Why use CCD instead of an analytic formula?

A 3R spatial arm with joint limits is awkward for a single closed-form solution. CCD is simple to implement: each joint rotates to pull the end effector toward the target, iterating until the error is small or progress stalls.

Yes. As a local method it can stall at joint limits, fold into awkward local minima, or slow near singularities. Re-seeding posture or relaxing limits may be needed — behavior you can provoke by dragging the target aggressively.

What do the helix and figure-8 paths test?

They force continuous tracking through changing orientations and workspace heights, revealing lag, folding of links, and whether the iterative solver keeps up as the target moves.

3-Link 3D Arm Inverse Kinematics (CCD)

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.

About this model

A spatial 3R arm with yaw and two pitch joints reaches a 3D target by inverse kinematics. This simulator extends planar two-link IK into three dimensions and solves joint angles with constrained Cyclic Coordinate Descent (CCD): iteratively adjusting one joint at a time to reduce end-effector error while respecting joint limits. Drag the target in 3D or command helix, lemniscate, or figure-8 trajectories and watch the arm track. CCD is a local geometric heuristic — not an analytic closed-form IK, not Jacobian pseudoinverse control, and not collision-aware motion planning. Move the target through reachable and near-singular postures to see convergence behavior and joint-limit interactions.

Who it's for: Robotics, mechatronics, and advanced kinematics courses on iterative inverse kinematics.

Key terms

Inverse kinematics
Cyclic Coordinate Descent
3R manipulator
Joint limits
End effector
Trajectory tracking

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)

Frequently asked questions

Why use CCD instead of an analytic formula?: A 3R spatial arm with joint limits is awkward for a single closed-form solution. CCD is simple to implement: each joint rotates to pull the end effector toward the target, iterating until the error is small or progress stalls.
Can CCD get stuck?: Yes. As a local method it can stall at joint limits, fold into awkward local minima, or slow near singularities. Re-seeding posture or relaxing limits may be needed — behavior you can provoke by dragging the target aggressively.
What do the helix and figure-8 paths test?: They force continuous tracking through changing orientations and workspace heights, revealing lag, folding of links, and whether the iterative solver keeps up as the target moves.

Other simulators in this category — or see all 48.

View category →

NewUniversity / research

Bicycle Model & Stanley Controller

Launch Simulator

Kinematic bicycle (rear-axle): δ = θ_e + atan2(k_e·e, v) Stanley path-following law. Pick oval, race-track, lemniscate, sine-road or S-curve and tune k_e, v, L; live cross-track e(t) and steering δ(t).

NewSchool

Stress–Strain & Hooke’s Law

Launch Simulator

Qualitative σ–ε curve: elastic Hooke region, yield, strain hardening, necking, and fracture. Drag strain and tune E, σ_y, σ_u.

NewSchool

Quadcopter 2D (Pitch)

Launch Simulator

Side view: two rotors, PD on thrust split vs pitch — whiteboard quad slice.

NewSchool

Watt Governor (schematic)

Launch Simulator

Flyballs and sleeve vs RPM; steam throttle gap — speed feedback cartoon.

FeaturedSchool

Logic Gate Simulator

Launch Simulator

AND, OR, NOT, NAND, XOR. Drag, drop, connect, see output.

School

Truth Table Generator

Launch Simulator

Build a circuit, auto-generate the truth table.

3-Link 3D Arm Inverse Kinematics (CCD)

About this model

How it works

Key equations

Frequently asked questions

More from Engineering

Bicycle Model & Stanley Controller

Stress–Strain & Hooke’s Law

Quadcopter 2D (Pitch)

Watt Governor (schematic)

Logic Gate Simulator

Truth Table Generator

3-Link 3D Arm Inverse Kinematics (CCD)

About this model

How it works

Key equations

Frequently asked questions