DOF Calculation:
To find the degrees of freedom for this mechanism, I used the following formula. There are 3 pin joints as well as D and E which are considered both pin and slider joints. In total, the DOF is 1.
Figure _. PMKS Simulation
In this section, I wanted to conduct kinematic analysis to find position, velocity, and acceleration for key components of the 6-bar mechanism. To begin, I split the 6 bar-mechanism into two vector loops. The figure below shows the figure split into different sized lengths and distinguished by color.
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 D.
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.
Second Loop Analysis
The second loop is B-E-C-A-B. The vector summation is as follows:
where Vd is the vector from B to A, VP is the vector from C to E and Vr is the vector from E to B.
Position Analysis
After conducting position analysis, I got these results.
Velocity Analysis
After conducting velocity analysis, I got these results.
I created a MATLAB program to plot the equations, shown below.
