Please Include all steps and explaination

$3\mathrm{.}3$ Inverted slider$-$crank: Multiple loops and auxiliary equations

Consider the inverted slider$-$crank shown here.

a$.$ MATLAB symbolic solution

Develop the loop equations and auxiliary equations necessary to identify the position of P $.$ Be sure

to perform all of the preliminary work, such as drawing the kinematic model, calculating the mobility,

etc. Use MATLAB symbolic variables with the solve and subs commands to solve for the equations

for the DVs and use these to solve for the vector P at any location $($note$,$ you do not need to

implement this is a loop and solve for multiple iterations, just develop the equations$).$

Submit the well commented code in MATLAB Grader and in your Brightspace submission.

Note: you should be able to code this problem in less than $20$ lines of code $($not including

comments$)$

b$.$ Geometric Derivation of DVs

Using the geometric process defined in the text, derive the analytical equations for the output

variables in the inverted slider$-$crank. Compare the process for the inverted slider$-$crank with that of

the for the four$-$bar mechanism and clearly describe the portions of this derivation that are unique

compared to the four$-$bar mechanism.

c$.$ Compare the results from part $1$ and part $2.$