# 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

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