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

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