Balancing the Four-Bar Linkage
Assigned: January 18, 2002
Due: February 8, 2002
Your team is to add counterbalance weights to the four-bar mechanism shown below so as to minimize the shaking forces that result from the motion of the linkage.
Figure 1: 4-Bar Mechanism on Cart
A 4-bar crank rocker mechanism has been built for this project and is mounted on a cart. The right disk as seen in Fig. 1 is the crank, and is driven by an electric motor. The left disk is the rocker and oscillates about the shoulder screw at the center of the disk. The coupler has two screw\washer\nut assemblies attached to it so as to simulate a coupler with a center of mass that is not along the pin line. To see the motion of the 4-bar mechanism, click on the following link to download a 232 Kb mpeg file that shows the operation of the 4-bar. (Click here to see a larger version that requires 900 Kb)
Shaking forces are applied to the cart from the mechanism
as the crank rotates. These shaking forces tend to set the cart in
motion. A one-way clutch has been assembled to the wheel axles such
that the cart can only move toward the left as seen in Fig. 1. Accordingly,
the cart travels to left under the influence of the shaking forces.
(Click here to see a .mov file showing the motion
without counterbalancing... note this is a big file, around 8Mb).
Your assignment is to determine the set of counterbalances that completely eliminates the shaking forces associated with this mechanism. Then you will take this information and determine the best way to minimize the shaking forces given the constraints of the real system. The constraints are that the only counterbalancing weight that you can use are the provided set-screws that can be placed in the pre-tapped holes shown in Figs. 2 and 3. Additionally, you may only use a total of ten set screws. You will not be able to perfectly balance the mechanism under these constraints, but you will be able to come close.
Figure 2: rocker with pre-tapped holes for counterbalance weights
Figure 3: crank with pre-tapped holes for counterbalance
Description of the Mechanism:
The link lengths for the mechanism are:
Radius to the counter balance holes:
Send an e-mail to Dr. Stamper (including sections 3&4) that lists your desired locations for the counterweights. This e-mail is due by mid-night February 7th. The e-mail must include the following:
The math model is intended to be a vehicle of communication between you and a person with some engineering background that doesn't have any prior knowledge of this assignment. Accordingly, your math model should at a minimum include:
The math model is due at the start of class on February
Math model (60 points):
Grading will be based upon how well the math model meets the described requirements.
Cart performance (40 points):
The performance of your counterbalance placement will be tested during a classroom demonstration. The instructor will first run the cart in the unbalanced state for 20 seconds and measure the distance traveled by the cart.
Then each combination of counterbalance placements that was e-mailed to Dr. Stamper will be tested. Four outcomes are expected:
1. The cart doesn't move (+/- 5mm): 40 points
2. The cart moves, but not as much as the unbalanced cart: 35 points
3. The cart moves the same distance as the unbalanced cart: 25 points
4. The cart moves a greater distance than the unbalanced cart: 15 points