3-Link 3D Arm Inverse Kinematics (CCD)

This interactive simulator explores 3-Link 3D Arm Inverse Kinematics (CCD) in Engineering. Continuation of two-link-arm-ik into 3D: 3 revolute joints (yaw + 2 pitches) solved with constrained Cyclic Coordinate Descent. Drag target in 3D or follow a helix / lemniscate / figure-8 trajectory. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Engineering.

Key terms

  • link
  • arm
  • inverse
  • kinematics
  • ccd
  • arm 3link ik 3d
  • engineering

How it works

**3-link 3D robot arm** with 3 revolute joints — base **yaw** (about Z), shoulder **pitch** and elbow **pitch** — solved with **Cyclic Coordinate Descent (CCD)** inverse kinematics. CCD walks from the end-effector back to the base, rotating each joint by the angle that would best align its remaining chain with the target — projected onto the joint's allowed hinge axis to honor the kinematic constraints. Drag the pink target around in 3D, run an automatic helix / lemniscate / figure-8 trajectory, and watch the joint angles tracked live. Continuation of `engineering/two-link-arm-ik` into 3D.

Key equations

CCD per joint j (axis a): align proj_a(e−p_j) with proj_a(t−p_j)
δq_j = atan2(∥a×·∥, a··), q_j ← clamp(q_j + step · δq_j, q_lim)