Please see the appendix for the MATLAB code used to perform the following analysis and produce associated figures.
When performing the kinematic analysis, much of the work was done focusing only on the cutting mechanism. This is because the cutting mechanism always moves in the same way along the cutting plane and remains stationary when the mechanism moves to the next cutting position. As such, there was no need to consider the motion of the cutting plane when performing the position and velocity analysis. However, a position analysis of the knife through the full onion cutting cycle was performed.
Mobility
The cutting mechanism has a total of 4 links and 4 full joints. Therefore, the mobility can be calculated as follows:
M = 3*(4-1) - 2*4 = 1 DOF
Position Analysis
The hand work for the position analysis can be seen in the image below.
This analysis was then replicated in MATLAB to perform the same calculation across the full range of motion of the cutting mechanism input. The following plot shows the path along which each point moves in the cutting plane.
Next, the path of the midpoint between points B and C was calculated in 3D space for multiple cut cycles. This path can be seen in the figure below.
Velocity Analysis
The first step in performing the velocity analysis was to determine the speed at which the cutting mechanism input was being rotated by the gearbox. The following calculations accomplish this based on the motor speed maintained by the PID controller.
This gives us a final value of 0.4819 rad/s.
The hand work for the rest of the velocity analysis can be seen in the image below. Note that omega_2 is slightly off from the final value used in the MATLAB code as the gearbox calculations had not yet been performed at this point.
The velocity of each point of the cutting mechanism along the cutting plane's X and Y axis can be seen in the two plots below, respectively.
