planar-arm-kinematics

Forward and inverse kinematics for planar revolute robot arms in the XY plane. Pure JavaScript, no dependencies.

Two levels of API:

1. 2-link (2R) closed form — exact, instant, returns both the elbow-up and elbow-down solutions.
2. General n-link — a forward map plus a damped-least-squares (Levenberg– Marquardt) numerical IK that handles redundant chains.

All joint angles are radians, each relative to the previous link.

Install

npm install planar-arm-kinematics

2-link arm

import { forwardKinematics, analyticIK2R } from "planar-arm-kinematics";

const tip = forwardKinematics(2, 1, 0, Math.PI / 2); // { x: 2, y: 1 }

const sol = analyticIK2R(2, 1, tip.x, tip.y);
// { elbowUp: { t1, t2 }, elbowDown: { t1, t2 } }  (or null if unreachable)

analyticIK2R returns null when the target lies outside the reachable annulus [|l1 - l2|, l1 + l2].

General chain

import { forwardChain, jacobianIK } from "planar-arm-kinematics";

const lengths = [1, 1, 1];
const seed = [0.1, 0.1, 0.1];

const res = jacobianIK(lengths, seed, 1.5, 1.0);
// { angles, error, iterations, converged }

forwardChain(lengths, res.angles); // { x, y, phi }

jacobianIK accepts { lambda, tol, maxIter }. The damping factor lambda trades convergence speed for stability near singularities — larger is safer, smaller is faster.

License

Released into the public domain under the Unlicense.