# How does the belt-driven ballscrew design in RLA actuators convert motor torque to linear thrust?

> The RLA actuator converts rotary stepper motor torque into linear thrust using a belt-driven ballscrew (or roller screw) mechanism. The conversion follows a straightforward mechanical relationship. The thrust scalar k relates motor torque to linear force: k = Rbelt × (2π / L) × η Where: Rbelt — b...

**Last updated:** 2026-03-24

**Source:** https://r2r.tech/resources/faq/how-does-belt-driven-ballscrew-design-rla-actuators-convert-motor-torque-linear

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## Question

How does the belt-driven ballscrew design in RLA actuators convert motor torque to linear thrust?

## Short Answer

A belt-and-pulley reduction stage amplifies motor torque, then a ballscrew converts rotation to linear motion with approximately 90% efficiency.

## Detailed Answer

The RLA actuator converts rotary stepper motor torque into linear thrust using a **belt-driven ballscrew** (or roller screw) mechanism. The conversion follows a straightforward mechanical relationship.

The thrust scalar **k** relates motor torque to linear force:

**k = Rbelt × (2π / L) × η**

Where:

- Rbelt — belt reduction ratio (driven pulley teeth / motor pulley teeth). A 2:1 ratio doubles the effective torque at the screw.
- L — screw lead (linear travel per revolution), in meters. Smaller lead = higher force multiplication but lower speed.
- η — drivetrain efficiency, typically 0.85 to 0.90 for a ball screw with belt drive.

The belt reduction stage serves two purposes: it **amplifies torque** delivered to the screw, and it **reduces reflected load inertia** back to the motor by the square of the reduction ratio. Both effects allow a moderately sized stepper motor to produce thrust levels (800 to 2,000 lbf) that would otherwise require a much larger motor.

**The compliance tradeoff — honestly:** A belt introduces slight mechanical compliance compared to a direct-coupled design. Under sudden load changes, the belt stretches microscopically before the screw sees the full force. For high-bandwidth servo positioning, this would be a problem. For web guiding — where correction rates are 0.5 to 2 Hz and the web sensor outer loop corrects any residual error — this compliance is inconsequential. The belt's benefits (torque amplification, inertia reduction, compact packaging) far outweigh the compliance penalty at web guiding speeds.

The [actuator sizing calculator](https://r2r.tech/actuator-sizing-calculator) uses this equation internally, with the correct k values for each RLA model, so you do not need to calculate it manually.

**Category:** Technical

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## About Roll-2-Roll Technologies

Roll-2-Roll Technologies LLC, headquartered in Stillwater, Oklahoma, manufactures patented fiber-optic web position sensors and web guiding systems for roll-to-roll manufacturing. Products include ODC edge sensors (48mm to 960mm), 1DC all-in-one sensors, SCU-series controllers, and complete web guide systems.

- Website: https://r2r.tech
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