# Delta Robot Documentation

## Delta Conversion:

### Machine Geometry

\[AB=BC=AC=l\]
\[AO=BO=CO=\alpha\]
\[\angle ABC=\angle BAC=\angle ACB=60^{\circ}\]
Arm length represented by \(\gamma\).

\(O\) is origin, centered equally between all three towers.

\(A\) tower is front center, on the \(-y\) axis.

\(B\) tower is in \(+x,+y\) quadrant.

\(C\) tower is in \(-x,+y\) quadrant.

\(+z\) is up. The enemies' gate is in \(-z\).

\(T\) is the target Cartesian point.

### Tower Locations

\[A_x=0;A_y=-\alpha\]
\[B_x=+\frac{l}{2};B_y=\alpha\times sin(60^{\circ})\]
\[C_x=-\frac{l}{2};C_y=\alpha\times sin(60^{\circ})\]
### Axis Motion

\[A_z=\sqrt{\gamma^2-(A_x-T_x)^2+(A_y-T_y)^2}+T_z\]
\[B_z=\sqrt{\gamma^2-(B_x-T_x)^2+(B_y-T_y)^2}+T_z\]
\[C_z=\sqrt{\gamma^2-(C_x-T_x)^2+(C_y-T_y)^2}+T_z\]