Laboratory 2
Slider-Crank & Scotch-Yoke
MECH324
Dynamics of Machines

OBJECTIVES:

BACKGROUND:
A single DOF experiment has been designed in which two similar "four-bar" mechanisms are used to drive an output cart. The bottom mechanism is a scotch-yoke which drives the output "link" in true sinusoidal motion; the top mechanism is a slider-crank and only approximates sinusoidal motion.

Slider-Crank
SLIDER-CRANK
       
LAB SETUP

The equation of motion for the slider can be determined from geometrical relationships:


where, from the law of sines: 

The equation can also be derived (MathCAD, PDF) using the law of cosines:

Click to see MathCAD file of deriviations.

This equation can be approximated by:

Notice that the equation contains two cosine terms.  When the forcing frequency Ωf equals the natural frequency Ωn of the slider system, resonance will occur.  Resonance will also occur, however, at half the natural frequency due to the cos(2Ωf t) term.  This phenomenon will be explored further in future labs.

For a given torque, T, supplied by the driving crank, the force in the x-direction (producing work) on the slider is given by (see MathCAD, PDF derivation):

Click to see MathCAD file of derivation.

The sin(Ωf t) term would suggest that the greatest force would occur at Ωf t = 90.  However, x is also a function of the driving crank angle (Ωf t); when this angle is 90, x is at its minimum value. How the force changes throughout the range of motion is one of the items we will be investigating in this lab.

The bottom cart is driven by a scotch-yoke mechanism that produces true sinusoidal motion:

MATERIAL AND METHODS:
The lab contains two setups, each with a slider-crank and a scotch-yoke; a computer records data from a data acquisition card gathering position and angular velocity information. The TAs should already have the aparatus set up.

EXPERIMENTAL DATA

RUNNING THE HARDWARE
  1. Ensure that the safety button is not depressed.  If it is, see the RESETTING THE SYSTEM directions.
  2. Flip the switch to ENABLE.
  3. Slowly increase the speed by turning the dial clockwise.
  4. The speed of motor is relatively unimportant, but 60 RPM (one cycle per second) is ideal because it will make analysis much easier.
  5. Once the system has settled on a given speed, make note of the speed of the driving link displayed on the LCD readout (in RPMs) on the computer cart.  You will need this value for calculations.
  6. Start recording data from LabVIEW (see RUNNING LABVIEW directons).
  7. Close LabVIEW and flip the switch on the controller to DISABLE.

RUNNING LABVIEW
  1. Open the LabVIEW program labeled "Cart Data-Based (Main)."
  2. Click on the white arrow at the top-left of the toolbar to run the program.  The screen should then display the cart motion.
  3. Delete any text in the filename box so that, once you're done recording, a dialog box will prompt for the save location.
  4. Data will only start being recorded after the "Stop to Save Data" button is clicked.
  5. A thousand data points will be recorded in one second and then automatically stop recording.
  6. Save to C:/My Documents/MECH324 - temp/  or your U: drive (you may have to map a network drive to get access to your U: drive)
  7. Save as <filename>.xls (whatever you save it as, at a ".xls" at the end so it opens in Excel).

MEASURING LINK LENGTHS
  1. Using a ruler or calipers, measure each of the two link lengths (the other two links of the 4-bar mechanism are ground and the slider which is a link of infinite length).
  2. Record these values on the worksheet. You will need these values for calculations and to input parameters into the SLIDER program.


RESETTING THE SYSTEM
  1. Go to C:\ME 324 Programs\Pacific Scientific SC750 Controller\
  2. Ensure the E-Stop button has been released.
  3. Launch "750.exe"
  4. Open the program "Analog.BAS"
  5. Press Control+R to run the program

THEORETICAL DATA

RUNNING THE "SLIDER" PROGRAM
  1. Start the SLIDER program. (Start | Programs | Design of Machinery | Slider)
  2. Enter each member of your group in the name (the name(s) you enter will appear on the printouts).
  3. Click in the Input button on the top menu bar.
  4. Choose Angle Steps as the Calculation Mode in the upper right-hand corner.
  5. Min Theta = 0, Max Theta= 360, Delta Theta = 1.0.
  6. Set Omega Zero to the speed you drove the experimental setup (remember to convert!).
  7. Alpha2 = 0, ThetaZero = 0.
  8. Set links 2 and 3 to the values you measured on the experimental setup and the other linkage values to zero.
  9. Click on Calculate and then Animate.
  10. Adjust the Animation Speed (by moving the slider to the left) to slow the playback speed, and click Run to animate again.
  11. Click on Next when finished viewing.
  12. Choose Plot from the top menu bar.
  13. Select Single Window. 
  14. Select Mix and Match.
  15. Under Function 1 Variable, select Slider Pos and choose X for the Component.
  16. Click OK just below the Component option for Function 1.
  17. Click on Next.
  18. Click on Print Form or Copy (and paste into Word). If you wish to save the plot data to a disk file instead, select Print instead of Plot in step 12 and use preset output "Theta3, Trans Ang, Slider X, Slider Y" and use Disk File output.
  19. Click on Back and plot Trans Ang instead.
  20. Again, print, copy, or save the plot data.
  21. Close the SLIDER program.
 
 

ANALYSIS

EXCEL
  1. The data you saved from LabVIEW is a tab-delimited text file with four columns containing position (in inches) information.

  2.  
    TOP MIDDLE CART
    -2.331
    -2.567
    ...
    TOP LEFT CART
    -5.381
    -5.767
    ...
    BOTTOM MIDDLE CART
    -3.338
    -3.560
    ...
    BOTTOM LEFT CART
    -6.378
    -6.541
    ...
  3. If the first row of the text file contains a header row with column labels ("TOP MIDDLE   TOP LEFT ..."), delete that row before pasting in the Excel template (see sample data).
  4. Open "Cart Lab Plots.xls" from either this link or from the computer's desktop.
  5. Make sure to enable macros (the macros do the calculations for you).
  6. Follow the directions on the "Directions" worksheet.
  7. On the "Info Sheet" worksheet, remember to change the values highlighted in yellow to match your recorded data.
  8. Play around with these values (i.e. change link lengths) and see how they affect the plots.
  9. Using your recorded values, print all four plots.

ADDITIONAL RESOURCES: