ME 240
Introduction to Dynamics

Computer Assignment #3: Three-Bar Linkage Dynamics

The due dates are 11/6, Thursday for Professor Comninou's class and 11/7, Friday for Professor Grosh's class.

Problem Statement: Linkage is a common mechanism used for connecting two bodies, usually two rods. In this assignment, we use Working Model to illustrate the kinematics of a three-bar linkage system. The general motion of these linkages is somewhat complex, as will be seen. However, the relative motion of the bodies, as seen from the rotating coordinate frames, can be surprisingly simple. It is the objective of this exercise to study velocities points on rigid bodies and the relative velocities of these points as seen from different frames of reference. Also we are interested in the relative motion of different points of the linkages as we choose different reference frames (in this Working Model program, we can choose from 4 different reference frames, "ground" , "bar AB", "bar DE" and "point C" where "point C" really means the frame of "bar BD") to observe the motion.

Below is the screen shot of the Working Model program for three-bar linkage system.

  • Questions

    Reference on the Ground

    1. Set the angular velocity of the bar AB as 200 rad/sec. by moving the slider or input a number in the box.
    2. Select a reference frame on the ground by clicking "ground" button. If the system is out of the window, using the scroll bar on the left-hand side and bottom of the window to move it back.
    3. Let the program Run for a while then stop it. What is the trajectory of point B? What is the trajectory of point D? And what is the trajectory of point C -- is it simple?

    Reference on the bar AB

    1. Hit Reset. Select a reference frame on the bar AB by clicking "AB" button. Now we are seeing the motion of the other bars relative to the rotating frame attached to bar "AB" (i.e., we are looking at the relative velocity of point "C" or "D", for instance). Let the program Run for a while then stop it.
    2. What is the trajectory of point C measured in this frame? And what is the trajectory of point E measured in this frame?

    Reference on the bar DE

    1. Hit Reset. Select a reference frame on the bar DE by clicking "DE" button. Now we are looking at the world from reference frame attached to "DE". Let the program Run for a while then stop it.
    2. What is the trajectory of point C measured in this frame? And what is the trajectory of point A measured in this frame?

    Reference at point C

    1. Hit Reset. Select a reference frame at point C by clicking "C" button. Let the program Run for a while then stop it.
    2. What is the trajectory of point A measured in this frame? And what is the trajectory of point E measured in this frame?

    Answer the following question.

  • Step by Step Instructions (Macintosh) :
    1. Run Working Model.
      • If the computer you are working on has Working Model on its hard drive, then you can run it directly from your hard drive.
        Goto Engineering & Science --> click on Working Model.
      • If you don't have it on hard drive, you should get it from the net.
      • Click on the apple on the left-top part of the screen --> click on chooser --> click on AppleShare --> highlight umich-ENG-CAEN --> click on CAEN Load Server and click ok --> login as a guest --> click on Lab Software and click ok --> on the back ground of the screen, now there's Lab Software folder, open it --> click Software --> click Working Model 2D --> click Working Model 2D 4.0.

    2. Open Working Model module in course folder on the net.
      • To load the module for this problem, do the following.
      • On Working Model menu, click File --> Open.
      • Click on Software --> Course Software --> CoE Course Folders --> ME240 --> linkage --> click on ok and open the module.