The first system is the Cams. The Cams convert a rotational motion into a repetitious linear motion. The followers (weighted by 2 nickles taped to the insides) look like Figure 1 where the Cam contacts the orange surfaces. The corresponding left and right maximum positions are shown in Figure 2. where the maximum left position is shown in red and the maximum right position is shown in blue. The axis of Cam rotation is marked by an X. The difference in displacement is .964”, so the follower only moves .482” in either direction.

Figure 1. Follower Diagram                                    Figure 2. Maximum Cam and Follower Positions

The racing cars in the foreground are mounted on the 2 misaligned Cam and Follower pairs.  These Cams are misaligned by 180º, so when one is at its maximum left position, the other is at its maximum right position. On the front Cam (Cam 1), there are 2 cars, McLaren in front and Ferrari in back. The offset between the 2 cars’ positions is .65”, but because they are on the same Cam, they will have the same velocity and the .65” displacement is constant. Cam 2 has one car: Red Bull. Red Bull is 0.125” behind the McLaren at the beginning of the race. The cars position are shown in Figure 3.

Figure 3. Starting Position of Cars

Car Kinematics

The Cams translate the linear rod in a sinusoidal pattern making kinematics easy to analyze. Using the McLaren’s initial position as the reference position: 0, the position graph over the course of the Cams’ revolutions is as follows in Figure 4. From the position graph, we know that Red Bull and Ferrari will not collide, and we know at what times Red Bull will overtake and fall behind the McLaren. In the case of Figure 4, the angular velocity is 2π rad/s, which will match the rotating background velocity shown in the next section. The cars velocities and accelerations are graphed similarly in Figures 5 and 6 according to the attached MATLAB Script [car_kinematics.m].

Figure 4. Positions of the Cars over the course of 2 seconds   

Figure 5. Velocities of the Cars over the course of 2 seconds      

Figure 6. Accelerations of the Cars over the course of 2 seconds

Note that the above diagrams are simplified kinematics of the system. In the real system, the Cams only contact the followers at certain points in the rotation represented by the yellow line in Figure 7.

Figure 7. path of contact between cam and follower

After construction, the cars moved according to the following video: