Introduction
Once we decided to use helical cam as a key mechanism, the most critical analysis necessary is the position analysis of the cam. During the proposal stage, we leveraged this website to design a position profile that approximates the bottom part of the longhorn. The website offers parameters p, a, b, c, and d which are used to change the prime radius and 4 different dwell heights. However, given that we need to design for a helical cam which contains profiles for more than one full rotation, and the fact that the actual longhorn has a more delicate shape than 4 dwell heights, we decide to write our own analysis tool using Python.
Disk cam design and analysis
To start, we first try to design a disk cam and follower system. To make our own life simpler, we choose the axis of translational motion by the follower to be aligned with the radial axis of the cam.
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Figure 18.3-2 Disk cam's radius profile v.s. rotational angle
Helical cam design
Now that we know how to design a disk cam given a certain curved path, we need to figure out how to follow multiple disk cams with different profiles/radii one after the other seamlessly. The solution is a helical cam, where we employ a z direction to have a continuously changing radius across multiple rotations. The design of z axis value is straightforward; we simply need to decide a pitch for the helix, then the z value can be calculated as
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Now putting everything together, we have a working helical cam and follower system.
Gear train to connect cam rotation and paper cylinder rotation
Based on the analysis above, the helical cam will rotate 4 full circles to draw the bottom part, and then another 4 full rotations to draw the top part. In this process, we will need the paper cylinder to rotate 1 full circle for drawing the bottom part and another full circle for the top part. Therefore, we need to design a gear train with an overall gear ratio of 1:4, where the motor will direct drive the paper cylinder while the output shaft that spins the helical cam will rotate at 4 times the angular speed.
Slider analysis
Since we use linear bearings extensively in our cam follower system, it's important that we get the ratios correctly to minimize binding.
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Thus, we have the following ratio constraints:
