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Basic Machines 1: Lever, Pulley, Gear, and Cam

There are a number of mechanisms common to mechanical systems of all sorts that are useful to know about when you want to control motion of any sort. While this page is by no means comprehensive, it will help get you started on understanding a few basics of how to move things.

Before we go much further, there is one important thing you need to know. All of these machines are used to do work of some kind. Work, in this case, is defined as a force applied over a certain distance. Machines are designed to allow you to vary the ratio of force to distance in order to get the job done. Read on, this will make more sense as you see the examples.

The Lever

The lever is about the simplest of machines, one we're used to deling with every day, from can openers to car jacks and millions of other everyday devices. A lever is used to change the direction of a force, and to apply Every lever has a fulcrum point, about which the lever pivots. The two arms of a lever are not equal. A lever lets you move a heavy weight with a small force, by taking advantage of this inequality. By applying half the force on the longer side of the lever, but moving it twice as far, we move the weight on the short side of the lever. In the lever below, we can move a 1 kilogram weight half a meter by putting a half kilogram weight on the long arm of the lever, and letting it push down one meter:

The ratio of the long arm to the short arm tells us the mechanical advantage of the lever, which is the ratio of work put into the system to work done. If the long arm is twice as long as the short arm, the ratio is 2:1, and the mechanical advantage is 2. So we could move the weight with half the force needed if we're willing to move our force twice as far. This comes in handy when you've got a motor that can apply only so much force.

The Pulley

Pulleys are series of moving wheels and ropes, chains or wires used to gain mechanical advantage. In the pulley system below, the mechanical advantage is 2. Note that we have to pull ourrope up two meters to move the weight 1 meter. What we lost in distance, we gained in force, because it takes only half the force of gravity acting on the weight to pull it up.

The more pulleys we add, the greater the mechanical advantage we get. At the same time, we increase the distance we have to pull in order to move our weight the same amount. In general, the mechanical advantage is equal to the number of ropes needed to lift the load. Below are a few pulley arrangements and their mechanical advantages:

These notes are heavily indebted to a number of sources:

Physics : Principles with Applications, Douglas C. Giancoli, ©1990-1998, Prentice Hall

Flying Pig's mechanics section

Animatronics: A Guide to Animated Holiday Displays, Edwin Wise, ©2000, Prompt Publications


And others I am doubtless forgetting.

The Gear

Gears are used to convert rotational motion, both by changing direction and by trading speed for torque. The gear ratio corresponds to the mechanical advantage of the gear, and is determined by measuring the ratio of the distances from the center of the gears to the point of contact between them. In the gear system below, the smaller gear is half the size of the larger, so the gear ratio is 2:1. The larger gear will move half the speed of the smaller, but will provide twice the torque.

Note also in the gears above that the direction is reversed. So if the smaller gear were attached to our motor, the larger gear would move at half the speed of the motor and provide twice the torque in the opposite direction of rotation.

Certain gears, such as bevel gears or helical gears, can be used to change the axis of motion as well. Bevel gears have their teeth mounted at an angle to the axis of the gear, so that the mating gear does not have to be mounted at the same angle. Helical gears have their teeth cut at an angle to the face of the gear, to provide greater mating efficiency.

Worm gear mechanisms combine a helical gear and a screw gear. They generally hve very high gear ratios, and convert the axis of motion. Worm gears look like this:

Rack and Pinion gears used to convert rotary motion to linear motion. In a rack and pinion, teeth are mounted along a linar track (rack) which moves by being run against a normal gear (pinion), as follows:

For more on gears, see HowStuffWorks' gear notes, or Boston Gear's Gearology Guidebook.

Jen Lewin also has an excellent set of notes on gears.

The Cam

The cam is a wheel mounted eccentrically (off-center) on a shaft. It seems so simple, but serves a number of purposes. The simplest use of a cam is as a vibrator. By spinning the motor, the weight of the cam causes the motor's axis to shift. If the motor is attached to some solid surface, say, a pager or cell phone body, the surface vibrates.

Cams can also be used to create oscillating motion from rotary motion. By placing a shaft against the edge of a cam, the shaft will move up and down as the cam rotates eccentrically on the motor. The image below shows a cam in motion, rotating on an axis. Notice how, as the cam goes through successive rotations, the shaft pushing against it follows a curve:

The curve is roughly a sine-wave oscillation. The cam has converted the rotary motion of the motor into a sinusoidal oscillating motion.

For more irregular motion, cams with irregular shapes can be used. For example, a cam like the following would produce smooth motion with two sudden jumps:

Another useful form of cam is the camshaft, in which a rotating shaft has bends in it to produce several cam-like protrusions all on the same axis. Camshafts are used in car engines to move the valves. A typical camshaft would look like this (this one's a little irregular, as all the cams are different offsets. It wouldn't work well in a car):

Camshafts are often used in mechanical automata, where one crank may turn several dancing figurines at a time. Check out some of the models from Cabaret Mechanical Theatre for examples.

Flying Pig has some cams in motion on their site.
Basic machines 2: Joints and linkages