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Activity 4.5

Cams in MotionIntroduction

A cam is a mechanism that moves in order to change the direction or rhythm of movement of other parts. A cam usually causes linear movement of another part when an axle rotates it. Cams are used to create motion in many engineering applications, such as clock mechanisms, sewing machines, toys, recording instruments, and engines.

In this activity, you will create a 3D solid model of a cam. You will place the 3D model in an assembly model, simulate the rotation of the cam, and study the resulting motion of another part called a follower. You will then collect data and create a motion graph to represent motion of the follower. By comparing your motion graph to those created by teammates, your team will develop a mathematical model for the vertical displacement of a follower resulting from the rotation of different sized cams of similar shape.

Later, you can use this computer model, and the mathematical models collected by classmates, to help you select an appropriate cam for your Automata design.

Part 1 – Create a motion graphWatch the Cams in Motion video

1. In a team of four, each team member will choose a different nominal diameter from the following list: 1.5 in., 2 in., 2.5 in., or 3 in.

The nominal diameter is a dimension used to describe the cam but is not necessarily the actual diameter of the cam. In this case, you will use the nominal diameter to calculate the actual dimensions of the cam according to the Cam Dimension Drawings.

2. Your teacher will assign a cam shape to your team: eccentric, pear-shaped, regular hexagon, or snail. Create a 3D computer model of a cam using your nominal diameter and assigned cam shape per the Cam Dimension Drawings.

3. Create a fully dimensioned part drawing of your cam. Use a 1/4” square hole (to match a ¼ in. square axle) or match the axle dimension your teacher provides.

4. Watch the Placing Work Features in Your Cam 3D Model video. Add the listed work features to your cam 3D solid model. These work features will later help you properly constrain your cam in an assembly:

a midplane work plane centered between the flat surfaces of the cam

a work axis through the center of the hole

a work plane that includes the center axis of the cam hole and, if the cam is symmetrical, represents the plane of symmetry of the cam. Rename this work plane Angle of Rotation Cam.


Note that a snail cam will not have a plane of symmetry. In this case, place a work plane parallel to the flat edge of the outside surface of the cam as shown below.

Eccentric Cam Pear Cam

Video: Placing Work Features within your Cam 3D

Snail Cam Hexagon Cam

Model

5. Watch the Simulating automata Motion video. Simulate the motion of a cam assembly using your 3D cam model using the following instructions.

Download the AutomataSimulation.zip file and extract the files.

Open the AutomataSimulation.iam file. Place your cam model into the assembly file.

Add assembly constraints as follows.

Mate the midplane work plane of the cam to the work plane that passes through the centerline of the follower rod.

Mate the center axis of the hole in your cam with the center axis of the axle.

Mate the plane of symmetry of your cam to the work plane through the center axis of the axle.

Test the assembly by rotating the handle attached to the axle. The cam should rotate with the axle. Ignore any interference between the cam and the follower.


Place a transitional constraint between the outside edge surface of your cam and the curved surface of the bottom of the follower.

Test the assembly by rotating the handle attached to the axle. The follower should move up and down as the cam rotates. You may wish to turn off the visibility of the box for now to better observe the mechanical motion.

Insert an angle constraint to help you measure the angle of rotation.Rotate your cam and orient it such that the follower is in its lowest position.

Turn on the visibility of the Angle of Rotation Work Plane associated with the follower part. [Note: you can toggle visibility of a feature on and off by right-clicking the feature in the browser and selecting Visibility.]

Turn off the visibility of the Mate with Midplane work plane associated with the follower.

Turn off the visibility of the midplane work plane of your cam.

Place a directed angle constraint with a value of zero degrees between the Cam Angle of Rotation work plane and the Angle of Rotation work plane associated with follower.

To test the constraint, try to rotate the axle. The axle should not move.

Edit the angle constraint and set the angle to 45 degrees. The axle should rotate 45 degrees, but once the constraint is applied, the axle and cam should remain in the same position despite your attempts to rotate the part in the assembly file.

Video: Simulating Automata Motion

Note that you can suppress the angle constraint (or any assembly constraint) at any time by right-clicking on the constraint in the browser and selecting Suppress. Suppressing a constraint removes the constraint between the parts but does not delete the constraint. You can reapply the constraint using the same procedure to clear Suppress.

6. Collect and record data related to the motion of the follower. Record the height data at every 45-degree interval. Note that you can change the angle of rotation by editing the angle constraint just applied.

Measure and record the height of the top of the follower rod above the center of the axle with respect to the angle of rotation of the axle.

Note that you may use the Distance tool in lieu of using the ruler provided in the assembly to measure the distance. Be sure to select the appropriate axis and surface to obtain the correct orthogonal distance.

Measure and record the radial dimension of the cam as the distance between the center of the axle and the point of contact between the bottom of the follower and the cam.


Angle of rotation (degrees) 0

Height of top of follower (in.)

Radial dimension of cam (in.) OR height of the bottom of the follower

7. Create a motion graph.

To graphically model the vertical motion of the top of the follower rod, create a scatter plot with smooth lines in Excel. Format the axes, label the axes, and title the chart. Note that you can choose a scatterplot with smooth lines or straight lines in the Scatter menu (Insert tab > Charts panel > Scatter tool).

Graphically model the motion of the bottom of the follower (which is also the radial dimension of the cam) on the same axes.

Print a copy of your scatterplot. An example is shown.


Add a line that represents the length of the follower (from bottom of the follower surface to the top of the rod) on your graph. Note that the length of the follower does not vary and is constant for all rotation angles.

Compare the motion graphs for the top of the follower and the bottom of the follower. Describe the difference(s). How does this align to the length of the follower?

Part 2 – Generalize the motion graph

8. Compare your motion graph with the motion graphs of your teammates. For each cam, record the nominal diameter of the cam and the resulting maximum displacement of the follower.

Nominal diameter of cam (in.) 1.5 2 2.5 3

Maximum displacement (in.)

9. Mathematically model the relationship between nominal diameter and maximum displacement.

Create a scatter plot of your maximum displacement versus nominal diameter data. Use the format shown.

Find a function to represent the maximum displacement with respect to the nominal diameter of the cam, where M(d) = maximum displacment and d = nominal diameter.

Print a copy of your graphical and mathematical model.

Explain the interpretation of the y-intercept of this equation in words.

Explain the interpretation of the slope of this equation in words.


Extend Your Learning

10. Research simple automata designs that use cams. Respond to each of the following.

Describe one interesting automata design (that incorporates at least one cam) and the motion that results when the cam is rotated.

Represent the motion of the follower created by the cam with a simple motion graph. If more than one cam is included into the design, choose the motion resulting from one of the cams. Represent one complete revolution of the cam.

11. Create a sketch to illustrate how a cam and follower might be oriented to cause the follower to twist about its own axis (for example, like an ice skater performing a spin or helicopter blades spinning around the drive shaft).


Conclusion

12. Create a sketch to represent a cam mechanism in which a single follower is moved by two different cams, and describe the resulting motion in words.

1. Create a motion graph of the top of the follower for a mechanism that has a 5-inch nominal diameter and a 3-inch follower.

2. Create a motion graph of the bottom of the follower for a mechanism that has a 3.75-inch nominal diameter and a 3-inch follower.


Cam Dimension Drawings


PLTW ENGINEERING

Activity 4.6

Design a CamIntroduction

Often engineers must design a mechanism to replicate a specific motion. In this project, you will design a cam to provide a specified motion. You will then create a physical model and test your design to compare the results against the desired outcome.

Equipment

Foam board, balsa or bass wood, corrugated plastic, 3D printer, or other prototyping material

Manufactured box

3/16”-diameter dowel

3/16”-square dowel

Resources

Polar Graph Paper

ProcedureWatch the Design a Cam Tutorial video to learn how to use a motion graph to design a cam.

Design a Cam Tu torial

Study the cam assembly shown below.


The motion graph represents the vertical follower motion created by a cam in an assembly similar to this assembly. Note that the cam shown is for illustration only and will not produce the motion displayed in the motion graph.

1. Assume that the minimum radial dimension of the cam is 1/2 inch. Replicate the motion graphof the position of the top of the follower above the box. Then draw a motion graph (on the same grid) to represent the radial dimension of the cam. This will require you to translate the follower motion graph down, such that the radial dimension at an angle of rotation of 0 degrees is 1/2 inch. Label your function “radial dimension of cam”.


2. On a polar grid, sketch the profile of a cam that will create the vertical follower motion represented by the motion graph in the cam assembly. Note that your cam will have a different profile than the cam illustrated above.

3. Calculate the length of follower needed to produce the motion graph shown in step 1, using the box manufactured in Project 3.9 Manufacture a Box. Show your work.

4. Sketch a multi-view drawing of your follower design.

5. Create a physical model of your cam and follower.

6. Test your cam assembly. Record your test data in a table and represent the test results using a motion graph.

7. Evaluate your solution with respect to each of the following. Explain each assessment.

Does the cam and follower design provide a smooth follower motion when the cam is rotated?

Is the cam/axle connection sufficient to ensure that the cam rotates with the axle without slippage?

Does the motion of the follower replicate the motion represented by the top of follower motion?

Conclusion

1. What real phenomenon might produce a motion that could be replicated by a cam of the shape you produced? Explain.

2. How would you improve your cam assembly design?

3. Based on your experience with this cam assembly, what considerations might be important in the selection of a linear motion and the resulting cam design that could affect the design of your automata?

4. You have developed several types of models to represent cam designs -- graphical models, computer models, and physical models. Evaluate the merits and limitations of each type of model in the process of designing a cam as part of a system (for instance an automata) to cause a desired linear motion.

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