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For Students · Inverse Kinematics

Inverse Kinematics for a tele-operated arm

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a tele-operated arm live below — adjust the inputs and watch it respond, right in your browser.

Inverse KinematicsLive

target → joint angles

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Link 1 length

Link 2 length

Elbow-up solution

Inverse kinematics is the hard direction: given where you want the tip, find the joint angles. For a 2-link arm the law of cosines gives a clean closed form — but with two solutions (elbow-up or elbow-down) and none at all when the target is out of reach. Drag the target, or click anywhere to move it there.

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Data Inspector

Joint 1-20.8°

Joint 291.4°

Target dist126

Total reach180

Reachableyes

Governing equation

θ_{2} = arccos \frac{x ^{2} + y ^{2} - 10 0 ^{2} - 8 0 ^{2}}{2 \cdot 100 \cdot 80} = 91. 4^{\circ}, θ_{1} = atan2 (40, 120) - atan2 (80 sin θ_{2}, 100 + 80 cos θ_{2}) = - 20. 8^{\circ}

Reading this result: This 2-link arm (segments 100 and 80, total reach 180) has a closed-form inverse: the law of cosines gives the joint angles that place the tip exactly on the target, with two branches — elbow-up and elbow-down. Iterative methods like CCD or the Jacobian transpose converge to one of them.

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Frequently asked questions

Is this good for students?: Yes — this version of "Inverse Kinematics for a tele-operated arm" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.