Position Analysis of a 4 Bar RRRR Grashofian Double Crank Mechanism            

Procedure

In this experiment you will guided through the position analysis of a 4 bar RRRR Grashofian double Crank. Position analysis can be approached analytically. Using complex numbers is a popular analytical approach. The animated guide that follows right next shows the analytical method of determining the position of a point on the coupler of a RRRR linkage as the linkage moves. The next animation shows the graphical constructions needed for the position analysis of a double crank linkage. A summary of what you are expected to do follows

  • In the Instruments tab use the first applet to choose a set of 4 link lengths. Enter your choices for link lengths. The applet will let you know if the lengths conform to a Grashofian Double Crank. If your link lengths are improper go back to the Introduction tab and check the Crashofs criteria Grashofian Double Crank and modify link lengths accordingly.
  • Use the Drawing Board applet in the Instruments tab to find the linkage configuration for a given input link orientation (theta 2). Below the Drawing Board applet there is a link to a step by step demo of how to use the Drawing Board to perform these constructions. If you feel it necessary you may go through that.
  • Finally there is a third applet in the Instruments tab which lets you verify your results. Enter your answers to see the correct values for coupler position and the accuracy of your answers obtained graphically. The following are animated guides for analytical and graphical methods of position analysis for a 4 bar RRRR Grashofian Double Crank.

Instruments

Choose link lengths, preferably keeping them within 10 units length for easy viewing of animations. Enter them and a coupler arm length and orientation of your choice in the following applet in the designated text boxes. Link 1 represents the ground link. Press the Enter button to verify if your data conforms to a Grashofian Double Crank. Note that coupler arm length and orientation play no role in Grashof's criteria, but you are merely asked to enter them for use in later stages. In case you get a message stating that your data does not conform to a Grashofian Double Crank, have a re look at the summary of Grashof's criteria provided in the Introduction tab and review and re enter your data.

Check if a linkage is a Grashofian RRRR Double Crank mechanism

Once your link lengths are validated, you can use the Drawing Board applet for graphical position analysis of your chosen linkage.

The Drawing board applet will open when you click the image below. A new browser window will open along with the applet. Since the linkage is a double crank, all values of crank angle are permissible. Find the location of the coupler point for any crank input angle you choose. The applet uses screen coordinates for drawing. Hence if you are using link lengths between 1 to 10 units it is advisable (although zoom is available for the applet) to choose a scale between 100:1 to 10:1 for easy on screen use.

Java Script Simulator

To get an animated guidance of the graphical analysis using the applet click below:

How to use the Drawing Board to find coupler position

Validate your answer using the applet below. Validate Graphical Analysis for Coupler Position for a Grashofian RRRRR Double Crank Linkage