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ME/AE 5478, CompE 5820, EE 5870 – Mechatronics
Questions: Sensors and Transducers
QUESTION 1
For the potentiometer in the Figure below determine the expression for the output voltage Vo
(i.e., the voltage across the load) as a function of linear displacement x when the load resistance
is on the same order of magnitude as the other resistances in the circuits and when the load
resistance is significantly larger than the magnitude as the other resistances in the circuits. The
total wiper length of travel is lm.
Vref
x
RC
RL
QUESTION 2
For the rotary potentiometer, the relative loading error is the loading error e divided by θ/θmax.
Determine the ratio of θ/θmax for which the maximum relative loading error occurs.
QUESTION 3
Explain how a piezoelectric element can be used to measure acceleration. Explain how a strain
gauge can be used to measure acceleration. Explain how the displacement of a mass can be used
to measure acceleration.
QUESTION 4
For the potentiometer in the Figure below determine the expression for the output voltage Vo
(i.e., the voltage across the load) as a function of linear displacement x when the load resistance
is on the same order of magnitude as the other resistances in the circuits and when the load
resistance is significantly larger than the magnitude as the other resistances in the circuits. The
total wiper length of travel is lm.
Re
Vref
x
RC
RL
Re
2
QUESTION 5
An encoder is to attached to shaft A. Shaft A is connected to shaft B through a gearing system
with gear gain Ng, which is the ratio of the velocity of shaft A to the velocity of shaft B. If the
encoder is used to measure the angular position of shaft B, what is the angular displacement
measurement resolution? If the encoder is used to measure the velocity of shaft B by counting
the number of encoder pulses during a time period T, what is the angular velocity measurement
resolution? If the encoder is used to measure the velocity of shaft B by counting the number of
clock cycles during one encoder pulse, what is the angular velocity measurement resolution?
QUESTION 6
Explain how a piezoelectric element can be used to measure force. Explain how a strain gauge
can be used to measure force. Explain how the deflection of a spring can be used to measure
force.
QUESTION 7
A motor drives a rack and pinion mechanism. Each motor revolution causes 10 mm displacement
of the rack. An encoder is directly attached to the motor shaft to sense the position and velocity
of the rack. If the encoder has 720 counts/revolution and quadrature encoding is utilized, what is
the rack displacement measurement resolution? If the motor encoder signal is measured at a
constant frequency of 100 Hz, what is the rack velocity measurement resolution?
QUESTION 8
For the capacitance displacement sensor shown below, complete the following:
a. Determine the transfer function
V0 ( s )
assuming the reference voltage is constant.
X (s)
b. For a constant displacement xss, determine the steady–state output voltage.
c. Determine the sensor’s time constant.
3
d. Determine the sensor’s bandwidth.
C = k/x
Cref
R
+
+
Vo
Vref
-
QUESTION 9
For the capacitance displacement sensor shown below, determine the transfer function
when sLL and RL are on the same order as R. Determine the transfer function
and RL are much larger than R.
4
E0 ( s )
Eref ( s )
E0 ( s )
when sLL
Eref ( s )
5