An XY gantry moves a drawing head over a work surface. You compare a coordinated straight move with axes that finish independently, then trace a circle under a vector feed-rate limit. The actual path and cross-track error come from two lagging axis models.
• A work bed with coordinate grid, X-axis guide rails and lead screw, a Y bridge and carriage, a drawing head and tool point, and command path and actual trail. • Controls for motion program (coordinated straight line, independent axis completion, circular interpolation), requested vector feed (40-240 mm/s), X and Y response times (0.02-0.3 s) and X and Y travel. • Readouts of actual X and Y, command X and Y, geometric contour error and actual vector speed. • Experiments: matched coordinated axes, independent completion, and a circle with mismatched axes.
For a straight move L = √(X² + Y²) and the command speed components are F(X, Y)/L. Independent mode commands each axis at speed F. The circle has center (150, 120) mm, radius 80 mm and angular speed F/80, and each axis follows ẋ = (rx − x)/τx and ẏ = (ry − y)/τy. The straight move cycles forward and back with a 1 s dwell at each end.
This is a kinematic trajectory generator plus independent first-order position servos with no acceleration planning, backlash, motor torque or collision solver. Independent mode can exceed the requested vector feed because each axis receives the full feed. Displayed error is geometric, not a machining tolerance guarantee.
No. Axis speeds must be proportional to their distances for simultaneous arrival.
No. Matched lag can preserve path shape while remaining behind the reference.
The shorter axis stops first, creating a bent route rather than a straight diagonal.
Different response lags distort the circle and increase contour error.