There are six simple machines — the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw — and almost every mechanical device you have ever touched is built out of them. This page walks each one with a working diagram, defines mechanical advantage in plain terms, shows how simple machines combine into compound machines like bicycles and cranes, and closes with a note from nearly two decades of financing the modern descendants of these tools: CNC machining centers, hydraulic presses, and the rest.
What a simple machine is
A simple machine is a device with few or no moving parts that changes the magnitude or direction of a force. That is the entire definition. There is nothing about engines, motors, electricity, or computers in it — the simple machines were known and used for thousands of years before any of those things existed.
The useful concept that goes with the simple machines is mechanical advantage. Mechanical advantage is the ratio between the force you get out of a machine and the force you put into it. If you push down on one end of a long lever with twenty pounds of force and the other end lifts a one-hundred-pound weight, the lever has a mechanical advantage of five. The work you do is roughly the same in both cases — you push down through five times the distance the load rises — but the force you have to apply at any one moment is one-fifth as large.
That trade is the deal every simple machine offers. Force times distance in equals force times distance out, minus whatever is lost to friction. You can have either a small force over a long distance or a large force over a short distance, but you cannot have both. Engineers call the geometry-only version the theoretical or ideal mechanical advantage and the measured version the actual mechanical advantage; the ratio between them is the machine’s efficiency.
Mechanically, the six simple machines split into two families. The lever family — the lever, the wheel and axle, and the pulley — works by balancing torques around a pivot. The inclined-plane family — the inclined plane, the wedge, and the screw — works by spreading a force out over a longer distance along an angled surface. Knowing which family you are looking at tells you how to think about the math.
The lever
A lever is a rigid bar that pivots around a fixed point called the fulcrum. It has three parts the engineer cares about: the place you apply your input force (the effort), the place the load is attached, and the fulcrum that separates them. By moving those three points around relative to each other, you get three classes of lever — and each class trades force, distance, and direction differently.
First-class lever. Fulcrum sits between the effort and the load. A seesaw, a crowbar, and a pair of scissors all work this way.
First-class lever — fulcrum in the middle
The fulcrum sits between the effort and the load. A long effort arm and a short load arm give you a large mechanical advantage. Examples: a seesaw, a crowbar prying up a nail, a claw hammer, a pair of scissors, the brake pedal in your car.
Second-class lever — load in the middle
The load sits between the fulcrum and the effort. A second-class lever always provides mechanical advantage greater than one and never reverses direction. Examples: a wheelbarrow, a nutcracker, a bottle opener, a doorstop pulled out by hand, a kayaker’s paddle braced against a rock.
Third-class lever — effort in the middle
The effort sits between the fulcrum and the load. A third-class lever has a mechanical advantage of less than one, which sounds bad until you remember that the trade goes the other way too — you give up force to gain speed and reach. Examples: tweezers, a fishing rod, a baseball bat, a shovel held with one hand at the top and one in the middle, your own forearm pivoting at the elbow.
The wheel and axle
A wheel and axle is two cylinders — a larger wheel rigidly fastened to a smaller axle — that turn together around a common center. It is mechanically a continuous lever: the radius of the wheel is the effort arm, the radius of the axle is the load arm, and the centerline is the fulcrum. The mechanical advantage is just the ratio of the two radii.
Wheel and axle. A small force on the rim of the large wheel becomes a larger force at the much smaller axle. The mechanical advantage equals the ratio of their radii.
Anywhere you turn one thing to do work somewhere else, there is probably a wheel and axle. A doorknob is a wheel and axle — the knob is the wheel, the spindle that operates the latch is the axle. A car’s steering wheel is a wheel and axle. So is a screwdriver handle, a wrench head, a winch drum, and the spindle inside every CNC machining center on a manufacturing floor in America. The wheels and gears of the wheels-and-gears system that makes a bicycle work are wheel-and-axle assemblies.
The pulley
A pulley is a wheel with a grooved rim that a rope, cable, or belt rides in. Pulleys come in three useful flavors, and the differences are entirely about how the rope is rigged.
Fixed pulley. A single wheel attached to a fixed point. It does not change the size of your effort — just its direction. Pull down to lift up.
Fixed pulley
A single pulley attached to a fixed point. The ideal mechanical advantage is one — you do not save any force. What you gain is direction. Pulling down to lift something up is much easier on the human body than pushing up directly. Flagpoles, garage-door springs, and old well buckets are all fixed pulleys.
Movable pulley
A pulley attached to the load itself, with the rope anchored above. As you pull the rope up, the pulley and the load both rise. The ideal mechanical advantage is two — you lift twice as much weight with the same force, but you have to pull twice as much rope. Crane hooks and the ropes on theatrical fly systems use movable pulleys.
Compound pulley (block and tackle)
Combine fixed and movable pulleys in a block-and-tackle arrangement and you can stack mechanical advantage as high as you have rope and patience. An ideal four-sheave block and tackle gives you a mechanical advantage of four — you lift four hundred pounds with one hundred pounds of effort, in exchange for pulling four feet of rope for every foot the load rises. Sailing-ship rigging, construction-site material hoists, and the chain hoist in the back of a machine shop all rely on the same principle.
The inclined plane
An inclined plane is a flat surface tilted at an angle. By rolling or sliding a load up the slope instead of lifting it straight up, you trade extra distance for less force. The mechanical advantage is the length of the slope divided by its vertical rise. A ramp that is ten feet long and rises two feet has a mechanical advantage of five — you push a five-hundred-pound barrel up it with a hundred pounds of force, ignoring friction.
Inclined plane. Trading distance for force — the steeper the ramp, the more force you need; the longer the ramp, the easier the lift.
Inclined planes are everywhere. A wheelchair ramp, a switchback road carved into a mountainside, the loading ramp on a moving truck, the staircase in a building, even the threads of a screw — these are all inclined planes. The trade-off is space: a longer ramp gives you more mechanical advantage but takes up more room. That is why parking-garage ramps spiral and why mountain roads switch back rather than running straight up the grade.
The wedge
A wedge is two inclined planes joined back to back — or in some designs, a single inclined plane on a moving body — used to split, cut, or hold. Its mechanical advantage is the length of the slope divided by the width of the back. A long, slender wedge can split a tough log with hammer blows that, applied directly, would barely dent it.
Wedge. A small force pushed in along the long axis becomes a large pair of forces splitting outward at the back.
Knives, axes, chisels, plow blades, splitting mauls, and wood-carving gouges are wedges. So are the cutting edges on every drill bit, end mill, and lathe tool that turns metal into a finished part. Doorstops and shims are wedges used not to split but to hold in place. The teeth of a saw blade are a row of small wedges, each one designed to remove a tiny chip on every pass.
The screw
A screw is an inclined plane wrapped in a helix around a cylinder. The surface you would walk along to climb the slope of the plane becomes the spiral thread along the body of the screw. Each full turn of the screw moves it forward (or pulls a fastener inward) by one pitch — the distance between adjacent threads. The mechanical advantage is the circumference the head travels through divided by the pitch, which is why a screw with very fine threads can develop enormous force from a moderate twist of the wrist.
Screw. An inclined plane wrapped around a cylinder. Each turn advances the screw by one thread pitch.
Wood screws and machine screws are obvious. Less obvious: the bolt and nut on a vise, the lead screw inside a mill that converts spindle rotation into table movement, the screw jack you use to hoist the corner of a house, the helical auger that drives a snow blower, the worm gear in an old elevator’s lifting drum, and the threaded base of every light bulb you have ever installed. The lid of a Mason jar is a screw too — a coarse-pitch one, designed to seal in a half-turn rather than to develop force.
Compound machines
A compound machine is any device made by joining two or more simple machines so they share the work. The mechanical advantages multiply. A pair of pliers is a compound machine: two first-class levers joined at a shared fulcrum, each of them ending in a wedge. Scissors are the same shape with different blades. A hand drill turns a screw with a wheel and axle. A pencil sharpener combines a wheel and axle (the crank handle) with a wedge (the blade).
Bicycles are a more interesting case. The pedals are levers. The crank arm and the chainring are a wheel and axle. The chain rides on toothed pulley-like sprockets at both ends. The wheels themselves are wheel-and-axle systems with the rim acting as the “wheel” and the hub as the “axle.” The hand brakes are compound levers that pull on cables, which then squeeze brake pads against the wheel rim — another wedge action. The whole machine is six different simple-machine principles cooperating.
Cranes, car jacks, sewing machines, garage-door openers, robotic arms, and CNC machining centers are all compound machines too. The point is not that compound machines are exotic. The point is that almost every machine you have ever used is a compound machine, and once you can name the simple machines inside it, you can usually figure out roughly how it works without anyone having to explain it to you.
A lender’s view of modern machine tools
I spend most of my working hours at Crest Capital structuring financing for the machines that built American manufacturing — and that still build it. Working from this catalog of six simple machines, a few patterns are worth pulling out of nearly two decades of deals.
When I started at the table in equipment finance, the most advanced machine tool I regularly financed was a three-axis CNC mill: a workpiece on a powered table that moved in two horizontal directions, with a spindle that moved up and down. Mechanically, that is a stack of lead screws (screw + wheel and axle) driving a heavy table along precision-ground ways, with a spindle that is itself a wheel and axle. Today I write deals on five-axis machining centers that add two rotary axes, so the workpiece, the spindle, or both can be positioned at angles that let a part be cut on multiple faces in one setup. Depending on the machine, those axes may come from a tilting/rotary table, trunnion, pivoting spindle head, direct-drive rotary axis, or geared drive. The leap from three-axis to five-axis is a leap in coordination, feedback, rigidity, workholding, and control, not a leap in basic mechanical principle.
The same trade-off the simple machines offer — distance for force — shows up in equipment finance as a trade-off between time and payment size. A shop owner buying a five-axis machining center for $400,000 has, in essence, two options: pay it down quickly with large monthly payments, or stretch the term out and trade time for a smaller payment per cycle. A longer term lowers the monthly payment but increases the total finance charges paid over the life of the deal — the right answer depends on the shop’s cash cycle, not on the machine. In my experience, the mistake is the same one the high-school physics class warns against: trying to get force and distance for free. The lender’s job is to keep the trade honest.
In many production environments — high-mix machine shops, contract manufacturers competing on lead time, suppliers feeding aerospace and medical — the wave of machine-tool advancement has been hard to sit out for long. Shops that did not move from manual mills to three-axis CNC in the 1980s often lost work to the ones that did. The move from three-axis to five-axis in the 2000s pushed the same way for parts that benefit from single-setup machining, and so does the current move toward in-line probing, automated tool changers, and pallet pools. Plenty of shops still run perfectly profitable three-axis work, and not every part needs five-axis. But the bar for what one operator can produce in a shift has shifted several times over, and the simple machines inside the spindle have stayed the same the whole time.
I also spend a few evenings a month with a FIRST Robotics team. Every robot the kids design uses some combination of these six machines — a four-bar lever to grip a game piece, a winch (wheel and axle) to lift it, a chain-and-sprocket drivetrain (pulleys, wheels and axles), a screw-driven linear actuator to extend an arm. They learn the math by building it, breaking it, and rebuilding it. That is, more or less, how the equipment-finance customers I work with learn it too.
Frequently asked questions
What are the six simple machines?
The six simple machines are the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw. They are the basic building blocks from which every more complicated mechanical device — bicycles, cars, cranes, CNC machining centers — is ultimately assembled. Each one changes the magnitude or direction of a force in a specific way, and the ratio between the force you put in and the force you get out is called the mechanical advantage.
What is mechanical advantage?
Mechanical advantage is the ratio of the output force a machine produces to the input force you apply. A first-class lever with a long effort arm and a short load arm gives you a mechanical advantage greater than one — a small push on your end becomes a large lift on the other end. Real machines also have friction, so the actual mechanical advantage you measure is always somewhat less than the ideal mechanical advantage you would calculate from geometry alone.
What is a compound machine?
A compound machine is any device that combines two or more simple machines to do a particular job. A bicycle is a compound machine: pedals and brake handles are levers, the wheels and gears are wheel-and-axle systems, and the chain wraps around toothed pulleys. A modern CNC machining center is also a compound machine — it uses lead screws to convert rotation to precise linear motion, levers in the tool changer, and wheel-and-axle assemblies throughout the spindle and drive train.
Why do real machines never reach their theoretical mechanical advantage?
Friction. Every contact surface — between a rope and a pulley wheel, between a screw thread and the material it bites into, between a sled and a ramp — turns some of the input energy into heat instead of useful output. The theoretical mechanical advantage is what the geometry of the machine would deliver in a frictionless world. The actual mechanical advantage is what you measure in the workshop, and engineers spend a great deal of effort closing that gap with bearings, lubrication, and surface finishing.
How do simple machines apply to modern manufacturing equipment?
Every modern CNC machining center is a stack of simple machines wrapped around a control computer. Lead screws and ball screws turn motor rotation into linear table motion at sub-thousandth-of-an-inch accuracy. The tool changer arm is a lever. The spindle is a wheel and axle running on precision bearings. Even the cutting tools themselves — drills, end mills, taps — are wedges, screws, or both. The leap from a manual mill to a five-axis CNC is not a leap in fundamental mechanical principles. It is a leap in coordination and feedback control.
Selected sources
- NASA STEMonstrations — Simple Machines A NASA video lesson in which an astronaut on the International Space Station explains the six simple machines and shows how they show up in spacecraft and on the ISS.
- NASA Next Gen STEM — Simple Machines Classroom Connection (PDF) NASA’s educator guide to teaching simple and compound machines, with definitions, classroom activities, and worked examples drawn from spaceflight applications.
- Encyclopaedia Britannica — Simple machine The Britannica entry defining simple machines, listing the canonical six, and walking through their history from antiquity through the Renaissance.
- Encyclopaedia Britannica — Mechanical advantage Britannica’s companion entry on mechanical advantage — the ratio of output force to input force, with worked examples for each of the simple machines.
- OpenStax Physics — Simple Machines (§9.3) A college-introductory physics chapter that defines mechanical advantage formally and works through each of the simple machines with diagrams, equations, and worked examples.
- Smithsonian Lemelson Center — Spark!Lab Network The Smithsonian Lemelson Center’s hands-on invention program for children, focused on problem-finding, prototyping, iteration, creativity, and practical invention learning.