Figure 1: 4-Bar Mechanism on Cart
ME304 Project
Balancing the Four-Bar Linkage
Assigned: January 18, 2002
Due: February 8, 2002
Objective:
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
Background:
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).
Assignment:
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
weights
Description of the Mechanism:
The link lengths for the mechanism are:
Radius to the counter balance holes:
Mass information:
Deliverables:
Counter-weight placement:
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:
Math model:
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
8th.
Grading:
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