Step 1
The very first step to take is to make sure all the numbers entered have the proper units.
The Numbers and Units window can be opened from the View menu located on the menu bar.
Step 2
Choose English (Pounds) as the standard so that length will be in inches but then click the button More Choices.
For Rot. Velocity we need to choose rad/s but only Rev/min is available. 15 rad/s = 143.239 rev/min.
Step 3
Draw a circle and a rod by using the Rectangle and Circle tool on the left side menu.
Step 4
Specify the geometry of each shape by typing ctrl+k after selecting each shape.
Step 5
The next step consists of placing one Point element and one pin joint on the circle.
Then place two point elements on the bar at each end.
The point elements must be placed on the outer edges of the bar and wheel.
This is because the geometry of these parts can only be selected from their edges, not from point to point.
So if the diagram calls for two points to be a give distance from each other the only way to specify
this distance is to make the geometry of the part the distance and placed the points on the ends of the part.
Step 6
Select a Point element on the bar and the one on the circle and select Join from the menu on the left side.
Step 7
Select the Slot joint on the left side menu and place it on the left side of the wheel.
Make sure the cross hairs appear as depicted in the picture to the left.
These cross hairs indicate that the slot joint will be placed tangential the the circle.
A Pin joint element will appear after left-clicking, delete this joint.
Step 8
After deleting the pin joint select, the free point element on the bar and the slot, then hit the Join button.
Step 9
At this point I decided to test the model to view its performance up to this time by hitting the Run button.
I was surprised to find that it swung side to side, I then realized that simulated gravity was causing this effect.
The disk under the force of gravity
Step 10
To turn off the simulated gravity go to the World menu and then hit Gravity....
Then select the none ratio button.
Step 11
Place the motor in the center of the disk and double-click it.
A window will open where we can put he rotational velocity calculated earlier.
The velocity was 143.239 rev/min CW, but all measurements are CCW so a negative is placed in front of the numbers.
Step 12
One of the most important aspects of Working Model is that it can show users
dynamic properties of objects while they are in relative motion.
These properties can include velocity and acceleration both linear and angular.
To view the velocity of a point select the point followed by selecting Measure then velocity.
Repeat this twice. There is an arrow in the upper left corner of each velocity window.
Clicking this arrow will display the velocity in different ways. Display velocity as a plot and enlarge it.
Step 13
Select the point 8 then click Measure followed by Position.
Step 14
Select the bar then make the following selections: Measure, Velocity, then Rotation Graph.
A graph will appear, expand it to a larger size.
Step 15
With the bar still selected click the following: Measure, Velocity, then All.
Step 16
For four of the windows shown there is extra information given that we don't need.
For every piece of information that is not needed click the box (all boxes are located underneath the white arrow for each little window).
Click all the boxes except Vy, y, and Vphi.
Step 17
Select the vertical slider joint and make the following selections: Define, Vectors, then Velocity.
Step 18
Select the joint on the radius of the circle and make the following selections: Define, Vectors, then Velocity.
With this joint still selected click the following: Define, Vectors, then Acceleration.
Step 19
Make the following selections Define followed by Vector Lengths.
The screen on the right will appear. Input the following:
for velocity put in 0.001, and for acceleration put in 5.000e-005.
Step 20
This is the result when played.
Step 21
The result can be seen in the video to the left.
Although only a few rotations are captured, the Working Model file can be
downloaded from the Dynamics of Machinery page where it may be played for an extended period of time.
The motion of the disk
Solution 1
The solution to the problem when theta is zero is given to the left.
The velocity of the collar in the y direction is 11.8 in/s up.
This value is close to the value given in the back of the book which is 12.25 in/s up.
The angular velocity of bar BD is -41.73 rev/min CCW = 4.37 rad/s CW.
This value is nearly identical to the answer in the back of the book of 4.38 rad/s CW.
Solution 2
The solution to the problem when theta is 90 degrees is given to the left.
The velocity of the collar in the y direction is 42.28 in/s down.
This value is nearly identical to the value given in the back of the book which is 42 in/s down.
The angular velocity of bar BD is 0.492 rev/min CCW = 0.05 rad/s CW.
This value is nearly identical to the answer in the back of the book of 0 rad/s.
Solution 3
The solution to the problem when theta is 180 degrees is given to the left.
The velocity of the collar in the y direction is 12.145 in/s down.
This value is very close to the value given in the back of the book which is 12.25 in/s down.
The angular velocity of bar BD is 41.73 rev/min CCW = 4.37 rad/s CCW.
This value is nearly identical to the answer in the back of the book of 4.38 rad/s CCW.