Servo & Reducer Sizing — Vertical Lift (Z) Axis
Motor torque and thrust for a vertical lift (z) axis from load, speed and ratio.
Vertical axes add the honest term horizontal ones skip: m·g thrust at all times, plus a holding brake sized for it. A ball screw's fine pitch is a force multiplier but also a speed cap — the 10 mm pitch default here tops out at 6,000 rpm for 1 m/s.
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 vertical lift (z) 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 — Vertical Lift (Z) Axis
Servo & Reducer Sizing — Vertical Lift (Z) Axis computes the governing relationship F = m(a + g·sinθ + µ·g·cosθ) · T = F·lead/(2π·η) live as you type. Vertical axes add the honest term horizontal ones skip: m·g thrust at all times, plus a holding brake sized for it. A ball screw's fine pitch is a force multiplier but also a speed cap — the 10 mm pitch default here tops out at 6,000 rpm for 1 m/s. 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 — Vertical Lift (Z) 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 — Vertical Lift (Z) 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.)
- ✓Vertical axes add the honest term horizontal ones skip: m·g thrust at all times, plus a holding brake sized for it.
- ✓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 — vertical lift (z) 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?+
Vertical axes add the honest term horizontal ones skip: m·g thrust at all times, plus a holding brake sized for it. 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 vertical lift (z) axis from load, speed and ratio. A free industrial robot kinematics & cell design tool. A ball screw's fine pitch is a force multiplier but also a speed cap — the 10 mm pitch default here tops out at 6,000 rpm for 1 m/s. 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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