The Robot

In the first examples you are to determine the forward kinematics for the following $5$ degree$-$offreedom robot manipulator. A drawing is shown to the right, and a schematic is shown below. The schematic is not drawn to scale, and the two schematics are not exact matches in order to make sure all links are visible. A version is included on the last page that is faded and might be easier for you to print and draw on if you want. 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 $5)$ corresponding to the opening of the gripper.

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

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

You need to determine the transformation from configuration space $($joint angles$)$ to the Cartesian location

of the tool frame $(\{T\})$ in base frame coordinates $(\{B\})$ using the DH convention and parameters.

Derivation$[35$ points$]$

a$.$ Determine the DH parameters for each joint$/$link$.$ Provide a table of all DH parameters. Feel free

to print out and use the figure above to show your axes, etc.

b$.$ Provide the transform matrices ${?}_{i-1}^{i}T$ for each link