Vizzy Denavit–Hartenberg parameters

2014-09-05T16:10:23Z

Miguelaragao:

<table border=0><tr><td align="center">
{| class="wikitable" style="text-align: center"
| style="background:#d0d0d0;" colspan="7" | Head center
|-
| style="background:#f0f0f0;"|'''Link'''
| style="background:#f0f0f0;"|'''alpha'''
| style="background:#f0f0f0;"|'''R'''
| style="background:#f0f0f0;"|'''theta'''
| style="background:#f0f0f0;"|'''D'''
| style="background:#f0f0f0;"|'''min/max'''
| style="background:#f0f0f0;"|''' '''
|-
| 0||Pi/2||0||0||0||0/0||virtual link
|-
| 1||Pi/2||0||0||0||-20/20||M0 → M1
|-
| 2||Pi/2||0||0||-0.37||-53/53||M1 → M2
|-
| 3||Pi||0.13221||19*Pi/17||0||-18/37||M2 → M3
|}

{| class="wikitable" style="text-align: center"
| style="background:#d0d0d0;" colspan="7" | Inertial sensor
|-
| style="background:#f0f0f0;"|'''Link'''
| style="background:#f0f0f0;"|'''alpha'''
| style="background:#f0f0f0;"|'''R'''
| style="background:#f0f0f0;"|'''theta'''
| style="background:#f0f0f0;"|'''D'''
| style="background:#f0f0f0;"|'''min/max'''
| style="background:#f0f0f0;"|''' '''
|-
| 0||Pi/2||0||0||0||0/0||virtual link
|-
| 1||Pi/2||0||0||0||-20/20||M0 → M1
|-
| 2||Pi/2||0||0||-0.37||-53/53||M1 → M2
|-
| 3||Pi||0.13221||-0.2611*Pi||0||-18/37||M2 → Inertial sensor
|-
| 4||Pi/2||0||0.7389*Pi||0||0/0||Orientation correction
|}

<table><tr><td align="center">
{| class="wikitable" style="text-align: center"
| style="background:#d0d0d0;" colspan="7" | Right eye
|-
| style="background:#f0f0f0;"|'''Link'''
| style="background:#f0f0f0;"|'''alpha'''
| style="background:#f0f0f0;"|'''R'''
| style="background:#f0f0f0;"|'''theta'''
| style="background:#f0f0f0;"|'''D'''
| style="background:#f0f0f0;"|'''min/max'''
| style="background:#f0f0f0;"|''' '''
|-
| 0||Pi/2||0||0||0||0/0||virtual link
|-
| 1||Pi/2||0||0||0||-20/20||M0 → M1
|-
| 2||Pi/2||0||0||-0.37||-53/53||M1 → M2
|-
| 3||Pi||0.13221||19*Pi/17||0||-18/37||M2 → M3
|-
| 4||Pi/2||0||2*Pi/17 + Pi||-0.111||-38/38||M3 → M4
|-
| 5||Pi/2||0||-Pi/2||0||-38/38||M5 → End-effector
|}
</td><td align="center">
{| class="wikitable" style="text-align: center"
| style="background:#d0d0d0;" colspan="7" | Left eye
|-
| style="background:#f0f0f0;"|'''Link'''
| style="background:#f0f0f0;"|'''alpha'''
| style="background:#f0f0f0;"|'''R'''
| style="background:#f0f0f0;"|'''theta'''
| style="background:#f0f0f0;"|'''D'''
| style="background:#f0f0f0;"|'''min/max'''
| style="background:#f0f0f0;"|''' '''
|-
| 0||Pi/2||0||0||0||0/0||virtual link
|-
| 1||Pi/2||0||0||0||-20/20||M0 → M1
|-
| 2||Pi/2||0||0||-0.37||-53/53||M1 → M2
|-
| 3||Pi||0.13221||19*Pi/17||0||-18/37||M2 → M3
|-
| 4||Pi/2||0||2*Pi/17 + Pi||0.111||-38/38||M3 → M5
|-
| 5||Pi/2||0||-Pi/2||0||-38/38||M5 → End-effector
|}
</td></tr></table>

<table><tr><td align="center">
{| class="wikitable" style="text-align: center"
| style="background:#d0d0d0;" colspan="7" | Right arm
|-
| style="background:#f0f0f0;"|'''Link'''
| style="background:#f0f0f0;"|'''alpha'''
| style="background:#f0f0f0;"|'''R'''
| style="background:#f0f0f0;"|'''theta'''
| style="background:#f0f0f0;"|'''D'''
| style="background:#f0f0f0;"|'''min/max'''
| style="background:#f0f0f0;"|''' '''
|-
| 0||Pi/2||0||0||0||0/0||virtual link
|-
| 1||-Pi/2||0||0||-0.0805||-20/20||M0 → M0R
|-
| 2||-Pi/2||0||0||0.212||-18/18||M0R → M1R
|-
| 3||Pi/2||0||Pi/2||0.10256||-135/75||M1R → M2R
|-
| 4||-Pi/2||0||-7*Pi/18||0||-75/0||M2R → M3R
|-
| 5||-Pi/2||0||Pi/2||0.16296||-85/85||M3R → M4R
|-
| 6||Pi/2||0||0||0||0/110||M4R → M5R
|-
| 7||Pi/2||0||0||0.18925||-85/85||M5R → M6R
|-
| 8||Pi/2||0||-Pi/2||0||-35/35||M6R → M7R
|-
| 9||-Pi/2||-0.1||0||0||0/0||M7R → End-effector
|}
</td><td align="center">
{| class="wikitable" style="text-align: center"
| style="background:#d0d0d0;" colspan="7" | Left arm
|-
| style="background:#f0f0f0;"|'''Link'''
| style="background:#f0f0f0;"|'''alpha'''
| style="background:#f0f0f0;"|'''R'''
| style="background:#f0f0f0;"|'''theta'''
| style="background:#f0f0f0;"|'''D'''
| style="background:#f0f0f0;"|'''min/max'''
| style="background:#f0f0f0;"|''' '''
|-
| 0||Pi/2||0||0||0||0/0||virtual link
|-
| 1||Pi/2||0||Pi||0.0805||-20/20||M0 → M0L
|-
| 2||-Pi/2||0||0||-0.212||-18/18||M0L → M1L
|-
| 3||Pi/2||0||-Pi/2||0.10256||-75/135||M1L → M2L
|-
| 4||-Pi/2||0||11*Pi/18||0||0/75||M2L → M3L
|-
| 5||-Pi/2||0||-Pi/2||-0.16296||-85/85||M3L → M4L
|-
| 6||Pi/2||0||0||0||-110/0||M4L → M5L
|-
| 7||Pi/2||0||0||-0.18925||-85/85||M5L → M6L
|-
| 8||Pi/2||0||Pi/2||0||-35/35||M6L → M7L
|-
| 9||-Pi/2||-0.1||0||0||0/0||M7L → End-effector
|}
</td></tr></table>

</td><td align="center">
[[File:Vizzymmotorsnumber.jpg]]
<table border=0>
<tr>
<td colspan="2" align="center">[[File:vizzy_torso_head.jpg|200px]]</td>
</tr>
<tr><td colspan="2" align="center">[[media:vizzy_torso_head.fig|Download matlab figure]]</td></tr>
<tr>
<td align="center">[[File:vizzy_right_arm.jpg|200px]]</td>
<td align="center">[[File:vizzy_left_arm.jpg|200px]]</td>
</tr>
<tr><td align="center">[[media:vizzy_right_arm.fig|Download matlab figure]]</td>
<td align="center">[[media:vizzy_left_arm.fig|Download matlab figure]]</td></tr>
</table>
</td></table>

Virtual link corresponds to:

<math>
H_0=
\begin{bmatrix}
1.0 & 0.0 & 0.0 & 0.0\\
0.0 & 0.0 & -1.0 & 0.0\\
0.0 & 1.0 & 0.0 & 0.0\\
0.0 & 0.0 & 0.0 & 1.0
\end{bmatrix}
</math>

or if you prefer code:
//H0 (1.0 0.0 0.0 0.0 0.0 0.0 -1.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 1.0) // given per rows (Very precise MATLAB Matrix)
Matrix H0(4,4);
H0.zero();
H0(0,0)=1.0;
H0(1,2)=-1.0;
H0(2,1)=1.0;
H0(3,3)=1.0;

''Parameters by Nuno Conraria. Updated by Miguel Aragão on September 2014''

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Vizzy Denavit–Hartenberg parameters