Intro to Robotics: Homework $5$: The Jacobian Inverse

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Observe the $2$ link planar robot shown below with $a_1=30$ and $a_2=20.$ With MATLAB, show that the joint velocities approach infinity as the robot end$-$effector approaches its workspace boundary under the following conditions:

The initial $(x,y)$ values of the end$-$effector are $(12,10).$

The end$-$effecter moves along a path in the direction of the vector $i+2j$

The total velocity of the end$-$effecter is constant: $v_x=2c\frac{m}{s}$;$v_y=4c\frac{m}{s}.$

Hand in this page, your MATLAB code, any work done by hand, and a single page of $4$ plots $(2$ rows, $2$ columns$).$ The four plots are:

A subplot of the $(x,y)$ coordinates of the end$-$effector until the manipulator arrives at the boundary of its workspace. Plot $y$ vs$.x.$

A subplot of the joint angles ${}_1$ and ${}_2$ vs$.$ time

A subplot of the rate of ${}_1$ vs$.$ time

A subplot of the rate of ${}_2$ vs$.$ time

Be sure that all plots are appropriately titled and all axes are labeled. Use the legend command where appropriate. Print your name in the title of the first plot. Indicate on one of the plots whether you chose the "elbow up$"$ or "elbow down" solution.

Inverse kinematic function doesnt work on matlab. Please help