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To perform kinematic analysis, the above model was mirrored and simplified to the following:
The unknown angles theta 3 and theta 4 were found by solving the system as a 4-bar linkage mechanism. Once all theta values were found, the position of point P (point p being the position of the cleaning sponge) was determined using the following equations:
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A MATLAB script (found in appendix) was then written to repeat this process for every input angle (theta 2). The full range of motion of theta 2 is 0 to 360 degrees. The MATLAB script generates the plot below which agrees with the path generated by the ‘Linkage’ software. The path was then scaled to the necessary size (i.e. link lengths were adjusted such that the motion covered the glasses area).
Velocity Analysis:
Vector Loop:
Velocity analysis was performed to determine the velocity at point P. After finding the angular velocities of omega 3 and 4 using the vector loop equations, the velocities in the x and y direction were found by taking the derivative of Rx and Ry and plugging them into the equations below:
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