In this homework you will use the skills you have developed so far to design a two-cam mechanism that will trace a laser along a shape of your choice. For sections 1-2 you will find “HW_4_boiler_plate.m” very useful. For sections 3-5 you will use the solidworks parts files in “laser_cams.zip”.

This project is directly inspired by the awesome mechanical laser show project on thingverse here

In this part you will generate a $(x_i, y_i)$ contour from hand selected keypoints.

1. Generate a list of $(x, y)$ coordinates that trace out the letters of your first and last name (your initials). This can be done using the provided matlab code, for best results keep the pattern within the dashed square region. Make sure to use at least 25 points and make sure to keep them closely spaced.

2. Save this list of $x, y$ points to a comma separated text file (hint: use dlmwrite).

3. Provide a plot of $x_i$ and $y_i$ versus $i$. Use the $\circ$ symbol for these coordinates.

   

Now we have to turn our desired $(x_i, y_i)$ coordinates into the profiles for the left and right cams.

1. Write out the equation for the $x$ and $y$ coordinates of the vertex laser center from the triangle diagram below.

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2. Solve these equations for the $A_i$, $\alpha_i$, $B_i$, and $\beta_i$ which are the instantaneous lengths and angles of the triangle that define the laser in the desired $(x_i, y_i)$ position.

3. Write out the kinematic relationship between the triangle angles $\alpha_i$, $\beta_i$, and the angle of the radius in the cam coordinate system $\theta_i^L$, and $\theta_i^R$ for the left and right cams respectively.

4. Write a matlab function to return the polar coordinates of the left and right cam profile ($A_i$, $\theta_i^L$) and ($B_i$, $\theta_i^R$) from the following input: a series of $(x_i, y_i)$ coordinates, an arbitrary follower radius $r_F$, and an arbitrary base circle radius $r_B$.

5. Generate the cam profiles using your function from your hand selected data. The input should be your $(x_i, y_i)$ pairs, using the $r_f$ and $r_B$ given above, and the output should be two sets of $x,y$ coordinates: $(x_i^{left}, y_i^{left})$ and $(x_i^{right}, y_i^{right})$.

6. Save the $(x_i^{left}, y_i^{left})$ and $(x_i^{right}, y_i^{right})$ points to individual comma-separated text files called cam_left.txt{} and cam_right.txt.

7. Check that your cam motion looks correct with code provided at the end of the matlab script provided (see gif below for Prof. G's trace).

8. Turn in a plot of your cam profiles generated from hand selected data.

We now need to input our matlab defined cam shapes into solidworks.

1. Download and open the zip file with the solidworks parts “laser_cams.zip”.

2. We now need to generate the cam profile. Open the left cam solidworks file.

3. In the top menu, select Insert $\rightarrow$ Curves $\rightarrow$ Curve through XYZ points.

4. Edit the cam sketch curve to follow the points you generated from matlab. (You can use convert entities to turn the curve into a sketch line that can be extruded.)

5. Rebuild the cam once you have generated the new cam profile.

6. Repeat for the right cam.

7. Assemble the solidworks parts as shown in the diagram below. Use mating constraints to align the parts.

8. Provide a snapshot of your cams in the assembly.

Lastly, we want to make a cad representation of our follower and use the cam-follower mate constraint in solidworks to generate a motion study of our cam assembly.

1. For the laser to track the cams we need to add a cam constraint to both cam faces:

   1. Make one flat face of the laser coincident with the flat face of the front bracket.

   2. Add a cam constraint with the round face of the cylinder as the follower, and the profile face of the left cam as the cam. (Hint: the cam constraint is under the mechanical dropdown selection in the mate sidebar).

   3. Enforce a second cam constraint between the cylinder and the right cam.

2. Make a motion study:

   1. In the solidworks tools toolbar import the “motion analysis” tool.

   2. In the motion study toolbar on the bottom add a motor motion profile and select the left cam. Make the cam rotate about the center shaft at a rate of 5rpm.

   3. Add a second motor motion to the right cam. Make sure this rotates in the opposite direction as the left cam.

   4. Select the motion analysis drop down box on the left side of the motion study toolbar. Add a plot item to the motion study and make this plot item be a traced point. Select the laser cylinder face and make the point trace the center of mass of this face.

3. Turn in a snapshot of the final motion profile with your traced curve (See below for Prof. G's snapshot and motion study).

4. Zip your parts, assembly file, and matlab code into one file and turn it into the lab email ([email protected]) with the subject “HW4 - Your Name”.

For extra credit 3D print your left and right cams and bring them to class on the day homework is due. You are welcome to print the full assembly for your own use but we only need the cams for the extra credit!