3D Inverse Kinematics – Robot Arm

3D Arm — Inverse Kinematics

Solver iterations 6

Target orbit speed 0.6

Target orbit radius 3.2 m

End-effector error

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Reach used

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Shoulder θ

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Elbow θ

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How it works

The controller never picks joint angles directly — it solves for them. Each frame, Cyclic Coordinate Descent (CCD) walks the chain from the wrist back to the shoulder: for every joint it rotates just enough to swing the end-effector closer to the target, then moves to the next joint and repeats. A handful of passes converges on a full-body posture that places the hand on the target, even though no joint ever "knew" the final answer in advance.

for pass in 1..iterations:
  for joint j from tip to base:
    toEnd    = normalize(endEffector − j.position)
    toTarget = normalize(target − j.position)
    j.rotate(axis = toEnd × toTarget,
              angle = acos(toEnd · toTarget))

Solver iterations — more CCD passes converge tighter on the target each frame, at higher compute cost; too few leaves visible lag when the target moves fast.
Target orbit speed — how fast the goal point moves; a fast target stresses the solver's ability to keep up frame-to-frame.
Target orbit radius — pushes the target toward or past the arm's maximum reach, showing what happens when no exact solution exists (the arm stretches fully and settles as close as geometry allows).

Real-world relevance: this is the same class of algorithm (CCD, or its close cousin FABRIK) that runs on real articulated arms and animation rigs whenever you specify where the hand should be and let the controller figure out the shoulder and elbow angles.

Joints Links Target

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3D Inverse Kinematics — Robot Arm