Gear ratio

Gear ratio – definition

Gear ratio is the relationship between the rotational speed of a driving shaft and the rotational speed of a driven shaft. In a mobile robot drivetrain, it usually describes the reduction between an electric motor shaft and a wheel axle. It is commonly written as motor revolutions to output revolutions, for example 20:1. Under this convention, the motor rotates 20 times while the wheel axle rotates once.

For a reduction gearbox, the gear ratio determines two primary drivetrain properties: wheel speed and available wheel torque. A higher reduction ratio decreases wheel rotational speed and increases torque at the gearbox output, subject to gearbox efficiency, motor limits, and mechanical losses. A lower ratio enables higher wheel speed but provides less torque at the wheel.

In UGV platforms such as Leo Rover and Raph Rover, gear ratio is a hardware property of the motor-gearbox assembly. It affects odometry scaling, velocity controller configuration, acceleration limits, climbing capability, wheel slip behaviour, and battery current demand. It is not a ROS 2 parameter by itself, but its value must be reflected in motor driver firmware and in the robot control configuration.

Gear ratio in a differential-drive UGV

Leo Rover uses a four-wheel-drive, skid-steer architecture that can be modelled using differential-drive kinematics. In this arrangement, the left and right sides of the platform are controlled independently. Wheel speed is generated from commanded linear and angular velocity, then converted into motor shaft speed through the gearbox ratio.

For a reduction gearbox, the basic relationship is:

N = ωmotor / ωwheel

Where N is the gear ratio, ωmotor is motor shaft angular velocity, and ωwheel is wheel axle angular velocity. Therefore:

ωwheel = ωmotor / N

Wheel linear velocity depends on wheel radius:

v = r × ωwheel

Where v is linear velocity in metres per second, r is effective wheel radius in metres, and ωwheel is wheel angular velocity in radians per second. ROS uses SI units by convention. REP-103 defines metres, radians, seconds, metres per second, and radians per second as the standard units for ROS coordinate and motion data.

For differential-drive kinematics, the controller calculates target left and right wheel velocities from the commanded linear.x and angular.z values. The output is typically sent through a ROS 2 control chain to a motor driver or embedded controller.

Gear ratio, torque and drivetrain efficiency

An ideal gearbox multiplies torque by the reduction ratio. Real gearboxes introduce friction and bearing losses, and may have backlash. Output torque should therefore be estimated with an efficiency term.

Tout = Tmotor × N × η

Where Tout is output torque, Tmotor is motor torque, N is the reduction ratio, and η is gearbox efficiency expressed as a value between zero and one. The efficiency figure must be taken from the motor or gearbox manufacturer’s datasheet. It should not be assumed from the nominal ratio alone.

A larger ratio can improve low-speed traction and reduce the motor torque required during starts, slopes, or operation with a sensor payload. It can also reduce maximum platform speed. On soft soil, grass, gravel, or construction-site surfaces, wheel slip may occur before the theoretical gearbox torque limit is reached. Odometry based only on wheel encoders will then diverge from the robot’s true motion.

Key parameters for motor and encoder integration

Gear ratio must be considered together with encoder resolution and wheel geometry. These values determine how encoder counts are translated into wheel angle, distance, and velocity estimates.

Parameter	Meaning	Effect on a UGV
Gear ratio	Motor shaft revolutions per wheel axle revolution	Sets the motor-to-wheel speed and torque conversion.
Encoder counts per revolution	Encoder resolution measured at the motor or output shaft	Determines odometry and velocity measurement granularity.
Wheel radius	Effective rolling radius under load	Converts wheel rotation to travelled distance.
Track width	Distance between left and right wheel contact lines	Affects angular velocity estimation in differential drive.
Gearbox backlash	Free angular movement between meshing components	Can reduce low-speed control accuracy and cause direction-change error.

If an encoder is mounted on the motor shaft, the wheel-side count estimate must include the reduction ratio. For example, the conversion implemented in firmware or a control node follows this form:

wheel_revolutions = motor_encoder_revolutions / gear_ratio

Incorrect ratio configuration produces systematic odometry errors. If the configured ratio is too low, the software will overestimate wheel rotation. If it is too high, the software will underestimate travelled distance and velocity.

Gear ratio in ROS 2 and ros2_control

ROS 2 navigation nodes do not usually require a gear ratio parameter directly. Packages such as diff_drive_controller operate on wheel geometry and joint interfaces. The motor controller, encoder driver, or hardware interface must expose wheel-side position and velocity consistently.

In a ros2_control system, wheel joints commonly provide position and velocity state interfaces in radians and radians per second. The hardware interface may convert raw motor encoder counts internally before publishing joint state data. This keeps the robot model independent of the motor’s internal transmission.

hardware_parameters:
  gear_ratio: 20.0
  encoder_counts_per_motor_rev: 2048
  wheel_radius: 0.095
  wheel_separation: 0.420

This YAML fragment is illustrative. Parameter names are hardware-interface specific and are not defined by a universal ROS 2 standard. The correct values must come from the installed motor, gearbox, encoder, wheel, and platform documentation.

Practical context for Leo Rover and Raph Rover

On Leo Rover, the drivetrain ratio should be treated as part of the base configuration before tuning autonomous navigation. A navigation stack cannot compensate for incorrect wheel odometry scaling. Before using Nav2, verify forward distance, in-place rotation, encoder polarity, and left-right wheel direction with measured tests.

Leo Rover supports ROS 2 on its Raspberry Pi-based compute unit. Supported ROS 2 distributions depend on the installed LeoOS image and software version. Its differential-drive base can publish odometry and transform data for use by localisation and navigation nodes, but autonomous operation requires integration of the required sensors and navigation stack.

Raph Rover may carry larger payloads, including LiDAR, GNSS/RTK hardware, depth cameras, and higher-performance compute units. Added mass changes rolling resistance and required wheel torque. When integrating payloads, verify that continuous and peak motor current, gearbox torque rating, and thermal limits remain within the drivetrain manufacturer’s specifications.

Normative references and technical sources

The following sources define relevant ROS conventions and describe interfaces used when integrating drivetrain hardware with ROS 2.