Wheels, Speed & Turning: The Math of Movement
Two wheels. Different speeds. Infinite paths.
Two wheels. Different speeds. Infinite paths.
Before we talk about speed, let's settle something fundamental. This trips up almost everyone at first. Look at this robot and ask yourself: which end is the front?
Use arrow keys or buttons below to drive:
The drive wheels are the front. They lead. The small caster wheel in the back just drags along for balance - like a shopping cart's back wheels.
Your feet step forward first, and your body follows. You don't walk backwards and call it "forward." The drive wheels are the robot's feet.
Try pushing a broomstick across the floor by the end. It flops everywhere! Now pull it - perfectly stable. Drive wheels PULL the robot forward. That's why they're in front.
A differential drive robot has two wheels. When both spin at the same speed, the robot drives perfectly straight. Try it!
Both wheels cover the same distance per second, so the robot moves in a straight line.
Higher speed means more ground covered. The direction stays the same when both are equal.
When one wheel goes faster than the other, the robot curves. The slower wheel is on the inside of the turn.
The slower wheel traces a smaller circle. The robot pivots around the slower side.
A large speed difference creates a tight arc. A small difference makes a gentle curve.
When wheels spin at equal speeds but in opposite directions, the robot pivots in place with zero turning radius!
The pivot point is exactly between the two wheels. The robot spins without moving forward.
This lets robots turn to face any direction without needing space to curve around.
One formula predicts every path. Adjust the sliders and watch the radius calculation update in real-time.
The distance between the two wheels. A wider wheelbase makes the same speed difference produce gentler turns.
The robot's forward speed is the average of both wheels: v = (vL + vR) / 2
How fast it turns: omega = (vR - vL) / L. Bigger difference = faster rotation.
Real robots don't just use one speed setting - they follow a program: a sequence of steps. Build your program below to trace the target shapes!
You've discovered how two simple wheels create infinite paths. Real robots use this exact math to navigate the world!
Same wheel speeds produce straight-line motion.
The ratio between wheel speeds determines the turn radius.
Equal but opposite speeds create zero-radius pivot turns.
A simple formula predicts every possible path.
Differential drive is how most wheeled robots navigate.
Put your new knowledge into practice!