~~NOTOC~~

===== Homework 03 - Forward Kinematics and Robot Workspace =====

=== Forward Kinematics ===

Implement the forward kinematic task for a general 6R manipulator.

<note warning>
**Allowed libraries**: numpy
</note>

Create a function ''fkt(mechanism, joints)'' which takes DH parameters of the manipulator ''mechanism'' and 6 joint angles (in **radians**) of the manipulator ''joints'' and returns the pose of the end effector. 

Input/Output specifications for ''fkt'':
  - ''mechanism'' : dictionary with 4 keys ''"theta offset"'', ''"d"'', ''"a"'', ''"alpha"''.
  - ''joints'' : list of 6 float numbers that define the configuration of the mechanism.
  - **Return value** : dictionary with 2 keys ''"r"'' and ''"t"'', whose values are the rotation (3x3 matrix of type ''np.ndarray'') and the translation (3x1 matrix of type ''np.ndarray'') of the end effector in the base coordinate system, respectively.

Implement the solution in a single file ''hw03.py''. The file must contain the ''fkt'' function, such that it can be imported (by the automatic evaluation) as

<code>
import hw03
pose = hw03.fkt(mechanism, joints)
</code>

=== Robot Workspace ===
Use the created ''fkt'' function to explore the range of motion of the end-effector when moving only the first joint of the Motoman MA1400 manipulator (that was used in the previous homework).

For this follow the next steps:
  - fix the $2$-$6$-th joints to the zero position
  - sample $n$ values for the first joint (you can fix $n=100$) starting from lower joint limit until upper joint limit
  - for each sampled value, compute ''fkt'' and record the end-effector position
  - visualize the end-effector positions projected to the $x$-$y$ plane. 

=== Upload ===

Upload a zip archive ''hw03.zip'' (via the [[https://cw.felk.cvut.cz/upload/|course ware]]) containing the following files:
  - ''hw03.py'' - python script containing the implemented function ''fkt''
  - ''hw03.pdf'' - report file describing your solution containing:
    - description of your implementation of ''fkt''
    - visualization of the end-effector positions projected to the $x$-$y$ plane.