Created Delta kinematics (mediawiki)

Delta-kinematics.mediawiki

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+Delta kinematics uses triangulation to control the nozzle position. Three coordinated carriages with rigid arms connect to a single effector where the nozzle is mounted. Delta triangulation has been documented extensively, perhaps nowhere better than in the PDF document [https://docs.google.com/viewer?a=v&pid=forums&srcid=MTgyNjQwODAyMDkxNzQxMTUwNzIBMDc2NTg4NjQ0MjUxMTE1ODY5OTkBdmZiejRRR2phZjhKATAuMQEBdjI Delta Robot Kinematics] by Steve Graves. Marlin performs delta kinematics in real-time during printing, and this can add significant processing overhead. The <code>DELTA_SEGMENTS_PER_SECOND</code> configuration option can be reduced to tune performance when movement is choppy. Combining delta kinematics with a [http://reprap.org/wiki/RepRapDiscount_Full_Graphic_Smart_Controller Full Graphic Smart Controller] will test the limits of a Mega2560.
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+The math for inverse kinematics can seem pretty daunting, but it comes down to these basic facts:
+
+* Three Carriages are mounted on three Towers and together move a single Effector.
+* Each carriage moves in coordination with the other two (but "doesn't care" about the other two).
+* The only numbers that really matter are the distances in the XY plane from each carriage to the effector perimeter.
+* Once you know the distance, you can easily get the carriage Z position:
+
+  H = DELTA_DIAGONAL_ROD      // The hypotenuse of all delta triangles is an arm's length
+  Dx = Tx - Ex                // X difference between carriage and effector center
+  Dy = Ty - Ey                // Y difference between carriage and effector center
+  Dte = sqrt(Dx^2 + Dy^2)     // Distance from carriage XY to effector center (A)
+  Dte -= EFFECTOR_RADIUS      // length to the edge, not the center
+  // H*sin(acos(A/H))
+  Ø = acos(Dte/H)             // Get the angle Ø from A/H
+  O = H * sin(Ø)              // Opposite side is solved, O=H*(O/H)
+  Zt = O + z                  // Add the carriage Z position
+  Zt += effector_thickness/2  // Now the effector will touch the bed when z=0.
+  Zt += nozzle_length         // Now the nozzle touches the bed at z=0. Done!