What is the difference between forward and inverse kinematics?

Forward kinematics (FK) computes the end-effector position from known joint angles. Inverse kinematics (IK) does the reverse — it finds the joint angles needed to reach a desired position. This tool performs IK.

Why are there two solutions?

A 2-DOF planar arm can generally reach any reachable point with two different elbow configurations: elbow-up (theta2 > 0) and elbow-down (theta2 < 0). Both are geometrically valid; the choice depends on obstacle avoidance or mechanical constraints.

What happens when the target is out of reach?

The tool shows an error. The target is unreachable if its distance from the origin is greater than L1 + L2 (arm fully extended) or less than |L1 - L2| (arm folded back on itself).

Are the angles absolute or relative?

Theta1 is measured from the positive x-axis (absolute). Theta2 is measured relative to the first link — consistent with the standard Denavit-Hartenberg convention for planar arms.

What units should I use?

Any consistent unit works for lengths (meters, cm, inches). The tool outputs angles in degrees and radians.

Can this be used for 3D robot arms?

No — this tool handles only planar (2D) arms with two revolute joints. A 3D arm with more DOF requires full Denavit-Hartenberg or Jacobian-based IK methods.

Inverse Kinematics 2DOF

Name: Inverse Kinematics 2DOF
Availability: InStock
Author: Nham Vu

Enter end-effector target coordinates and link lengths to compute the two joint angles of a 2-DOF planar robot arm.

Robot Parameters

Link Lengths

L1 — First link length

L2 — Second link length

Target End-Effector Position

X — Horizontal coordinate

Y — Vertical coordinate

Arm Diagram

Elbow-up Elbow-down

Both solutions overlaid. Dashed circle = max reach.

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Summary

Enter end-effector target coordinates and link lengths to compute the two joint angles of a 2-DOF planar robot arm.

How it works

Enter the length of the first link (L1) in any consistent unit (meters, cm, inches).
Enter the length of the second link (L2) in the same unit.
Enter the desired end-effector target position X and Y.
The tool checks reachability: the target must lie within the annular workspace defined by |L1 - L2| and L1 + L2.
Using the law of cosines, theta2 is solved from cos(theta2) = (x^2 + y^2 - L1^2 - L2^2) / (2*L1*L2).
Theta1 is then derived from the atan2 formula, yielding two solutions: elbow-up and elbow-down.
Both solutions are displayed numerically and rendered on a live canvas diagram.

Use cases

Compute joint setpoints for a 2-link robotic arm reaching a target position.
Verify IK solutions during mechanical design and workspace analysis.
Teach and learn inverse kinematics in robotics and mechatronics courses.
Prototype path-planning algorithms before implementing them in firmware.
Check reachability constraints for a given link configuration.
Compare elbow-up vs. elbow-down configurations for collision avoidance.
Validate hand-calculated IK results against a known-correct reference.
Explore how link length ratios affect the reachable workspace.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu