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

Base radius (f) mmDistance from center of machine to center of each motor shaft
End Effector radius (e) mmDistance from center of the end effector to the center of the end effector joints
Bicep length (rf) mmDistance from motor shaft to elbow
Forearm length (re) mmFrom the EE joint to the elbow joint
Steps per turnThe motor precision
Cube envelopeHow big a box can the end effector reach? (end effector can actually move more than this)
CenterWhere is the middle of the cube 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