Servo & Reducer Sizing — Base (Axis 1) Rotation
Motor torque through the reducer for a base (axis 1) rotation from load, speed and ratio.
Axis-1 carries the entire arm's inertia but no gravity moment — sizing is pure J·α plus friction. The huge reflected-inertia reduction (÷i²) is why a 120:1 reducer lets a palm-sized servo swing a quarter-tonne arm: the motor mostly sees itself.
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 through the reducer for a base (axis 1) rotation 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 — Base (Axis 1) Rotation
Servo & Reducer Sizing — Base (Axis 1) Rotation computes the governing relationship T_m = (J·α + T_static) / (i·η) · n_m = n_joint·i live as you type. Axis-1 carries the entire arm's inertia but no gravity moment — sizing is pure J·α plus friction. The huge reflected-inertia reduction (÷i²) is why a 120:1 reducer lets a palm-sized servo swing a quarter-tonne arm: the motor mostly sees itself. 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 — Base (Axis 1) Rotation
- 1Enter your values — Load inertia at joint, Joint speed, Time to reach speed, Gravity/static torque at joint and more (sensible defaults are pre-filled).
- 2Read the live results: Peak motor torque, Acceleration share, Motor speed.
- 3Check the "with your numbers" line to see T_m = (J·α + T_static) / (i·η) · n_m = n_joint·i substituted step by step.
- 4Adjust inputs until the scenario matches yours, then copy or share the result.
Why use Servo & Reducer Sizing — Base (Axis 1) Rotation?
- ✓Instant, free and private — every calculation runs client-side in your browser; nothing is uploaded
- ✓Built on the stated formula T_m = (J·α + T_static) / (i·η) · n_m = n_joint·i with authoritative sources cited on the page (Nabtesco / Harmonic Drive sizing guidelines; Siciliano & Khatib (eds.), Springer Handbook of Robotics, 2nd ed.)
- ✓Axis-1 carries the entire arm's inertia but no gravity moment — sizing is pure J·α plus friction.
- ✓Niche-specific defaults give a meaningful worked answer the moment the page loads
Frequently asked questions
What formula does the servo & reducer sizing — base (axis 1) rotation use?+
It evaluates T_m = (J·α + T_static) / (i·η) · n_m = n_joint·i, 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?+
Axis-1 carries the entire arm's inertia but no gravity moment — sizing is pure J·α plus friction. 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 through the reducer for a base (axis 1) rotation from load, speed and ratio. A free industrial robot kinematics & cell design tool. The huge reflected-inertia reduction (÷i²) is why a 120:1 reducer lets a palm-sized servo swing a quarter-tonne arm: the motor mostly sees itself. For neighbouring scenarios, the related tools below cover the same engine with different presets.
Do I need to install anything or create an account?+
No. The tool is pure client-side JavaScript: open the page and it works, offline once loaded, with no account, no quota and no data leaving your device.
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