The link length are defined as follows: $l_0=0\mathrm{.}35m{l}_1=0\mathrm{.}25m{l}_2=0\mathrm{.}15m{l}_3=0\mathrm{.}2m$

There are displacements between some of the joints: $d1=0\mathrm{.}03md2=0\mathrm{.}04md3=0\mathrm{.}04md4=0\mathrm{.}025m$

The picture above shows the robot in the configuration where all joint angles are $0.$ The direction of

positive rotation is shown about each joint.

The simulator will actually show one additional joint $($joint $6)$ corresponding to the opening of the gripper.

This, however, is not relevant for the kinematic functions and can be ignored.

Determine and implement the inverse kinematic function for this Robot. $[50$ Points$]$

Derivation$[35$ points$]$

You are to derive and implement a partial inverse kinematic solution for the robot manipulator. To make

this problem tractable, we assume ${}_5=0$ and require that the X $-$axis of the tool frame is pointed straight

down $($i$.$e$.$ hat$(x{)}_T$ is parallel to $-$hat$(z{)}_B).$ Turn in a hand$-$written and scanned or typed solution.

HINT: To determine this inverse kinematics you should decompose the problem. Draw the system from

above and from the side for angles other than ${}_i=0.$ I recommend an "elbow up$"$ configuration. $1)$ You

can determine ${}_1$ without considering the other joints using trigonometry. $2)$ Simplify solving for

${}_2,{}_3,{}_4$ by first moving up the wrist frame $($i$.$e$.$ to where $\{4\}$ is in my FK solution. Attached are hints and the figure.