~~NOTOC~~

===== Homework 02 - Denavit-Hartenberg Convention =====

=== Task ===

  - Describe the kinematics of {{http://cmp.felk.cvut.cz/cmp/courses/PRO/2012/Labs/Motoman-MA1400.pdf|Motoman MA1400}} manipulator using its {{http://cmp.felk.cvut.cz/cmp/courses/PRO/2012/Labs/Motoman-MA1400-dimensions.pdf|dimensions}} in Denavit-Hartenberg convention as explained in {{http://cmp.felk.cvut.cz/cmp/courses/PRO/2012/Lecture/PRO-2012-Lecture-03.pdf|Lecture 03}}. In order for the automatic evaluation to check your solution correctly, choose the 0-th and the 6-th coordinate frames as shown {{https://cw.fel.cvut.cz/b211/_media/courses/pro/labs/coord_frames_0_and_6.pdf|here}} (the $x$-axis is marked in red, the $z$-axis is marked in blue).
  - Visualize DH notation of the manipulator (axes of motion and $O_i$ coordinate systems) in Python. Provide XZ plane view and side view (see below example code snippets and expected plots for the manipulator from the lecture). Please use the same view-points as in the code snippets, so it is easier to check. 

For XZ plane, you can use this snippet of code:
<code>
fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111, projection='3d')
for system in systems:
    plot_system(ax, system)
ax.set_proj_type('ortho')
ax.view_init(azim=90, elev=0)
ax.set_yticklabels([])
ax.set_ylabel('')
ax.set_xlim(-0.05, 1.45)
ax.set_ylim(-0.75, 0.75)
ax.set_zlim(-0.05, 1.45)
plt.show()
</code>

{{:courses:pkr:labs:xz_view.png?400|}}

For side view:
<code>
fig = plt.figure(figsize=(10, 10))
ax = fig.add_subplot(111, projection='3d')
for system in systems:
    plot_system(ax, system)
ax.view_init(azim=50, elev=20)
ax.set_xlim(-0.05, 1.45)
ax.set_ylim(-0.75, 0.75)
ax.set_zlim(-0.05, 1.45)
plt.show()
</code>

{{:courses:pkr:labs:side_view.png?400|}}

You will need to implement ''plot_system()'' function and use your own ''systems''.
=== Upload ===

Upload a zip archive ''hw02.zip'' (via the [[https://cw.felk.cvut.cz/upload/|course ware]]) containing:
  - ''hw02.json'' - json file containing DH parameters of the given manipulator (see below for the description of how to create it).
  - ''hw02.pdf'' - report file describing your solution containing
    - an illustration of all axes of motion;
    - an illustration of all DH coordinate systems ($O_i$ and $H_i$);
    - a table with DH parameters;
    - comments on the choices of DH coordinate systems;
    - visualization of DH parameters of the given manipulator.

**Creating** ''hw02.json'':

Create an empty dictionary in Python:

<code>
mechanism = {}
</code>

The dictionary has 4 keys: ''"theta offset"'', ''"d"'', ''"a"'', ''"alpha"''. The values are lists of 6 float numbers. Fill in the values with DH parameters of the given manipulator. Consider the distances in **meters** and angles in **radians**.

Finally, save ''mechanism'' to ''hw02.json'':

<code>
import json
with open("hw02.json", "w") as outfile:
    json.dump(mechanism, outfile)
</code>