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.
Initial Physical Prototype:
Here is our first prototype of our mechanism. Although the gears are not grounded in the picture, we were able to create the proposed path from above. Laser-cut gears and links and used M3 nuts and bolts to bring together the prototype. We do plan to do multiple iterations in the coming weeks to test out different link lengths and find a ratio that gives us a larger surface area. A thought we have is to add a rack and allow the gears to move back and forth along it. This would increase the surface area and give us a greater challenge regarding our mechanical components.