...
We divided our kinematic analysis into two parts: the knife mechanism and the slider mechanism. These two mechanisms are linked via bevel gears, but since the link is only at one joint, we can model link 2 in the slider mechanism as having an independent angular velocity that is twice the angular velocity of link 2 in the knife mechanism. From there, we were able to derive the following equations using hand calculations:
Using these derivations, we were able to plot the kinematics for links and points of interest using MatLab. Matlab code can be found in the appendix. The plots of interest can be found below:
Figure 1: Knife horizontal position as a function of input angle 2, which ranges from 0 to 180 degrees. The units we used in our build were in millimeters. Once finished, the knife then reverses along the same curve.
Figure 2: Knife vertical position as a function of input angle 2, which ranges from 0 to 180 degrees. The units we used in our build were in millimeters. Once finished, the knife then reverses along the same curve.
Figure 3: Knife velocity as a function of input angle 2, which ranges from 0 to 180 degrees. The units we used in our build were in millimeters. The maximum velocity is 0.233 m/s, and the minimum velocity is 0.069 m/s. Once finished, the knife then reverses along the same curve.
Figure 4: Knife acceleration as a function of input angle 2, which ranges from 0 to 180 degrees. The units we used in our build were in millimeters. The maximum velocity is 0.663 m/s2, and the minimum velocity is 0.036 m/s2. Once finished, the knife then reverses along the same curve.
Figure 5: Slider horizontal position as a function of input angle 2, which ranges from 0 to 360 degrees. The units we used in our build were in millimeters, but the slider is able to be uniformly scaled up or down as needed.
Figure 6: Slider velocity as a function of the input angle 2. The units of the slider velocity are in mm/s. The maximum speed of the slider is 0.181 m/s. The minimum speed of the slider is -0.105 m/s.
Figure 7: The slider acceleration is a function of the input angle 2. The acceleration is in units of mm/s2. The maximum acceleration is 0.483 m/s2. The minimum acceleration is -0.331 m/s2.
And finally, we have the animation video of our Solidworks Assembly below:
| View file | ||||
|---|---|---|---|---|
|