This simulator shows a robot tool-calibration fixture with a base translation and yaw stage, a pitching wrist and a tool offset carrying a tagged probe point. You drive the joints and watch the probe's world coordinates update, making it clear that one physical point can be described in several frames without the point itself moving.
• A 3D scene with a world reference triad (y up), a base stage at b = (0.3, 0.4, -0.2) m, a pitch wrist, a tool frame and a tagged probe point with projection lines. • Sliders for base yaw (-180° to 180°), wrist pitch (-70° to 70°), tool offset (0.1-0.6 m along the local tool x axis) and probe local y (-0.3 to 0.3 m), plus a check box that sweeps base yaw automatically. • Live readouts of the probe's world x, y and z, its distance from the tool origin, and the current base yaw. • Four tabs: the 3D laboratory, curves and measurements, preset experiments with model checks, and a learn-and-assess tab with a short quiz.
The probe's world position is pW = b + Ry(yaw) Rz(pitch) [offset, localY, 0]ᵀ. The base translation is applied last, the yaw rotation acts about world up, the wrist pitch acts in the already-yawed frame, and the tool offset sits at the end of the chain. Because rotations do not commute, swapping yaw and pitch generally moves the probe to a different place. Try a 90° yaw with the tool pointing along x: the offset swings to point along negative world z.
The lab uses rigid transforms with world y up and states that convention explicitly rather than copying any one manufacturer's frame definition. It isolates a wrist and tool fixture; it is not a full robot model and does not include joint limits, link dynamics or calibration error.
A coordinate is a description of a point relative to a chosen origin and set of axes. Changing the frame changes the numbers but not the physical point. In this lab the probe stays fixed to the tool while its world x, y and z change as the base and wrist move.
Yes. Rotations about different axes do not commute, so applying yaw then pitch generally gives a different probe position than pitch then yaw. The equations shown in the lab apply yaw about world up first, then wrist pitch, then the tool offset.
Position is where the frame origin sits; orientation is how its axes are rotated. A rotating wrist can change the world coordinates of a point on the tool without changing that point's distance from the tool origin, which the distance readout demonstrates.
No. It is a teaching fixture with stated assumptions and a fixed base location. Real robots use manufacturer-specific frame conventions, so always check the controller documentation for the exact definitions.