Proposed Path:
Click the figure below to see animation.
Mobility:
M = 3*(L-1) - 2*J1 -J2 where L = 5, J1 = 5, J2 = 0
M = 3*(5-1) - 2*5 - 0 = 2
Therefore we have 2 degrees of freedom
Position Analysis:
Below are the equations that lead to finding the unknown thetas; numbers 3 and 4. After all the theta values were found, we need to find the position of point B (also seen as P above).
Since we knew the desired path, we knew what the position plot would look like for our data.
Velocity Analysis:
Let's start off with our Vector Loop:
We performed a velocity analysis to determine what the velocity at point B is. From the vector loop above we solved for omega 3 and omega 4 values. From the newly calculated angular velocities around each point we then solved for the velocities of point A, B relative to A, and C. Using our relative velocity formula we then calculated for the velocity at point B. With our velocity of point B in hand we could now plot it versus our theta 2. Below are the equations that were solved and used to create the plot.
The speed at point B was plotted against the range of theta 2 that is expected to occur within our mechanism when it is in action at an angular velocity of 10 degrees/sec.
