Rotary Delta Robot Forward/Inverse Kinematics Calculations

Tweak your robot dimensions and see how it will affect your work envelope and your precision. Then adjust your motor angles (thetas) or your tool position (XYZ) and see that the forward and inverse kinematics match.

We use this program to design our delta robots. If you are building a custom machine and need a consult on firmware, wiring, or mechanical parts, we'd be happy to contribute. Please contact us at Marginally Clever Software and include your numbers from this page.

Robot dimensions

rotary Delta Robot Calculation
Base radius (f) mmDistance from center of machine base to center of each motor shaft.
Bicep length (rf) mmDistance from motor shaft to elbow
Forearm length (re) mmDistrance from elbow to the wrist
End Effector radius (e) mmDistance from wrists to tool
Base to floor distance (b) mmDistance from floor to base
Steps per turnThe motor precision. 1.8 deg steppers are 200 steps per turn. At 1/16th microstepping that's 3200 steps per turn.
Rectangular cuboid envelopeHow big a box can the end effector reach? (end effector can actually move more than this)
motor angle limitsHow must the motors turn to move throughout the rectangular cuboid?
CenterWhere is the middle of the envelope relative to the base (0,0,0)?
HomeWhere is the tool when the arms are parallel to the floor?
ResolutionHow precise can the movements be?


Forward Kinematics: Change motor angles to see new XYZ position.

Inverse Kinematics: Change XYZ to see new angles.

0 degrees is when the bicep is horizontal to the floor.

Motor 1 degrees
Motor 2 degrees
Motor 3 degrees
X mm
Y mm
Z mm

Original equations from Trossen Robotics Forums

© Marginally Clever Software 2012