# Robot arm playground: two-link inverse kinematics you can drag

> Drag a target and watch a two-link robot arm solve inverse kinematics live: shoulder and elbow angles, reach limits and elbow up or down.

Canonical: https://roboticsengineering.in/robot-arm-playground/ | Published: 2026-11-03 | Updated: 2026-11-03

**Drag the target and see the two joint angles that put the hand on it.** Change the link lengths to see how reach and the unreachable zone change.

Link 1 length (m)Link 2 length (m)Elbow up

Shoulder angle: **–** degreesElbow angle: **–** degreesHand position: **–** m

Drag or tap the canvas to move the target. This is a flat two-link arm, so it shows the geometry of inverse kinematics, not a full 3D arm.

## How it is calculated

For a target at distance d from the shoulder, the elbow angle comes from the law of cosines: cos(elbow) = (d² − L1² − L2²) ÷ (2 × L1 × L2). The shoulder angle is the direction to the target minus a correction angle, atan2(L2 × sin(elbow), L1 + L2 × cos(elbow)). Elbow up and elbow down are the two mirror solutions. The arm can reach any distance between the difference of the two link lengths and their sum.

## A worked example

With links of 0.25 m and 0.2 m the arm reaches out to 0.45 m and cannot reach closer than 0.05 m to the shoulder. Drag the target beyond 0.45 m and the dot turns red while the arm stretches toward it.

## Common mistakes

- Forgetting that every reachable point has two solutions, and picking the one that hits the base.
- Ignoring joint limits. Real servos rarely turn a full circle.
- Using this flat model for an arm that also rotates at its base.

## Related

[inverse kinematics of a 2-link arm in Python](https://roboticsengineering.in/inverse-kinematics-2-link-arm-python/), [robot arm kinematics basics](https://roboticsengineering.in/robot-arm-kinematics-basics/), [servo torque calculator](https://roboticsengineering.in/servo-torque-calculator/).

Last reviewed: November 2026. This tool runs in your browser and sends nothing anywhere. Treat its output as a first check, not a guarantee.