I use cookies to count visits and to see how well my ads work.
An interactive kinematics lab for a six-axis industrial robot arm. Drag any of the six joint angles or the six link lengths and watch the homogeneous transformation matrices A₁…A₆ recompute, multiply out to T₀₆ and move the tool centre point — live, in the browser, with nothing to install and no account to create.
Column vectors, right-handed frames, Z up, millimetres and degrees. Every joint contributes Aᵢ = Rᵢ(θᵢ) · Tᵢ(Lᵢ) — a rotation about the joint axis followed by a translation along the link — and the pose of the flange is the product T₀₆ = A₁ · A₂ · A₃ · A₄ · A₅ · A₆. The rotation axes of the six servos run Z, Y, Y, X, Y, X; the link offsets run Z, Z, X, X, X, X. Click any factor in the chain to see that single 4×4 matrix written out with the term each cell comes from.
Moving a slider is the forward problem: angles in, pose out. Typing a target X, Y or Z — or a roll, pitch and yaw — runs the inverse problem instead. The solver uses damped least squares on the Jacobian and only publishes a pose once position error falls below 0.005 mm and orientation error below 0.001°. The roll / pitch / yaw panel rotates the tool while the tool centre point stays where it is, so you can watch the wrist rearrange itself around a fixed target rather than watching a drawing spin.
Students meeting homogeneous coordinates for the first time, anyone revising for a robotics or control exam, and teachers who would rather point at a matrix product that moves than at one on a slide. Six link lengths are adjustable too, so the same arm can be stretched into a different machine and the reach recomputed.
This is a teaching model. The silhouette is inspired by a FANUC R-2000iC/165F, but it carries no manufacturer's data and no logo, it is not factory kinematics and not a CAD model. It does not detect collisions and says nothing about safe trajectories on real hardware. Treat the numbers as a demonstration of the mathematics, not as a machine specification.
More from DaisyMath: the rocket landing simulator — grid fins, RCS thrusters and control allocation on a vehicle you can push around with wind — and DaisyMath, the times-tables game for iOS and Android that pays for both.