Gear Ratios and Mechanical Principles

Lesson

Motors give you a fixed amount of power. Gears, sprockets and pulleys let you decide how that power is used: lots of speed with little force, or lots of force with little speed. Understanding this trade-off is the key to choosing the right motor and mechanism for every job on your robot.

What a gear ratio is

In a pair of gears, the driver gear is attached to the motor and the driven gear is attached to the output, such as a wheel or an arm. The gear ratio compares their tooth counts. When a small gear drives a big gear, the output turns slower but with more torque. This is called a reduction. When a big gear drives a small gear, the output turns faster but with less torque.

A small driver gear turning a large driven gear: slower output, more torque.

TEXT

1gear ratio    = driven teeth / driver teeth
2output speed  = input speed / gear ratio
3output torque ≈ input torque x gear ratio

The three rules you will use most often. Friction always takes a little away.

Worked example 1: a simple reduction

1
Count the teeth
A 20-tooth gear on the motor drives a 60-tooth gear on the arm.
2
Find the ratio
60 / 20 = 3, so the ratio is 3:1, a reduction.
3
Find the speed
If the motor output turns at 300 RPM, the arm shaft turns at 300 / 3 = 100 RPM.
4
Find the torque
The torque is about 3 times larger, minus a little lost to friction.

Worked example 2: drivetrain top speed

1
Start with the motor
A 312 RPM gearmotor drives a 96 mm wheel directly (1:1).
2
Wheel circumference
Circumference = pi x diameter = 3.14 x 96 mm, which is about 301.6 mm, or 0.3016 m per turn.
3
Turns per second
312 RPM / 60 = 5.2 turns every second.
4
Top speed
5.2 x 0.3016 m is about 1.57 m per second. A real robot will be slower because of weight and friction.
5
Add a reduction
With an extra 2:1 reduction the wheel turns at 156 RPM, so top speed drops to about 0.78 m/s, but the wheels push with about twice the torque.

Gear stages multiply. A 3:1 stage followed by a 4:1 stage gives 3 x 4 = 12:1 overall. An idler gear placed between two gears does not change the ratio at all; it only changes the direction of rotation and fills a gap. The same rules work for chains and belts: just use the tooth counts of the sprockets or pulleys.

Torque, friction and center of gravity

Torque is a turning force: torque = force x distance from the pivot. Imagine an arm holding a 0.3 kg game element 0.4 m from its pivot. The weight is about 0.3 x 9.8 = 2.9 N, so the torque needed just to hold it is about 2.9 x 0.4 = 1.2 N·m, before adding the weight of the arm itself. Double the arm length and the torque doubles. This is why long arms need large gear reductions.

Principle	What it means	What to do in the workshop
Torque	Turning force, equal to force times distance from the pivot	Keep arms short and light, and choose a reduction with plenty of margin
Friction	Force that resists sliding between surfaces	Use grippy wheels for traction, and reduce friction in mechanisms with bearings, alignment and lubrication where allowed
Center of gravity	The average position of all the robot's weight	Keep heavy parts such as the battery and motors low and centered

The center of gravity decides whether your robot tips over. A low, centered center of gravity keeps the robot stable. When a lift extends high or an arm reaches out, the center of gravity moves up and outward, and hard braking or turning can tip the robot. Wide wheel spacing, low battery placement and slowing the drivetrain while a lift is raised all help.

Key terms

Gear ratio: The number of teeth on the driven gear divided by the number of teeth on the driver gear.
Reduction: A gear arrangement that makes the output slower and stronger than the input.
Torque: A turning force, calculated as force multiplied by the distance from the pivot.
Friction: A force that resists sliding between two surfaces, giving wheels grip but also wasting energy in mechanisms.
Center of gravity: The point where the robot's weight can be considered to act, which affects how easily it tips.
Idler gear: A gear placed between two others that changes rotation direction but not the overall ratio.

Practical exercise

Gear Ratio and Stability Lab

1Pick two gears, sprockets or pulleys from your kit, count their teeth and calculate the ratio both ways (small driving big, and big driving small).
2Mount the pair on a motor, or turn it by hand, and count how many times the output turns for 10 turns of the input to check your calculation.
3Calculate the theoretical top speed of your drivetrain (or a kit drivetrain) from its motor RPM, any extra reduction and its wheel diameter.
4Calculate the torque needed to hold a 0.3 kg object at the end of a 0.25 m arm and at the end of a 0.5 m arm.
5Find your robot's approximate center of gravity by balancing it carefully on a round rod or broom handle, front to back and side to side, and mark it on a sketch.

Deliverable: A one-page worksheet showing the gear ratio calculations and test result, the drivetrain top speed, both arm torque values and a sketch marking the center of gravity.

Knowledge check

Answer every question, then check your answers.