Relationship Between Velocity and Force in Air...

ROCHESTER INSITUTE OF TECHNOLOGY

Relationship Between

Velocity and Force in Air

Muscles

Final Report for Summer 2013 Co-op

DANIEL SZE (RIT Student)

8/21/2013

Abstract:

Within the experiment that was conducted, a series of tests on air muscles was performed with

three goals in mind: to determine if a relationship between the velocity at the air muscle contracts and

the force that it contracts with does exist, to quantify the relationship if it does exist and, most

importantly, to build a foundation that future researchers could use to further research the relationship.

In order to experiment with the air muscles, a testing assembly was designed and built. The testing

assembly was then wired with all the electronic devices necessary to measure and record data in

addition to control the electronics that make the assembly work. Once the assembly was built, a

procedure was developed to efficiently collect and process the data required to meet the goals. The

data collected was ultimately about the air muscle’s contraction force and velocity. For the forces, data

about the voltages output from an attached load cell was collected and processed to find the

corresponding voltage. For the velocities, video footage of each repetition cycle was collected with a

digital camera and analyzed with ImageJ, an image and video analysis program. Finally, the data was

graphed and conclusions were drawn from the data and the graph concerning if there was a relationship

or not.

From the graphs and the data, we observed that, within the conditions, parameters, and

methods used for the experiment, there seemed to be no visible relationship between the air muscle’s

contraction velocity and contraction force. According to the graph, the velocity remained relatively

constant throughout the range of weight points that was tested in the experiment without a clear

pattern. As a result, it could be concluded that the velocity and force are independent of each other.

However, in order to get to a more concrete conclusion, more experiments under different conditions,

parameters, and procedures would need to be conducted. Suggestions would include calculating and

using average velocity instead of maximum velocity, testing the air muscle using extreme weight points,

and parameterizing the effects of inflating air pressure on both force and velocity.

In conclusion, the experiment was a relative success in that we have accomplished our main

objectives in determining that, within the context of the experiment’s parameters and procedures, the

was no relationship between velocity and force for air muscles. In addition, we had laid the foundation

for future students or researchers to build upon to reach a better conclusion about this relationship.

Experimental Procedure and Parameters:

Notice:

To avoid damage to the equipment and personal injury while operating the assembly:

o Do not use air pressure in excess of what the air muscle can handle.

o Do not attempt to load excessive weight onto the air muscles.

o Make sure all the parts are tightly secured together before operating the assembly.

o Follow all safety rules in regards to pressurized air hoses.

o Do not use or test damaged or improperly assembled air muscles.

o Use Teflon Tape when screwing together piping parts.

Refer to the pictures in the back of the report for information about the assembly as well as

other important information:

o Figure 1-15: Labeled Pictures with part tables of the assembly, associated devices, and

wiring.

o Figure 16-20: Pictures of the LabVIEW program used to control the assembly and its

block programming.

Make sure that units were recorded with the data.

Clean up the area and setup once the experiments were completed.

Parameters:

The air muscle was made of a 6” length of .25” rubber tubing.

5 different weight points with 4 repetitions for each point.

50 psi of air pressure will be used to inflate the air muscle.

Experimental Procedure:

1. Secure the assembly firmly to the table to prevent excess vibration.

2. Open the controlling LabVIEW Program.

3. Screw in the air muscle to be tested into the tee. Make sure Teflon Tape was used with the air

muscle.

4. Mount the camera to be used onto the platform.

5. Mount the weights to be used for the particular weight point onto the hook of the air muscle.

6. Run the LabVIEW Program.

7. Turn on camera and start recording the video footage.

8. Press the button in the LabVIEW Program.

9. Wait for the program to run its course.

10. After the program if finished running, stop the camera from recording and hit the stop button

on the LabVIEW Program.

11. Find the file that LabVIEW have written the data in.

12. Rename the file into something more reasonable.

13. Repeat steps 6 through 12 until all repetitions required for the weight point are complete.

14. Replace the weight hanging on the air muscle with the next weight point.

15. Repeat steps 6 through 14 until all the required data has been gathered.

16. Take off and put away all of the weights.

Calculations Procedures:

Force Calculations:

1. Open one of the data files in Excel

2. Plot the data on a graph

3. Locate a reasonable maximum point and its corresponding minimum point

4. Average the two value points to get the average voltage.

5. Use the calibration data to convert the voltage into a force.

For this experiment, the calibration equation comes out to be:

6. Repeat the procedure for all repetitions and points.

Velocity Calculations:

1. Open the video footage in ImageJ.

2. Set the scale in ImageJ to get accurate distance measurements.

3. Choose a feature or spot that you can use to track the motion of the air muscle.

4. Locate in the video where the air muscle starts moving.

Optional: to save disk space and loading time, have ImageJ save a new file

containing the footage trimmed of excess, unneeded frames.

5. Use the crosshair tool, mark out the location of the spot.

6. Have ImageJ measure the spot.

7. Move to the next frame and mark out the moved spot again.

8. Have ImageJ measure the new spot.

9. Repeat steps 7 and 8 until you get all of the measurements needed to make an accurate

velocity plot.

10. Transfer the measurements onto an Excel spreadsheet.

11. Process the data to get displacement and instantaneous velocity.

12. Locate the maximum instantaneous velocity from the data chart to get the velocity

value for that repetition.

13. Repeat all of the prior steps for all of the repetitions and weight points.

Data Results:

Below is the final table of values for the voltages, forces, and velocities for each repetition as

gathered and processed by the above procedures. The averages of force and velocity will be

used for the graph.

Table for Force vs Velocity calculations.

Weight Point 1 Voltage (volts) Force (lbs) Velocity (in/sec)

Repetition 1 3.2373045 1.150098133 3.771

Repetition 2 3.208008 0.995655774 4.654

Repetition 3 3.2055665 0.982784918 3.980

Repetition 4 3.2055665 0.982784918 3.806

Average 3.214111375 1.027830936 4.052825491


Repetition 1 3.466797 2.359913745 4.038

Repetition 2 3.466797 2.359913745 4.728

Repetition 3 3.466797 2.359913745 3.997

Repetition 4 3.466797 2.359913745 4.346

Average 3.466797 2.359913745 4.277450508


Repetition 1 4.0942385 5.6675971 3.981

Repetition 2 4.0942385 5.6675971 4.562

Repetition 3 4.099121 5.693336176 4.562

Repetition 4 4.0966795 5.68046532 4.413

Average 4.096069375 5.677248924 4.379379338


Repetition 1 4.489746 7.752593988 4.995

Repetition 2 4.489746 7.752593988 4.878

Repetition 3 4.4873045 7.739723133 4.576

Repetition 4 4.489746 7.752593988 4.988

Average 4.489135625 7.749376274 4.859505089


Repetition 1 4.9658205 10.26231593 4.408

Repetition 2 4.9682615 10.27518415 4.435

Repetition 3 4.9731445 10.30092586 4.410

Repetition 4 4.970703 10.28805501 4.529

Average 4.969482375 10.28162024 4.445450788

Below is the Results’ Force vs Velocity graph, made from the averages as calculated above. From

visual inspection, the velocity is relatively constant over the range of force values tested, but

there is no clear pattern to derive an equation from.

0

1

2

3

4

5

6

0 2 4 6 8 10 12

Ve

loci

ty (

in/s

ec)

Force (lbs)

Results: Force vs Velocity

Discussion:

Results:

From the data collected from the experiment and the graph of the results, it was observed that,

over the entire range of tested force values, the resulting velocity values remained relatively the same

and consistant, with the minimum value being about 4.053 inches per second and the maximum value

being about 4.860 inches per second. The mean value of the velocities was about 4.403 inches per

second while the standard deviation was about .295 inches per second. The graph’s shape was relatively

flat without a clear pattern in it. Based on all of these observations, we can conclude that there is no

relationship between the force the air muscle contracts with and the velocity that the air muscle exhibits

as it contracts.

Possible Sources of Error:

However, it should be realized that the experiment was not as perfect as it should have and

there were two major possible sources of error that might have affected our data. The first source of

error was the vibration and stray movement that the air muscle was subjected to while the experiment

was conducted. While it was expected that vibrations would occur as the assembly was working, there

might be a chance that the vibrations and stray motions was excessive enough to throw off the data to a

significant degree. The best possible remedy would be to secure the entire setup more solidly to the

table. That would help cut down on any stray movement and vibrations.

A second source of error to consider is the blurring of the spot used for video analysis. As the air

muscle moved quickly, some of the frames with the video footage became a slight blur. This is a problem

since it also blurs the spot that was being used as a reference point for velocity analysis. With the spot

blurred, I would then have to estimate where the spot was within the frames. That would throw off the

velocity data and calculations by a significant degree. There are two possible solutions to this problem.

The simpler solution would be to mark the spot more clearly so even if the blur takes into effect, the

spot would be visible enough to not require estimating. Something as simple as a drop of brightly

colored paint would do the job nicely. The other solution is to use a camera that is more capable of

taking high speed footage. While the solution might work, it may be very pricey to implement.

Things to Look into in the Future:

From this experiment, we have concluded that there was no relationship between contraction

force and contraction velocity within air muscles. However, to get to a more concrete conclusion, more

experiments would need to be conducted in the future to explore possibilities that could change the

conclusion of this experiment. There are three possibilities of interest that could be explored almost

immediately after this experiment.

The first possibility that could be explored is the modification in the method used to calculate

the velocities at each repetition. The current method said that the maximum velocity calculated in each

repetition would be the velocity for that repetition. An alternative method that was brought up but was

not explored meaningfully was that the average velocity over the period of time the muscle is moving

would be calculated and used instead. This is important since the gathered data does suggest that the

muscle stops moving at different points of time, which would result in vastly different velocity amounts

should the alternative method be used.

The second possibility that could be explored is to use more extreme weight amounts when

testing these air muscles. For the experiment just conducted, the weight range goes up to ten pounds

mainly out of safety concerns and the fact that there were no heavier weights available. If more safety

precautions were developed and heavier weights become available, then it would be very possible to

test the air muscles under greater weight loads. It was known that air muscles have the potential to life

much more than ten pounds, so it would be interesting to see if the velocities would remain constant if

the air muscle was loaded with twenty-five or even thirty pounds of force instead.

The third possibility that could be explored is to parameterize the effect the air pressure has on

both contracting force and velocity. Early in the experiment, the air pressure used to inflate the air

muscle was fixed to 50 psi in order to eliminate whatever possible effects that varying the air pressure

could have on the experiment. However, it is possible that the air pressure could have a large effect on

the outcome of the experiment so it would be advisable to make a procedure to determine how does air

pressure affect the outcome.

Conclusion:

In conclusion, the experiment is a relative success. We have achieved all of main goals. First, we

have determined that there is no relationship between the contraction force and contraction velocity in

air muscles under the conditions and methods we used. But most importantly, we have laid down a

foundation and developed resources that could be used to help further research into the relationship in

meaningful ways.

Appendex A: Diagrams and Photos of the Testing Assembly

Figure 1: The final Solidworks model of the Testing Assembly. Dimensions for parts were taken from this model and were

used in the production of the Assembly.

Figure 2: A labeled photo of the Testing Assembly. Figure 3 has the table to show which label corresponds to which part. Not

shown in the photograph was the camera used to take the video footage. The camera was a Nikon Coolpix S3200. Other

cameras would be sufficient as long as the threaded hole is a ¼”-20 hole.

Label Number Part Name

1 Air Muscle to be tested

2 Wooden Baseboard

3 Aluminum Extrusion for Load Cell and Air Muscle

4 Bracket for Load Cell and Air Muscle Mounting

5 Load Cell’s Data and Power Cable

6 Transducer Techniques DSM-50 Load Cell

7 .25” MNPT x .25” Push-to-Connect Adapter

8 .25” x .25” x .25” NPT Aluminum Tee

9 Aluminum Extrusion for Camera

10 Platform for Camera Mounting

11 Pressurized Air Hose

12 One of the Weights used for testing

Figure 3: The Table containing all of the parts’ names to go with the labeled picture in Figure 2.

Figure 4: A labeled photo of the Solenoid Valve Assembly and its controlling electronics. Figure 5 has the table to show which

label corresponds to which part. The plastic tubing at label 3 is connected to the .25” Push-to Connect Adapter in Figure 2

(part #7).


1 Clippard MME-2QDS Solenoid Valves

2 .25” Push-to Connect Tee

3 .25” Plastic Tubing

4 .25” MNPT x .25” Push-to-Connect Plastic Adapter

(From Pressurized Air Supply)

5 .25” MNPT x .25” Push-to-Connect Brass Adapter

(From Pressurized Air Supply)

6 .25” MNPT x .25” Push-to-Connect Brass Adapter

(To Exhaust)

7 .25” MNPT x .25” Push-to-Connect Steel Adapter

(To Exhaust)

8 .25” Pressure Regulator x .25” Push-to-Connect

Plastic Adapter (To reduce loudness of discharge)

9 Measurement Computing USB-SSR24 Relay Board

10 Wiring Setup for Relay Board (see Fig. 12)


Figure 6: A photo labeling the power supplies for the electronic equipment used for the experiment.


1 AC Adapter for Relay Board (9V, 300mA)

2 AC Adapter for Solenoid Valves (12V, 1.5A)

3 Power to the Strain Gage Transducer Amplifier


Figure 8: A labeled photo of the tested Air Muscle. This air muscle is 6” in length.


1 .25” Rubber Bladder Tube with Appropriate Air

Muscle Sleeve

2 .25” Crimp Ring

3 .25” Plastic Hose Barb with Plug and Hole for the

Hook

4 Metal Hook for Weights

5 .25” Brass Hose Barb x .25” MNPT Adapter


Figure 10: A labeled photo of the Data Acquisition Card used for the experiment, showing off the wire connection setup.


1 Positive Signal Wire Connecting to Strain Gage

Transducer Amplifier

2 Negative Signal Wire Connecting to Strain Gage

Transducer Amplifier

3 Wire Connecting to Ground


Figure 12: A labeled close-up photo of the Relay Board Wiring, showing off the wire connection setup.


1 Connection to Power

2 Connection to Intake Solenoid Valve

3 Connection to Exhaust Solenoid Valve


Figure 14: A labeled Photo of any additional wiring used in the experiment.


1 Strain Gage Transducer Amplifier

2 Data Signal Wires Connecting to Data Acquisition

Card

3 Data Signal Wires Connecting from Load Cell


Figure 16: The Main Interface for the LabVIEW Program controlling apparatus.

Figure 17: Part one of the Block Diagram for the LabVIEW Program.

Figure 18: Part two of the Block Diagram for the LabVIEW Program.

Figure 19: The Block Diagram for the LabVIEW Sub-Program that controls the Solenoid Valves through the relays.

Figure 20: The Block Diagram for the LabVIEW Sub-Program that captures the data from the Data Acquisition Card and writes

them to a file.

Relationship Between Velocity and Force in Air...

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