Cam Analysis
Plausibility Analysis:
In order to establish that a cam (and therefore an image) was viable for the mechanism, both followers had to be able to traverse the entire outer edge of their cams and the motor must be able to rotate through the forces introduced by the springs of each follower. The two immediate failure cases for an image are as follows:
- 1.) If the change in cam radius from one degree to the next is greater than the radius of the follower, the follower will not be able to climb up to the next degree, the mechanism will bind up, and the image will be incomplete.
- 2.) If the motor cannot produce an adequate reaction force to counter the force of each follower’s spring, the follower will pinch the cam in place, the mechanism will jam, and the image will be incomplete.
Resolution Analysis:
Once the cams were deemed viable, we found it of interest to know how well the cam's information would be transmitted to the output drawing. The metric we used for resolution is the percentage of radii that the follower would be able to read off of the cam. We reasoned that the only time an outside follower on a cam would not be able to keep contact with the cam is if there was a radius that was smaller than its neighbors so that the follower would simply glide over the notch. In the case that the follower loses contact with the cam, we know that the x or y value (depending on which cam had the failure) for that radius will be mistranslated to the resulting image.
These analyses were handled by a Matlab function we created that would take in the stall torque of the motor, diameter of the follower, spring length, spring k value, and arrays of x and y values from the cam synthesis code. The code would evaluate each point from the arrays relative to the other information provided and return a 1 or 0 to indicate if the cam is possible or not, a percentage of the cam's accuracy, and two arrays- one array indicating if a point will cause the cam to fail and one array indicating if the point will have a resolution error. The points from these arrays are then marked on the previously generated images of the cams and the source image to show the user where any errors would occur and what type of error is present (blue circles represent accuracy errors, red x's represent points that cause the cam to fail.)
Analysis Results
The first set of images are the Matlab results for an imagined setup where the motor has very little max torque, meaning that it will fail to counter-act the spring force in some places, resulting in not only resolution errors (blue circles), but points where the cam will fail completely (red x's.) It stands to reason that the points further to the right (where the x spring experiences more compression) and the points further down the image (where the y spring experiences more compression) would be prone to failure as those are the regions where the springs' forces are stronger.
This next set of images show a setup where the diameter of the follower is very small, meaning that there are fewer resolution errors, but in practical implementations the smaller diameters seemed to bind up easier.
The final set of images are the Matlab results for the setup of our final design where there are no points of failure, but some points where accuracy will be lost from the original image (marked with the blue circles.)
The final product image is placed below for comparison to the prediction of our analysis.
