A cam mechanism is a rotating or sliding device used to transform rotary motion to linear motion. There are two parts to this mechanism, a cam and a follower (Figure 1A). The Karakuri “Ready to Fly” penguin utilizes a snail cam to move (Figure 1A). A snail cam mechanism gradually pushes the follower up to a maximum height and then creates a sudden drop (Figure 1B). In the penguin model, the cam follower is connected to the body of the penguin. Rotation of the cam causes the penguin body to rise slowly and fall quickly.
Figure 1: Geometry of a snail cam. Figure A) shows the components of the snail cam. The snail cam, shown in yellow, rotates as the cam follower, shown in blue, moves up and down. The cam follower reaches a maximum height at this orientation of the snail cam. Figure B) shows the position of the rod relative to the angle of the cam. (Graphic taken from [1].)
To determine the height of the penguin, I first determined the shape of the cam. Figure 2 shows an outline of the snail cam located inside of the penguin mechanism.
Figure 2: Cam inside of the “Ready to Fly” penguin mechanism. (Graphic taken from [1].)
I first measured the radius at various points on the cam (Table 1).
Delta (Degrees) | Outside Radius (CM) |
0 | 1.5 |
45 | 1.5 |
90 | 1.5 |
135 | 1.55 |
180 | 1.85 |
225 | 2.2 |
270 | 2.75 |
315 | 3.25 |
360 | 3.7 |
Table 1: Outside radius of the snail cam, measured at 9 different deltas.
Delta is defined as zero when the radius of the snail cam is at a maximum. Delta is positive in the CCW direction (Figure 3).
Figure 3: Definition of delta. Delta defined as zero when the radius is the largest and is positive in the CCW direction. (Graphic modified from [1].)
To determine the outside shape of the snail cam, I had to find a curve that fit these measured points. To create a desired linear trajectory of a cam follower, trigonometric and polynomial functions can be used to describe the outside radius of the cam. Rothbart created several equations that can be used to create a desired linear motion [2]. Some of these equations, with the motion of the follower, are shown in Figure 4.
Figure 4: Common curve fit equations for cam design. Beta is the angular displacement of the cam while h is the total follower displacement. (Figures taken from [2].)
I used these equations, taken from Rothbart, and a second degree polynomial to fit my experimental data.
Figure 5: Experimental data versus fits equation fits for the data
I determined that the third equation fit the data the best. I used the following function to describe the outside radius of my cam:
(1)
Then I could find the height (y distance) on each point on the outside of the cam:
(2)
where theta is the orientation of the cam (Figure 6).