Laboratory 3
Fourbar Linkages
MECH324
Dynamics of Machines

OBJECTIVES:

BACKGROUND:
A Grashof mechanism exists when a four-bar mechanism meets the following criterion:
                    s + l <= p + q
where:

  s:length of shortest link
 l:length of longest link
 p,q:lengths of intermediate links

If this condition is met, at least one link will be capable of making a full revolution with respect to the ground link.  Otherwise, no link will be capable of a complete revolution relative to any other link.

If a link is capable of making a complete revolution, it is termed a crank. If it can only oscillate back and forth, it is a rocker. Note - the terms "crank" and "rocker" usually apply only to links pivoted to ground, but they can also be used to describe a complex-motion link (e.g., a coupler), based on whether or not the link can make a complete revolution.

A toggle position occurs when two of the moving links are collinear (linkage forms a triangle such as A'B'C'). When in a toggle position, the linkage will not allow further input motion in one direction from one of the rockers.

As shown in the figure below, the transmission angle (μ) is the angle between the output link (C) and the coupler (B). It is always positive, and always acute (less than 90°).  If the measured angle between the coupler and output link is greater than 90°, the transmission angle is calculated as 180° minus the measured angle.  Thus, the maximum possible, and optimal, transmission angle is 90°. At this angle, all of the force (generated from the torque) is transferred to the output link. As the transmission angle deviates from 90°, some component of the force is not acting on the output link. At 45°, only about 70% of the force is producing desirable work. As a rule of thumb, machine designers try to keep the minimum transmission angle above ~40°.

An inversion occurs when a different ground link is chosen for the mechanism. Thus there are as many inversions for a given linkage as there are links.

Fourbar Linkage

 

PROBLEM STATEMENT:

(3-15) Figure P3-4 shows a non-Grashof fourbar linkage that is driven from link O2A. All dimensions are in centimeters (cm).

  1. Find the transmission angle at the position shown.
  2. Find the toggle positions in terms of angle AO2O4.
  3. Find the maximum and minimum transmission angles over its range of motion.
  4. Draw the coupler curve of points A, B, and P over their range of motion.
Figure P3-4 (p. 134 of text)
Figure P3-4

MATERIAL AND METHODS:
You will need:

  1. thick poster board or thin foam board
  2. scissors
  3. ruler
  4. protractor
  5. nails, brads, or paper fasteners to serve as pivots

It's suggested you bring your own scissors, ruler, and protractor so you don't have to wait for others to finish using the few sets that will be provided.  Also, if you don't already have a protractor, you might want to buy one; they will definitely come in handy for future homework.

Cut out strips (1/2-1" thick) of foamboard in lengths as defined in the problem statement.  You may want to cut them a little longer than the length suggested so that you can tack them at the specified lengths (i.e., cut a "two-inch" bar 2-1/2 inches and tack it 1/4" from each end).  Assemble the "bars" using the thumbtacks or brads, leaving them free to rotate

 

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CARDBOARD MODEL
  1. Build a model of the fourbar linkage shown in Figure P3-4.
  2. Using trig (law of cosines), solve for the transmission angle in the configuration given.
  3. On a blank piece of paper, draw the path of points A, B, and P over their range of motion (by replacing the tack at that point with your pencil and tracing the curve as the linkage moves).
  4. Label the paths and include the relative position of the ground link.
  5. Find and sketch the toggle positions on the same piece of paper.
  6. Using trig and geometry, calculate the driver angle, θ, range. Round these values DOWN to the nearest degree.

 

FOURBAR & EXCEL
  1. Start the FOURBAR program. (Start | Programs | Design of Machinery | Fourbar).
  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. On the left side of the screen, define the link lengths according to the problem statement (don't worry about the 14° ground offset).
  5. For the Start and End Thetas, use the minimum and maximum (respectively) values for the range of the driver angle you calculated on the worksheet (Question 7).
  6. Let Delta Theta and Omega2 be 1.
  7. Click Calculate and then Animate. If FOURBAR gives you any errors or warnings, you probably entered a value incorrectly.
  8. Adjust the Animation Speed (move the slider to the left) to slow the playback speed, and click Run to animate again.
  9. Note: Checking the "Trace" option at the top may help you visualize the motion of the linkage.
  10. On the right side of the screen, you can choose between a Crossed Circuit and Open Circuit. What is the difference between the two? (Question 1)
  11. Click Next.
  12. Choose the Print button from the top menu bar.
  13. Select "Preset Formats", choose "Coupler Point Coordinates..." (the last option).
  14. Set "Direct Output" to "Disk File"
  15. Click on Next.
  16. Save the file as <filename>.xls (add ".xls" to whatever you call it).
  17. Note: you will need to create two files to get the ENTIRE coupler path. (See Question 1 on the worksheet).
  18. Choose Print again from the top menu bar.
  19. Repeat the above steps but select "Theta magnitudes for all links" (first option).
  20. Again, save the file as <filename>.xls
  21. Quit the FOURBAR program.
  22. Open the three Excel files you just created (two for the coupler path, one for the theta magnitudes).
  23. Plot Coupler X vs. Coupler Y (Question 2).
  24. Note: this will require two pairs of X-Y data columns (one from each of the two coupler files you created).
  25. Plot Trans Ang vs. Angle Step Deg (driver angle). (Question 3)
  26. Print both plots.
 
 

ADDITIONAL RESOURCES: