Servo & Reducer Sizing — Linear Track (7th Axis)
Motor torque and thrust for a linear track (7th axis) from load, speed and ratio.
A rack-driven track turns rotary servo torque into tonne-moving thrust through pinion radius. Friction (entered through η) is the silent thief on long rails — plan a torque margin for the day the rail is dirty and the grease is cold.
Formula
Note: Planning-level engineering estimate — final robot selection, guarding layout and risk assessment must follow the integrator's calculations and a documented ISO 12100/10218 risk assessment.
Motor torque and thrust for a linear track (7th axis) from load, speed and ratio. A free industrial robot kinematics & cell design tool — no sign-up, no upload, instant results in your browser.
About Servo & Reducer Sizing — Linear Track (7th Axis)
Servo & Reducer Sizing — Linear Track (7th Axis) computes the governing relationship F = m(a + g·sinθ + µ·g·cosθ) · T = F·lead/(2π·η) live as you type. A rack-driven track turns rotary servo torque into tonne-moving thrust through pinion radius. Friction (entered through η) is the silent thief on long rails — plan a torque margin for the day the rail is dirty and the grease is cold. Defaults are pre-filled with realistic values for this exact scenario, and the worked example substitutes your numbers step by step so the math is never a black box.
How to use Servo & Reducer Sizing — Linear Track (7th Axis)
- 1Enter your values — Moved mass, Acceleration, Max speed, Screw lead / pinion circumference and more (sensible defaults are pre-filled).
- 2Read the live results: Peak thrust, Motor torque, Motor speed at v_max.
- 3Check the "with your numbers" line to see F = m(a + g·sinθ + µ·g·cosθ) · T = F·lead/(2π·η) substituted step by step.
- 4Adjust inputs until the scenario matches yours, then copy or share the result.
Why use Servo & Reducer Sizing — Linear Track (7th Axis)?
- ✓Instant, free and private — every calculation runs client-side in your browser; nothing is uploaded
- ✓Built on the stated formula F = m(a + g·sinθ + µ·g·cosθ) · T = F·lead/(2π·η) with authoritative sources cited on the page (Nabtesco / Harmonic Drive sizing guidelines; Siciliano & Khatib (eds.), Springer Handbook of Robotics, 2nd ed.)
- ✓A rack-driven track turns rotary servo torque into tonne-moving thrust through pinion radius.
- ✓SI ⇄ Imperial toggle converts your inputs in place, so you can work in the units your drawings use
Frequently asked questions
What formula does the servo & reducer sizing — linear track (7th axis) use?+
It evaluates F = m(a + g·sinθ + µ·g·cosθ) · T = F·lead/(2π·η), exactly as published. Sources: Nabtesco / Harmonic Drive sizing guidelines; Siciliano & Khatib (eds.), Springer Handbook of Robotics, 2nd ed.. The substituted worked example on the page lets you verify every step against the textbook.
How should I read the result — and how far can I trust it?+
A rack-driven track turns rotary servo torque into tonne-moving thrust through pinion radius. Planning-level engineering estimate — final robot selection, guarding layout and risk assessment must follow the integrator's calculations and a documented ISO 12100/10218 risk assessment.
When is this calculator the right tool for the job?+
Motor torque and thrust for a linear track (7th axis) from load, speed and ratio. A free industrial robot kinematics & cell design tool. Friction (entered through η) is the silent thief on long rails — plan a torque margin for the day the rail is dirty and the grease is cold. For neighbouring scenarios, the related tools below cover the same engine with different presets.
Does it support both metric and imperial units?+
Yes — the SI ⇄ Imperial toggle converts the values already in the fields, preserving the physical quantity, so you can flip mid-calculation without re-entering anything.
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