the strain gauges. FDt is not measured as it is not needed for further
calculations or safety precautions. The two circuits for measurement of MDy and FDy are switched in series
to decrease power consumption. In the microcontroller unit, directly mounted on the crank, the output
signals of the three Wheatstone bridges are amplified, digitized and then capacitively transmitted from the
rotating to the fixed electrode mounted on the crank bearing. Another microcontroller receiver conducts
the data to the main data acquisition unit where the magnitudes of the measured forces and knee angle are
compared to the predetermined maximum values.
The output signals of the 3 DMS Wheatstone bridges are amplified by instrumentational amplifiers to
a level of 5 V full scale. The amplified signals are sequentially digitized by a multichannel analog to
digital converter (ADC) with a resolution of 12 bit and a sampling rate of 100 Hz. A microcontroller (mC)
controls the ADC and transmits the 4 channels (3 channels and battery voltage) by means of a universal
asynchronous receiver transmitter (UART). The values are transmitted every 10 ms as a data block with a
start byte, 4*2 data bytes and a checksum. The transmitter parameters are: 57600 Bd, 8 bit, 1 stopbit, no
parity. The signal of the rotating transmitter is capacitively coupled to the not rotating receiver. The
ground is connected at least capacitively through the bearings. The dc-component of the signal is lost
through the capacitive coupling and must be restored. This is simply done by a passive highpass filter
consisting of the coupling capacity and a resistor at the receiver with a time constant of much less then
one bit (1/57600 1/s) and a following comparator with a small hysteresis. After a level shift the signal is
RS232 compatible. The capacitive coupling principle is used because of the very low power consumption,
high data rate, low cost and good noise immunity. The small possible transmitting distance of only a few
mm is no problem in this application.
Figure 1: Front and side view of the force measuring crank and connection of the strain gauges to full Wheatstone bridge
circuits. The numbers in brackets identify the strain gauges mounted on the back
Figure 2: Force measuring crank
The dynamics of the moving crank while pedaling are described by the equations of motion
.
A $ ë + B $ e 2 + C $ g = t
(1)
.
where ε is the crank angle, A is the generalized system mass matrix, B $ e 2 represents the gyroscopic
effects, C $ g includes gravitational terms and t are the applied forces and moments. The small damping
effects are not taken into account.
For the calculations of the forces applied to the pedal at the point F the crank is split up at point D (see
Fig. 3), where the strain gauges are placed. Substituting MDy and FDr into the equations of motion (1) (with
correspondingly adjusted system matrices) the pedal forces FFx and FFz (i.e., the forces in the parasagittal
pedaling plane which are effective for the generation of drive torque at the end of the crank) can be
determined. For safety demands, monitoring of the force component FDy is sufficient and detailed
information on the magnitude of FFy is not necessary. With FFt and the crank length lFC (distance F-C) and
the moment of inertia of the crank assembly IC, it follows for the drive torque Mped:
M ped = F Ft $l FC −I C $ ë
(2)
Figure 3: Forces at the crank
Results & Discussion
Figure 4 shows results of isometric measurements (stimulation of quadriceps of a paraplegic subject with
surface electrodes at 30 Hz) at 20 equiangular points along the pedal path performed with the measuring
crank. At each position the crank was locked, 0.5 seconds of settling time were allowed, and then the
chosen muscle was stimulated for 0.75 seconds. 1.75 seconds were allowed as fall time before the crank
was moved to the next position.
F Dr
F[N], Mž10 [Nm]
100
50
0
M Dy
-50
FDy
-100
18
36
54
72
90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360
ε [°]
Figure 4: Results of isometric measurements (stimulation of quadriceps) at 20 points along the pedal path
The force measuring crank allows 3-dimensional force recording while pedaling. Results of static
and/or dynamic measurements can be used for the calculation of optimal stimulation patterns and
investigations on the influence of individual parameters. Out of safety reasons 3D force monitoring while
cycling is especially important for paraplegic cycling, but the force measuring crank can as well be used
for investigations on cycling of neurologically intact subjects. Due to its compact construction the
measuring crank can be mounted on every standard cycle.
References
Hull M.L. and Davis R.R., “Measurement of pedal loads in bicycling: I.Instrumentation,” J. Biomech., 14,
pp. 843-856, 1981.
Acknowledgement
This work was sponsored by the Austrian Science Foundation - FWF.