LeverLab
The Journal
Wheel and Axle: The Rotating Lever Behind Doorknobs, Steering Wheels, and Winches
A doorknob, a screwdriver, a steering wheel, and a capstan are all the same machine: a lever whose fulcrum sits at the center of a circle instead of along a straight bar. Here's the wheel-radius-over-axle-radius math behind all of them.
Designing a Simple Machine to Hit a Target Mechanical Advantage
Predicting a machine's mechanical advantage from its dimensions is arithmetic. Designing dimensions to hit a target MA reverses the problem — here's the method for all six machines, worked to MA 4, plus why you must verify the rounded, buildable version.
Mechanical Advantage vs. Efficiency: Why No Real Machine Hits Ideal
Mechanical advantage describes a machine's geometry. Efficiency describes what friction takes back once that geometry meets the real world. Here's why a screw loses the most, a lever loses the least, and where the missing effort actually goes.
Choosing a Gear Ratio for Speed or Torque
Winches want torque; fans want speed. Here's how to work backward from what a job actually needs to a gear ratio — and real tooth counts — including when a multi-stage gear train beats one oversized pair.
Pulley Mechanical Advantage: It's the Rope Segments, Not the Pulleys
Count the pulley wheels and you'll often get the wrong answer. A pulley system's mechanical advantage is the number of rope segments actually supporting the load — here's the counting method, named rigging patterns, and a quiz that catches the common mistake.
Ramp Length vs. Effort: Where Friction Eats the Gains
Doubling a ramp's length always halves the ideal force — but not the force you'll actually feel. Here's the diminishing-returns curve friction puts on ramp length, and how to find the shortest ramp that actually meets your target effort.
Why Thread Pitch Changes a Screw's Mechanical Advantage
Halve a screw's pitch and its mechanical advantage exactly doubles — a longer handle does the identical job. Here's the inverse relationship worked out step by step, plus the pitch-vs-lead gotcha on multi-start threads.
Spotting the Three Lever Classes Around Your House
Once you know to look for the fulcrum, the effort, and the load, levers turn up in pliers, a stapler, a shovel, an oar, and a bike brake — a room-by-room identification guide with worked numbers for each stop.
How Levers Work: The Three Classes Explained
A lever is a rigid bar and a pivot — nothing more — yet it's the oldest force-multiplying machine we have. Here's the moment-balance math behind it, worked examples for all three lever classes, and why a mechanical advantage below 1 is a design choice, not a flaw.
Block and Tackle: How Pulleys Multiply Your Pulling Force
A single pulley just changes the direction you pull. Add a second, movable pulley and you start multiplying force — here's how counting rope segments (never pulley wheels) tells you exactly how much, and what friction takes back.
Gear Ratios Explained: Trading Speed for Torque
Every meshed pair of gears is really a rotating lever, and the tooth-count ratio between them tells you exactly how much speed you're trading for torque — plus why an idler gear flips direction without touching the ratio.
Why Ramps Make Heavy Loads Easier to Move
An inclined plane doesn't reduce the work needed to lift a load — it spreads that work over a longer distance so the force required at any moment is smaller. Here's the ideal math, and why friction always makes the real force higher, never lower.