Assembly example: XY Cartesian gantry

A combined example for an XY gantry: it highlights the 'axis carries axis' principle — the X-axis moving mass includes the whole Y axis, so the X motor torque exceeds Y.

How to use

Enter the calculation conditions
Enter the dimensions, loads, speeds or operating conditions requested by the form.
Run the calculation
The tool applies the formulas shown on this page to the entered values.
Review the result
Review the resulting specification and checks, then verify them against the cited source, current standard and real operating conditions before use.

Core formula

M_Y=m_pl; M_X=m_pl+m_Yassy; Dp=z·p/π; F=μ·M·g; T=(F·(Dp/2)/η/N + J·n/(9.55·t₁))·Sf

Example using default values

payload 5 + Y-assembly 12 → M_X=17 vs M_Y=5 kg; T_X≈3.19 N·m vs T_Y≈0.97 N·m @200 rpm

Source: Oriental Motor Sizing (motor); timing belt JIS/maker; KTR/NBK (coupling).

Frequently asked questions

Why is the X-axis motor usually bigger than Y?

Because the X axis must move the entire Y axis (beam, Y motor, rail, cables) plus the payload, while the Y axis only carries the payload. The X-axis moving mass is much larger → higher tractive force and acceleration torque.

What goes into the Y-assembly mass?

Everything the X axis carries: the Y beam/rail, Y motor, Y rail and blocks, mounting plate, cables/cable chain, and the payload. Missing any of these underestimates the X-axis torque.

What about a dual-drive gantry?

Large gantries often drive X on both sides to prevent racking; the X load is then split between two motors but needs synchronization (gantry control). This example models a single X motor; for dual-side, halve the load and add the sync constraint.

MINATA — minatavn.com