12.4 Kinematic Analysis
For the kinematic analysis of the prototype, the Gruebler Equation was utilized in order to determine the mobility of the system. Below are the calculations:
Gruebler Equation
M=3(L-1)-2J1-J2
=3(4-1)-2(4) = 1 DOF
This Gruebler calculation ensures that there is 1 DOF for our mechanism which aligns with intended goals. The mechanism should be able to achieve linear motion in the vertical direction for the motion.
Next, we used the Grasshof condition to verify that a full rotation can be done with our links as seen below:
Grasshof Condition
S + L < P + Q
given S = 0, L =5 in. , P= 2 in., Q=5 in.
5 < 7
L2 can rotate through a complete revolution
After confirming both conditions, we then moved to kinematic analysis to calculate our position, velocity, acceleration, and mechanical advantage. Plots were made utilizing MATLAB. As well, a GIF of the motion was created, however it had 360 degrees of full motion while we later realized that we only needed 180 degrees of motion. Nonetheless the mechanism functions correctly and displays all proper motion. Below is the animation as well as all relevant plots.
