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've used this program to design our delta robots.

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 the center of the hand
Steps per turnThe motor precision
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)?
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