Tutorial 1.2: Gears and Torque

Time: ~15 minutes Prerequisites: Tutorial 1.1: Forces and Motion

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The Bicycle Analogy

Have you ever ridden a bicycle with gears? Think about what happens when you switch gears:

flowchart LR
    subgraph LOW["LOW GEAR (for hills)"]
        direction TB
        L1["Pedal: Many rotations"]
        L2["Wheel: Few rotations"]
        L3["Easy to pedal<br/>Slow movement<br/>Lots of pushing power"]
    end
    subgraph HIGH["HIGH GEAR (for speed)"]
        direction TB
        H1["Pedal: Few rotations"]
        H2["Wheel: Many rotations"]
        H3["Hard to pedal<br/>Fast movement<br/>Less pushing power"]
    end

This is exactly how robot motor gears work!

What is Torque?

Torque is rotational (spinning) force. Instead of pushing in a straight line, torque pushes in a circle.

    Force (Linear)              Torque (Rotational)

         →→→                         ⟳
    ════════════                  ┌──────┐
    Pushes straight               | Motor|
                                  └──────┘
                                  Spins around

Torque is measured in Newton-meters (N·m) or inch-pounds (in·lb).

Think of torque as "twisting strength" - how hard the motor can twist.

VEX V5 Motor Gear Cartridges

VEX V5 Smart Motors can use different gear cartridges that change the torque vs. speed trade-off:

Cartridge	RPM	Torque	Best For
BLUE (6:1)	600	Low	Flywheel, intake
GREEN (18:1)	200	Medium	Drivetrain
RED (36:1)	100	High	Lifting, pushing

Understanding the Ratios

6:1 ratio means: For every 6 rotations of the motor, the output spins 1 time. - Motor spins fast → output spins fast - Less mechanical advantage → less torque

36:1 ratio means: For every 36 rotations of the motor, the output spins 1 time. - Motor spins fast → output spins slow - More mechanical advantage → more torque

    6:1 (Blue)                   36:1 (Red)

    Motor: ⟳⟳⟳⟳⟳⟳              Motor: ⟳⟳⟳⟳⟳⟳⟳⟳⟳⟳....(36 times)
    Output: ⟳                    Output: ⟳

    FAST, weak                   SLOW, strong

Torque vs. Speed: The Trade-Off

You can't have both maximum speed AND maximum torque. It's a trade-off:

    TORQUE ↑
           │
    RED────┼────────────●
    (36:1) │            │
           │            │
           │       ●────┼──── You can be somewhere
           │       │    │     in between!
           │       │    │
    GREEN──┼───●───┘    │
    (18:1) │   │        │
           │   │        │
           │   │        │
    BLUE───┼───┼────────┼───────────● ──→ SPEED
    (6:1)  │   │        │
           │   │        │
           └───┴────────┴──────────────────→

Which Should You Choose?

Mechanism	Recommended	Why
Drivetrain	GREEN (18:1)	Balance of speed and pushing power
Intake rollers	BLUE (6:1)	Need to spin fast to grab blocks
Lift arm	RED (36:1)	Need strength to lift heavy loads
Flywheel	BLUE (6:1)	Need maximum speed for launching

The Math Behind Gear Ratios

Here's the formula:

Output Torque = Input Torque × Gear Ratio
Output Speed = Input Speed ÷ Gear Ratio

Example with GREEN (18:1): - Motor provides 1 N·m of torque - Output torque = 1 × 18 = 18 N·m (18× stronger!) - Motor spins at 3600 RPM internally - Output speed = 3600 ÷ 18 = 200 RPM

Example with BLUE (6:1): - Motor provides 1 N·m of torque - Output torque = 1 × 6 = 6 N·m - Motor spins at 3600 RPM internally - Output speed = 3600 ÷ 6 = 600 RPM (3× faster than green!)

Code Connection: Gear Settings in robot_config.py

Look at src/robot_config.py, lines 19-30:

# Gear Settings:
#   RATIO_6_1  = 600 RPM (blue cartridge)  - high speed, low torque
#   RATIO_18_1 = 200 RPM (green cartridge) - balanced (default)
#   RATIO_36_1 = 100 RPM (red cartridge)   - high torque, low speed

# Left side motors (not reversed - standard mounting)
left_motor_front = Motor(Ports.PORT1, GearSetting.RATIO_18_1, False)
left_motor_back = Motor(Ports.PORT2, GearSetting.RATIO_18_1, False)

# Right side motors (reversed - mirror mounting spins opposite)
right_motor_front = Motor(Ports.PORT3, GearSetting.RATIO_18_1, True)
right_motor_back = Motor(Ports.PORT4, GearSetting.RATIO_18_1, True)

See how all four drive motors use RATIO_18_1 (green)? That's the balanced choice for a drivetrain!

Changing Gear Cartridges

If you want to change to RED for more pushing power:

# Change GearSetting.RATIO_18_1 to GearSetting.RATIO_36_1
left_motor_front = Motor(Ports.PORT1, GearSetting.RATIO_36_1, False)

:warning: Important: You must also physically swap the cartridge inside the motor! The code just tells the Brain what to expect.

External Gear Ratios

Besides the internal cartridge, you can add external gears between the motor and wheel:

    Motor Gear (12 teeth)      Wheel Gear (60 teeth)
          ┌──┐                      ┌────────┐
          │⟳ │ ────── chain ─────── │   ⟳    │
          └──┘                      └────────┘
          Small                     Big

    Ratio = 60 ÷ 12 = 5:1

    Motor spins 5 times → Wheel spins 1 time
    = More torque, less speed

This is configured in robot_config.py:

EXTERNAL_GEAR_RATIO = 1   # Change if using external gearing

If you have a 60:12 external ratio, you'd set:

EXTERNAL_GEAR_RATIO = 5   # 60 ÷ 12 = 5

Torque and Wheel Size

Bigger wheels cover more distance per rotation, but need more torque to accelerate:

    Small Wheel (2")              Large Wheel (4")

         ⟳                             ⟳
        [O]                          [  O  ]
    ════════════                ════════════════════

    Circumference:              Circumference:
    2" × π = 6.28"              4" × π = 12.57"

    Less distance per spin      More distance per spin
    Needs less torque           Needs more torque

Your robot uses 4-inch wheels:

# From robot_config.py
# 4" omni wheel circumference = 4 * pi * 25.4 = 319.19 mm
WHEEL_TRAVEL_MM = 319.19

Each wheel rotation moves the robot 319.19 mm forward!

Calculating Robot Speed

With all the pieces, we can calculate maximum robot speed:

Given:
- GREEN cartridge = 200 RPM
- 4" wheel circumference = 319.19 mm
- External gear ratio = 1 (direct drive)

Wheel RPM = Motor RPM ÷ External Ratio
          = 200 ÷ 1 = 200 RPM

Distance per minute = 200 × 319.19 mm = 63,838 mm = 63.8 m

Speed = 63.8 m ÷ 60 s = 1.06 m/s (about 3.5 ft/s)

That's walking speed - fast enough for a robot!

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Summary

Term	Definition	Trade-off
Torque	Rotational force	More torque = less speed
Gear Ratio	How much the motor is geared down	Higher ratio = more torque
Blue (6:1)	High speed, low torque	For fast mechanisms
Green (18:1)	Balanced	For drivetrains
Red (36:1)	High torque, low speed	For lifting/pushing

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Exercise: Gear Selection Challenge

Scenario 1: You're building an intake mechanism that needs to spin rubber rollers really fast to grab blocks quickly. Which cartridge?

Scenario 2: Your robot has a lift arm that needs to raise 2 kg of blocks. Which cartridge?

Scenario 3: You're in a pushing match and your opponent keeps pushing you backward. What could you change?

Bonus: Calculate your robot's speed if you switched to RED (100 RPM) cartridges.

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Answers

Scenario 1: BLUE (6:1) - you need speed, not torque

Scenario 2: RED (36:1) - you need torque to lift heavy loads

Scenario 3: Options: - Switch to RED cartridges for more torque - Add weight to your robot (more mass = harder to push) - Use traction wheels instead of omni (more friction)

Bonus:

Speed = (100 RPM × 319.19 mm) ÷ 60 s
      = 31,919 mm ÷ 60 s
      = 532 mm/s = 0.53 m/s (about 1.7 ft/s)

Half the speed of green, but much more pushing power!

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