...
Figure _. Annotated Drawing of 6 Bar Mechanism
First Loop Analysis
The first loop consists of A-C-D-A and the second loop is B-E-C-A-B. Creating vector loops helped to break down the analysis into small chunks that were easier to solve. If we take the first loop as example, the first thing I did was write the vector summation equation, as shown below:
...
where Va is BLUE, Vb is GREEN and Vc is the vector from A to B.
Position Analysis
After using Euler's equation and splitting the equation into real and imaginary components, we get the following result:
...
Since θC = 0, that simplifies two terms in both real and imaginary equations. Finally, we can solve both of the equations and we get:
Velocity Analysis
To find velocities, I started with the initial vector loop equation and took the derivative with respect to time. Then, I followed similar steps to position analysis to get the real and imaginary components, as shown below.
...
Since thetaC is equal to 0, we can simplify the equation and solve for the pertinent variables. The final solution is shown below.
Acceleration Analysis
To find acceleration equations, I simply took the derivative of the velocity equations with respect to time. It is important to note here that, there are double derivatives due to Coriolis acceleration. Due to the complexity of the equations, I chose to only include the final solutions below.
...
I created a MATLAB program to plot all 6 functions, shown below.
