Compute the forward kinematics of the Piktul manipulator. The home configuration should have the robot arm straight out and up at some height. Doing so defines the zero transformation for the rotational joint variables. The linear joint coordinates should go to whatever value is specified (for these zero as a length should be sensible). Most of the piktul robotic arms can't quite manage a zero gripper height (except for one or two of the super-saggy ones), and it is best not to let the gripper finger width go to zero either.

* First, provide the solution to the forward kinematics in symbolic form. Since it is roughly planar, the solution can be written as what I would call $SE(2) \cross \mathbb{R}$, which is the planar special Euclidean space plus the height (lies in $\mathbb{R}$).