S 458 Biomedical Instrumentation and Design BME/EECS 458 LAB HANDOUT

Fall 2000
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___
Force Transducer and EMG

7-1
BME/EECS 458 Biomedical Instrumentation and Design

Experiment
# 7
1


Force Transducers and Electromyographic Signals

As a leader in research on bone and muscle tissue, the University of Michigan has many biomedical labs
investigating the mechanical, structural and biological properties of the skeleto-muscular system. In
these labs investigators often simultaneously measure the force that a muscle produces with a load cell
or strain gage and record the muscular activity with an electromyographic (EMG) signal acquisition
system. This experiment will introduce you to the basic procedures and problems of this type of data
acquisition.

A. Force Transducers: Strain Gauges and Load Cells


PURPOSE

First we will focus on a force transducer consisting of strain gauges in a Wheatstone bridge configuration
to measure strains and forces on a cantilever beam model of the forearm. Biomechanical information is
often difficult to obtain directly and the cantilever beam will serve as an ideal model to investigate the
mechanical properties of the forearm. Different loads will be applied to the end of the beam to study
force-strain relationships, hysteresis, and natural frequencies of the system.

Secondly, we will investigate a special force transducer called a load cell. The load cell is commonly
used in both research and industry to measure strains and loads. The load cell will be used to measure
the maximum possible elbow moment at elbow angles of 45, 90, and 135 degrees. The maximum rate
of the developing moment will also be determined.


I. INTRODUCTION

A. Strain Gauges Mounted on a Cantilever Beam

A strain gauge is a short, thin length of wire attached to the material of interest to obtain strain
information. The gauges are bonded to the surface of the object of interest allowing it to experience the
same strain as the surface of the object. Three typical strain gauges are shown below (Webster 3
rd
ed.
pg. 49):





1
This experiment was originally designed by Charles D. Choi. BME/EECS 458 LAB HANDOUT

Fall 2000
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Force Transducer and EMG

7-2

Backing
Backing
Backing
Leads
Leads
Leads
Gage
wire
Felt
Foil
Helical
wire



Figure 1. Strain Gauges (a) Resistance-wire type. (b) Foil type. (c) Helical-wire type. Arrows above
units show direction of maximal sensitivity to strain.

Strain ( ) is defined as the differential deformation in the beam and has dimensionless units (Nash 3):
=
L
L

where L is the deformation and L is the length of the beam.

Tensile strains on the gauges result in increasing length and decreasing cross-sectional area of the wire.
These two effects increase the resistance in the gauge as follows (Myers 20):

R
L
A
R
L
A
L A
A



=
= 2


where R is the resistance, A is the cross-sectional area, L is the length, and is the resistivity.

The sensitivity of the device, called the gauge factor (GF), usually supplied by the manufacturer of the
device, is given by (Myers 20):





R
R
L
L
R
R
GF = =




For this lab, a gauge factor of 2.0 will be used. Thus, a strain gauge serves as a transducer, varying in
resistance in proportion to the strain on the surface of the cantilever beam. This change in resistance can
be measured using the Wheatstone bridge circuit. The Wheatstone bridge circuit consists of only
passive resistive elements and is used to improve the sensitivity of the transducer (Myers 20). BME/EECS 458 LAB HANDOUT

Fall 2000
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Force Transducer and EMG

7-3


Figure 2. Wheatstone Bridge Circuit

The variable resistor, r
b
, is used to balance the bridge circuit so that the current through R
1
and R
4
is
equal to the current through R
2
and R
3
. This adjustment can also compensate for the initial weight of
beams and eliminate small differences in the R values between the gauges.

The equations below illustrate how the change in resistance, R (proportional to the strain at the surface
of the beam) is reflected in the output voltage for a 4 strain gauge Wheatstone bridge. As force is
applied the strain develops in the material and the open-circuit voltage, V
out
, becomes

V
V
V
V R
R
R
R
R
R
V GF
out
a
b
in
in





= =
+

=
[
]
2
2


Thus, small changes in resistance of the strain gauge will produce a voltage V
out
. V
out
can then be
amplified and collected using either analog or digital data acquisition. The larger the DC excitation, V
in
,
the greater the output voltage of the bridge circuit. This greater output occurs at the a cost of greater
power consumption from the power supply and greater power dissipation of the strain gauge elements.

Another way to analyze the problem is to assume the gauges are balanced so that r
b
is not needed.
Then R1 and R4 can be considered as a voltage divider with an output voltage of V1. Likewise R2
and R3 can also be thought of as a voltage divider connected across the excitation voltage of Vin with
an output of V2. BME/EECS 458 LAB HANDOUT

Fall 2000
_________________________________________________________________________________________
___
Force Transducer and EMG

7-4

We can see that the output voltage of the circuit can be found from the difference between these two
voltages V1 and V2:


V
Vout V
Vout V
V
1
2
1
2
=
+
=
If a strain gauge is stretched, its nominal resistance R will increase by an amount R, and if it is
compressed by an equal amount the resistance will decrease by an amount of R. If a strain gauge is
attached to the top of the beam, it will be stretched as the beam bends (R1 = R - R). Likewise, a
strain gauge attached to the underside of the beam will undergo compression (R4 = R + R). Two
gauges arranged so that one decreases by the same amount that another increases are called a
complementary pair. We can solve as follows:


(
)
(
)
V
Vin
R
R
R
R R
R
V
Vin
R
R
R
1
2
3
3
2
=
+
+
+
=
+







The usual situation is for R2 = R4 = R, so the solution for Vout is:


Vout
Vin
R
R
=




2

for a complementary pair (2 gauges)

For practical purposes, often just 1 or 2 strain gauges are usually used with the rest of the resistors
being conventional resistors. Using 2 strain gauges allows one to measure the strains on the beam and
the other to compensate for thermal strains. However, rarely are 2 or 3 resistors exactly the same and
often the bridge circuit is balanced using a potentiometer, r
b
(Myers 21). Often times, the V
out
will not
read 0 when =0. Using the potentiometer with no applied loads, the potentiometer is adjusted until
V
out
reads 0.
BME/EECS 458 LAB HANDOUT

Fall 2000
_________________________________________________________________________________________
___
Force Transducer and EMG

7-5
Instead of deriving the stress-strain-force relationships, only the relevant beam theory will be stated
here.







Figure 3. Cantilever Beam Apparatus


The surface strain, , is related to the surface stress, , by Youngs modulus of elasticity (E) (Nash 4):

=



for Al beam
E
E
N m
= 69 10
9
2
/




In this experiment, a calibration curve of strain vs. force will be computed using known forces and the
dimensions of the beam. These calculations will be compared with the measurement of strain obtained
by the strain gauges.

The surface stress of the cantilever beam shown below is given by the following equation (Nash 128):


b h



2
=
=
= =
M y
I
M
M
F l
y
h
6
2
I
b h
=
for a rectangular solid
1
12
3


where I is the area moment of inertia, l is the length of the beam, h the thickness, b the base width, M is
the bending moment, and F the externally applied force/load (in Newtons). Thus, the theoretical strain
would be:
th
M
E bh
=
6
2

BME/EECS 458 LAB HANDOUT

Fall 2000
_________________________________________________________________________________________
___
Force Transducer and EMG

7-6

Recall, L
L
=


The effective spring stiffness of a theoretically massless cantilevered beam with a load, F, is (Myers 22):

K
F
L
E I
l
=
=
3
3


where I is the area moment of inertia.

Thus, the undamped natural frequency is simply the square root of the effective spring stiffness, K,
divided by the mass, m (Myers 22):
n
K
m
=



B. Load Cell

The load cell is a force transducer used to obtain strain and force information. It is commonly used in
biomechanics research and heavily used in industrial applications. A diagram of the load cell is below:



Figure 4. Load Cell

The four strain gauges are mounted on the inside and outside surfaces of the outer parts of the two
circles. The outside strain gauges will be in tension