# Project 2 Velocity Estimates

```ENGR-2300
ELECTRONIC
INSTRUMENTATION
Project 2
Project 2
Velocity Estimates
For this project, each team will investigate two approaches to estimating the velocity of the end of the cantilever
beam using measurements of acceleration and position. Velocity can be estimated by taking the integral of the
acceleration (using an accelerometer) as a function of time or by taking the derivative of the position (using a strain
gauge) as a function of time. You are to do both and compare the results.
Figure 1.
When you connect these devices to the scope, you get a voltage signal. The strain gauge output is proportional to
beam position. The accelerometer gives a signal proportional to the acceleration. We know that the unit of
displacement is meters, m; the unit of velocity is m/s; and the units of acceleration is m/s 2. We also know that all of
these signals are time dependant functions that look like decaying sinusoids. In this project, we will take data from
both devices, calibrate them, convert them into velocity, and compare the results.
Part A of this handout discusses how to use the accelerometer chip (available from your instructor) to find the
acceleration of the beam directly. Part B discusses methods of using measurements taken by the strain gauge (which
is proportional to the displacement of the beam) and comparing it to the acceleration measurement of the beam. Part
C discusses converting both signals to velocity and comparing the results. Part D discusses some ideas for extra
credit. Appendix I contains a task list for the project. Please note that the handout for the project (Parts A-D)
contains background information that you need, but the task list provides the order in which the tasks should be
performed. Appendix II contains what your appendix for the project report should contain. Appendix III outlines
the project report. For additional background information consult the links and spec sheets on the course links page.
Note: Many groups end up taking their data more than once for this experiment. It is a good idea simply to practice
the first time. Get your circuits working. Take practice calibration measurements. Make sure you are absolutely
sure you know all the data you need to take. Then, when you are ready, all the data can be taken in about 15
minutes under the same conditions. As in Experiment 5, write down the number of the beam taken on the first day
and use the same one throughout the project for more consistent results.
Part A - Building an AD Accelerometer circuit
This section discusses how to build and calibrate an accelerometer circuit that you can use to find the acceleration of
the cantilever beam directly.
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
-1-
Revised: 17 April 2016
Troy, New York, USA
ENGR-2300
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The Circuit
The following circuit can be used to create a signal proportional to the acceleration of the beam using a commercial
accelerometer. The Analog Discovery boards have built-in voltage supplies labeled V+ = 5V and V- = -5V to power
the accelerometer. You will only need V+ and ground. Do not connect anything to V-!
Connect
to V+ = 5V
10µF
Connect
to 1+
Connect to
Ground
Accelerometer configuration for Analog Discovery (from the device spec sheet)
Figure 2.
Note: The accelerometer chip is powered by a 5V source. Connect V+ and the 0.1µF capacitor to pin 14 and
ground pin 7. The output is found at pin 10. Connect to the output using a capacitor to block the 2.5V offset.
No connections are necessary at pins 5, 8, 9.
The accelerometer is surface mounted and, thus, cannot be plugged into a protoboard. It also needs to be oriented
vertically in order to record the acceleration of the beam. Therefore, we have mounted the chip on what is called a
surfboard. You will have to be careful that you connect things correctly, since the surfboard has 16 pins and the
accelerometer has only 14. (We do not use the two in the center). The pin numbering is given in the figure below.
Figure 3.
You only need 3 connections between the Analog Discovery and the accelerometer, +VS,
Ground, and VOUT. These are pins 14, 7 and 10 respectively. Wires from these pins should be long,
and should run down the beam. This will reduce the effects the wires have on the motion. The output of the
accelerometer is sufficient to be recorded directly with Analog Discovery. Be very careful with the accelerometer.
It is mechanically robust, but the surfboard is not. Also it is electrically sensitive. If you apply the wrong voltages,
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
-2-
Revised: 17 April 2016
Troy, New York, USA
ENGR-2300
ELECTRONIC
INSTRUMENTATION
Project 2
you may damage it. (Circuit components cannot be repaired). Please have a TA or instructor check your circuit
before applying power. Mount your small protoboard to the end of the beam and test to see if your circuit is
working. The accelerometer signal should have only a small dc offset. The smaller the offset the better the
integrator will work later in Part C. If the offset is significant (i.e. causes problems with the integrator), modify the
circuit by adding a capacitor and an offset nulling pot, as shown in figure 18 of the accelerometer data sheet.
Important Note: This experiment does not work unless all your measurements are taken when the ‘effective mass’
at the end of the beam is the same. You may recall from experiment 5 that adding additional mass to the end of the
beam slows down the frequency. This means that you need to have the accelerometer mounted to the beam when
you take all your measurements or else your frequencies (and data) will be off. The wires attached to the
accelerometer circuit also contribute to the effective mass at the end of the beam. Heavy connectors tend to add
extra weight and make the damping excessive. Supporting the wires by hand (every time you take data) can help
alleviate this problem. A better method is to use long wires (cut from the spools in the classroom) to make
connections to the accelerometer. Make sure these wires can move freely to minimize their influence on the data.
Build this circuit and record a voltage trace. Save the trace as a file. You will use MATLAB to plat the data, see
section E of this document on plotting data in MATLAB.
Calibration
The signal you get from the accelerometer circuit is not acceleration in m/s2. It is a voltage proportional to the
actual acceleration. The data sheet for the ADXL150 accelerometer states the sensitivity of the output is 38mV/g
where g is the acceleration due to gravity, 9.8m/s2. Thus, we get:
ab [t ]  Va [t ]
9.8
0.038
(equ 1) .
Using this scale factor, you can calculate ab[t] in m/s2.
Part B – Calibrating the Strain Gauge
This section discusses the calibration of the strain gauge and a simple comparison between the strain gauge and the
accelerometer.
Circuit
In experiment 5 you built the diff amp circuit to measure the output from the strain gauge bridge. Hopefully this
circuit is still intact. Reconnect the circuit below. Be careful building or rebuilding this circuit. It is probably the
largest source of troubleshooting problems in this project.
Vbat1
9Vdc
Red wire on beam
No wire
Gray
R2beam
350ohms
U1
3
StrainGauge2
350ohms
+
OS2
1k
OUT
Ra2
2
1k
-
0
7
Ra1
Vbat2
V+
StrainGauge1
350ohms
100k
4
R1beam
350ohms
Rb1
uA741
OS1
5
6
Vout
1
V-
Black resistors on beam
9Vdc
0
Black wire on beam
Prewired on beam frame
Rb2
0
100k
Wire neatly on protoboard
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
-3-
Revised: 17 April 2016
Troy, New York, USA
ENGR-2300
ELECTRONIC
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Project 2
Figure 4.
Figure 5.
Calibrate the strain gauge:
Use a ruler and measure the output voltage vs. the displacement of the beam. Take 5 measurements. For example,
measure VOUT with the beam displaced by -1cm, -0.5cm, 0, 0.5cm and 1cm. You may pick different positions, but
don’t bend the beam too far or it will be permanently bent. This will void any measurements made before the
bending. Plot VOUT vs. position using Excel or MATLAB and fit a line to the data. The slope of the line gives the
sensitivity of the strain gauge circuit. Call this constant k1. The point where x = 0 is arbitrary, so equation 2 can be
used to find position of the beam as a function of time. V sg is Vout of the strain gauge circuit, k1 is the constant for
the calibration of the strain gauge circuit and xb is the position of the end of the beam.
xb [t ]  Vsg [t ]
1
k1
( equ 2)
Comparing the strain gauge and the accelerometer signals
Connect channel 1+ of the Analog Discovery to the accelerometer. Connect channel 2+ to the output of the strain
gauge circuit. Be sure to ground both 1- and 2-. Record both for one plunk of the beam. Save this data to a file.
The two signals should look similar even though one is proportional to acceleration and one is proportional to
position. For the moment, ignore the fact that the oscillation is decaying with time, then:
xb [t ]  C1 sin t
and therefore
vb [t ]  C1  cos t
( equ 3)
( equ 4)
and
ab [t ]  C1 2 sin t   2 xb [t ] ( equ 5)
The signal from the accelerometer should look the signal from the strain gauge with only a difference in magnitude.
Determine ω from the data, and combine this with k1 (the strain gauge calibration constant) and the accelerometer
constant and make a conclusion as to whether the two measurements are in agreement or if something is wrong.
(Remember that  is 2f.)
Part C – Estimating the velocity
The velocity of the end of the beam is our desired quantity. The velocity can be found by taking the integral of the
acceleration signal or by taking the derivative of the position signal. You will do both.
Build the circuits:
You built an integrator circuit in experiment 4. You now need to build another one to integrate the accelerometer
signal. In experiment 4, a differentiator circuit was presented but not built. Now you will build one.
Integrator:
Build the circuit below, using the uA741 op-amp. The power connections aren’t shown; use +9V and -9V from the
batteries. It is assumed that you are more than capable of adding these at this point. You do not need to use separate
batteries for each circuit; you can share the voltages if you wish. Using separate batteries for each circuit may
produce slightly less noise.
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
-4-
Revised: 17 April 2016
Troy, New York, USA
ENGR-2300
ELECTRONIC
INSTRUMENTATION
Project 2
R2
120kohm
C1
1uF
U1 7
3
Accel_signal
+
0
R1
OUT
2
8.2kohm
V+
OS2
-
4
uA741
OS1
V-
5
6
Velocity _acc
1
Figure 6.
The input is the signal from the accelerometer (after the DC blocking capacitor). Connect 1+ to the input of this
circuit. Connect 2+ to the output. Record a good signal. Save it to a file. Return to the material for experiment 4
and determine the gain of this circuit at the frequency of the beam. Does the circuit function as an integrator? (You
may want to test this with the function generator to be sure.)
The values for R1, R2 and C1 were chosen for you. Comment on if these are appropriate. What is the corner
frequency for this Miller Integrator? At the frequency of the beam oscillations, what is the relative magnitude of
Velocity_acc vs. Accel_signal? Is this a good choice, why or why not? Remember also that the DC blocking
capacitor must be considered as part of the input impedance for the integrator. If the integrator is to be working as
designed, the impedance of the capacitor must be much smaller than R1. Check to be sure this is the case for the
Differentiator:
R3
OS2
OUT
2
0.68uF
7
0
-
uA741
4
C2
+
V+
U2
3
OS1
5
6
Velocity _strain_gauge
1
V-
Strain_gauge_signal
10kohm
Figure 7.
Build the circuit above, again use the uA741, and include power. Don’t take apart the diff amp or the integrator, you
need them all. The 0.68μF capacitor is labeled as 684, this 68x10 4pF or 0.68μF. The strain gauges should still be
connected to the diff amp. The output of the diff amp is the input to this circuit.
Connect 1+ to the input of this circuit. Connect 2+ to the output. Record a good signal. Save it to a file. Return to
the material for experiment 4 and determine the gain of this circuit at the frequency of the beam. Does the circuit
function as a differentiator? (You may want to test this with a function generator to be sure.) Note that it may be
very noisy. Why? What can you do to reduce the noise? The values or R3 and C2 are given to you. Based on the
way that the circuit works and the frequency of the oscillation, were these good choices? Why or why not?
Final data:
For one plunk, record the outputs of both the integration of the accelerometer and the differentiation of the strain
gauge signal. Even though one may be noisy, determine if they are in agreement. You will need to include all of
the gain constants, which are: 1) the sensitivity of the accelerometer, 2) the gain of the integrator, 3) the sensitivity
of the strain gauges with the diff amp, and 4) the gain of the differentiator.
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
-5-
Revised: 17 April 2016
Troy, New York, USA
ENGR-2300
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INSTRUMENTATION
Project 2
In the conclusion of your report, we want you to consider the following:
 Accelerometers are used extensively these days in cars. How would you use accelerometer signals in a car to
enhance the driving experience? If there are so many accelerometers in present day cars, why is acceleration
typically not displayed for the driver?
 If you had a portable accelerometer, what would you do with it?
 Details about the report conclusion are contained in Appendix III of this handout. You will need to include
several MATLAB plots. See Appendix II of this handout for details.
Part D – Extra Credit
A small amount of extra credit will be offered to teams that do one of the following. Extra credit will only be
offered for one topic. We will only read the 1 st extra credit submission received in each report.
a) Calibrate the cantilever beam as a scale and demonstrate it to a TA.
The cantilever beam combined with a Wheatstone Bridge form the basic components of an electronic scale.
Calibrate the beam as a scale for the same range of masses that can be measured with the commercial scale found on
the center table.
b) Nice tutorial on plotting from MATLAB
For this to count, you need to finish it 2 weeks before the Project 2 due date. That way it can be sent to the other
teams before they finish their reports. This tutorial should be submitted as a separate item before the main body of
the report. It needs to include examples of titles, legends, grids, axis control. These examples should be relevant to
this experiment.
c) Clean up the Data
Some of the data is noisy. Find a way to process the data to keep the required information and reduce the noise.
This can be either by using a filter circuit or by processing the data on your computer. You need to explain what
you did, why you did it, how you did it, and show results.
The data sheet for the ADXL150/ADXL250 has some filter circuits that might be useful. The accelerometer signal
may already be clean, so you might consider applying these circuits to the strain gauge circuit.
MATLAB is capable of processing the data.
d) Do the integration and differentiation using MATLAB
Create a software version of the two circuits and process the data traces. You need to give a complete description of
what you did and why. And of course you need to show that the processing works. This might be easy if you know
e) Other Extra Credit Ideas
If you have something else you would like to try for extra credit, ask your professor.
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
-6-
Revised: 17 April 2016
Troy, New York, USA
ENGR-2300
ELECTRONIC
INSTRUMENTATION
Project 2
Part E – Plotting data in MATLAB
Start MATLAB
1) Importing data
a. Click on File menu > Import Data
b. Select the file with the data
c. Note in the top right – “number of text header lines”
i. This should be set to at least 1
ii. Play with it if you have some extra info at the beginning of your data file
d. The default name for the import data is: data
e. If you had one channel of the Analog Discovery active, then you will have n by 2 matrix.
i. The first column is the time of each data point
ii. The second is the voltage recorded, channel 1
f. If you had both channels active, then there is a third column that is data for channel 2.
2) Using the data – below are lines from a MATLAB session:
Figure 9.
3) You need to add annotation to the plots for them to be acceptable. Titles, legends, and appropriate axis
settings are expected for the report.
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
-7-
Revised: 17 April 2016
Troy, New York, USA
ENGR-2300
ELECTRONIC
INSTRUMENTATION
Project 2
Part F - Appendices
The following appendices summarize what you need to do, what the appendix of your report should contain, and
what should be included in your report. Appendix I of this handout gives you a task list of things you need to do.
Appendix II of this handout gives you a list of things to include in the appendix of your report. Appendix III of this
handout summarizes the parts of the report. In general, every response plot of data generated in the studio should be
signed and dated by a TA or instructor and included in the report.
A. Build the accelerometer circuit.
1. Put the accelerometer on a protoboard. Clamp it to the beam as near to the end as practical.
2. Have your circuit checked by a staff member. This is important because the accelerometer chips are
expensive and easily damaged if wired incorrectly.
3. Test your circuit to make sure that it functions.
4. Use MATLAB to plot the raw data vs. time. Have this signed.
5. Convert the raw data and plot acceleration vs. time by including the calibration constant given on page 3 of
this project. This can be done outside of class and doesn’t need a signature.
B.1 Reconnect your diff amp circuit to the strain gauge.
1. Measure the output voltage while holding the beam at 5 positions. Plot the output vs. position using
MATLAB or Excel. Find the slope. This is the calibration constant for the strain gauge.
2. Take a data set just recording the output of the strain gauge circuit, (the strain gauge circuit includes the
bridge and the diff amp.) Plot the raw data vs. time using MATLAB. Have this signed.
3. Convert the raw data to position and replot. No signature for this plot.
B.2 Record both the accelerometer signal and the strain gauge circuit signal at the same time.
1. Plot both on the same plot using MATLAB. This plot shouldn’t include any calibration constants. Have
this signed.
2. Pick a point of the plots and analyze that point. Apply the calibration constants. Calculate the frequency of
the oscillation to determine ω. Show the data points used for this calculation.
3. Determine if equation 5 on page 4 is satisfied. Discuss this.
C.1 Estimate the velocity from the acceleration.
1. Build the integrator circuit and connect the accelerator signal to the input.
2. Record the input and output for a plunk of the beam.
3. Plot the raw signals, both on one plot. Have this signed.
4. Use the output of the integrator, equation of the integrator and the accelerometer gain constant to plot the
velocity as a function of time in real units.
C.2 Estimate the velocity from the position.
1. Build the differentiator circuit and connect the strain gauge circuit output to the input of this circuit.
2. Record the input and output of the differentiator for a plunk of the beam.
3. Plot the raw signals, both on one plot. Have this signed.
4. Use the output of the differentiator, equation of the differentiator, and the strain gauge gain constant to plot
the velocity as a function of time in real units.
C.3 Data from both velocity measurements.
1. Record the output of the integrator and the differentiator at the same time for a plunk of the beam.
2. Plot both with all calibration constants included.
D. Analyze your data and the circuits.
1. Compare the velocity measurements by both methods.
2. Comment on the effectiveness of the integrator circuit.
a. Are the components chosen reasonable. Are there better options?
b. Did it work?
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
-8-
Revised: 17 April 2016
Troy, New York, USA
ENGR-2300
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3.
Comment on the effectiveness of the differentiator.
a. Are the components chosen reasonable. Are there better options?
b. Did it work?
E. Assemble the appendix (as described in Appendix II).
F.
Write your group report (as described in Appendix III).
Appendix II: The Appendix of Your Report
General note: plots that are signed don’t need to be nicely formatted. These can have hand notes to indicate what is
being displayed. Processed plots, which include the calibration constants, must be professional in appearance.
The following list of items must be included in the appendix of your report, numbered and ordered as listed. This
will help make sure that everyone includes everything that is required. In your report you should refer to each
appendix specifically as needed to help illustrate your descriptions and conclusions. If you would like, you can
include a second copy of what is in the appendix in order to better illustrate what you are trying to say, however, this
is not necessary and cannot be used as a replacement for the contents of the appendix.
Appendix A: Accelerometer
1. Plot of raw acceleration data vs. time, signed.
2. Plot of acceleration including calibration constant.
Appendix B: Strain and Accelerometer
1. Plot of strain gauge voltage vs. position. Indicate the slope of data.
2. Plot of raw position data vs. time, signed.
3. Plot of position vs. time, includes the calibration constant.
4. Plot of raw from accelerometer and strain gauge, signed.
Appendix C: Velocity
1. Plot of input and output of the integrator, signed.
2. Plot of velocity using the output of the integrator, scaled and labeled.
3. Plot of input and output of the differentiator, signed.
4. Plot of velocity using the output of the differentiator, scaled and labeled.
5. Plot of velocity from sensors on the same plunk, scaled and labeled.
Appendix D: References (Must be included.)
1. Names of websites referenced.
2. Title, author, etc. of any books used.
Appendix E: Extra Credit
 Any additional materials you would like to include for extra credit.
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
-9-
Revised: 17 April 2016
Troy, New York, USA
ENGR-2300
ELECTRONIC
INSTRUMENTATION
Project 2
Appendix III: Your Group Report (80 points)
General note: plots that are signed don’t need to be nicely formatted. These can have hand notes to indicate what is
being displayed. Processed plots, which include the calibration constants must be professional in appearance.
Introduction (5 points)
 State the purpose of the project.
 Also include at least 2 topics you studied in this course that helped you understand the project.
Theory (20 points)
 Describe the basic theory. What is the relationship between displacement, velocity, and acceleration? How
does the accelerometer measure acceleration? How does the strain gauge measure strain?
 Describe how the circuits work. What are the basic elements of your strain gauge circuit, (bridge and diff amp).
Describe the integrator and the differentiator circuits, are the component values reasonable for this task? How
did you determine if they were reasonable or not? For what frequencies would the integrator be expected to act
like an integrator? The same question for the differentiator. Given the frequency of the beam oscillation – what
is the maximum input signal that can be applied to these circuits without causing the output to go into
saturation?
 Describe the calibration process. What calibration constants are needed? Where do the constants come from
(data sheets or experiment)?
 Describe the gain constants associated with the integrator and differentiator circuits. How are they determined?
(Feel free to reference a previous experiment.)
 Use your own words and be sure to site any resources you used in appendix D.
 Demonstrate to the grader that you understand what is happening.
Circuit operation (10 points)


Accelerometer circuit
o Document the entire accelerometer circuit including the integrator (schematic).
o Is the output of the integrator consistent with the measured acceleration and the component values used?
Amplitude and phase?
o Include references to relevant material in the appendix.
Strain gauge circuits
o Document the entire strain gauge circuit, including the bridge, diff amp and differentiator.
o Is the output of the differentiator consistent with the measured strain and the circuit components used?
Amplitude and phase?
Final Analysis and conclusions (11 points)







Given the raw signals.
o What was the peak acceleration of the beam?
o What was the peak deflection?
o If you assume the motion is a pure sin wave, are these traces consistent? Amplitude and phase? If not,
speculate why not?
Compare strain gauge and accelerometer measurement of velocity.
o Is one better suited to determine the velocity? If so, why?
o What is the peak velocity measured?
o Do the calculated velocities have the same amplitudes and phases?
o Explain.
How could each measurement be improved? What are the errors associated with each measurement?
State you conclusions on measurements of strain, acceleration and velocity, as they apply to the instrumented
beam.
Include references to relevant material in the appendix.
Discuss any extra credit activities you did and why.
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
- 10 -
Revised: 17 April 2016
Troy, New York, USA
ENGR-2300
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INSTRUMENTATION
Project 2
Personal Responsibilities (4 points)

How were the tasks divided between group members?
Appendices (20 points)


Many of the sections contain points for things included in the appendix.
See Appendix II of this handout.
Extra Credit (0-5 points)

Include any details that you would like to include about anything you tried above and beyond the basics of the
project.
Your grade will also include a general assessment of project understanding and quality worth up to 10 points. You
do not need to write a general assessment.
Total:
70 points for project report
+10 points general assessment
+20 points attendance
100 points
Attendance (20 possible points)
3 classes (20 points), 2 classes (10 points), 1 class (0 points)
Minus 5 for each late
No attendance at all = No grade for project
K.A. Connor, S. Bonner, P. Schoch
Rensselaer Polytechnic Institute
- 11 -
Revised: 17 April 2016
Troy, New York, USA
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