Grade by Grade
D. Structures and Mechanisms · Machines and Mechanisms

Changing the Kind and Plane of Motion

D2.4 D2.3 A1.3About 45 minutes
Learning goals
  • I can describe mechanisms that change rotary motion into linear or reciprocating motion, and back.
  • I can explain how a rack and pinion, a cam, a crank and slider, bevel gears and a worm gear change motion.
  • I can explain what it means to change the plane of motion.
  • I can build a cam toy that changes rotary motion into up-and-down motion.

Words to know

transform
To change something into a different form. A mechanism can transform one kind of motion into another.
plane
A flat surface, real or imaginary, that a motion happens in. A merry-go-round turns in a flat, level plane; a Ferris wheel turns in an upright plane.
rack and pinion
A small gear (the pinion) that meshes with a straight bar with teeth (the rack). It changes rotary motion into linear motion, or linear into rotary.
cam
An off-centre or oddly shaped wheel. As it turns, it pushes a follower up and down.
cam follower
The rod or part that rests on a cam and moves up and down as the cam turns.
crank and slider
A crank joined by a rod to a part that slides back and forth. It changes rotary motion into reciprocating motion, or the other way.
bevel gears
Gears with slanted teeth that mesh at an angle, usually a right angle. They change the plane of rotary motion.
worm gear
A screw-shaped gear (the worm) that turns a regular gear. It changes the plane of motion and slows it down a lot.

Turn a knob, slide a part

Look at a microscope that has a focusing knob. You turn the knob (rotary motion), and part of the microscope slides up or down (linear motion). The mechanism has transformed the motion: it changed one kind of motion into another kind!

In the last lessons, gears and belts transmitted motion and changed its speed and direction. In this lesson, mechanisms change the kind of motion and the plane it happens in.

A white school microscope on a classroom table, with large and small focusing knobs on its side.
Turning the focusing knobs on a microscope (rotary motion) makes part of the microscope slide up or down (linear motion). The mechanism transforms the motion. AI-generated image

Rack and pinion: rotary ↔ linear

A pinion is a small round gear. A rack is a straight bar with teeth. When the pinion turns, its teeth push the rack's teeth, and the rack slides in a straight line.

It works the other way too: push the rack, and the pinion turns.

Where you find it: the steering of many cars (turn the steering wheel, and a rack slides sideways to point the front wheels), the focusing knob of some microscopes, and some toy cars.

pinion (gear)turns: rotaryrack slides: linear
Rack and pinion. When the pinion turns counterclockwise, its bottom teeth move right and push the rack to the right.

Cam and follower: rotary → up and down

A cam is a wheel that is not round, or a round wheel with its axle off-centre. A rod called the cam follower rests on top of it. As the cam turns, its bumpy edge lifts the follower up, and then lets it drop back down. Rotary motion becomes reciprocating (up-and-down) motion.

The shape of the cam controls how the follower moves. An egg-shaped cam lifts the follower once per turn. A cam with two bumps lifts it twice.

Where you find it: car engines (cams open and close valves), wind-up toys with bobbing parts, and moving toys and displays.

follower movesup and downcam turnsround and roundguide
A cam and follower. As the egg-shaped cam turns, it lifts the follower and lets it drop: rotary motion becomes up-and-down motion.

Crank and slider: back and forth ↔ rotary

A crank turns in a circle. A connecting rod joins it to a part that can only slide back and forth (the slider).

  • Turn the crank: the slider moves back and forth (rotary → reciprocating). A sewing machine uses rotary motion from its motor to move the needle up and down.
  • Push the slider back and forth: the crank turns (reciprocating → rotary). In a car engine, pistons move up and down and turn the crankshaft.

Your legs on a bicycle work a bit like this: they push up and down, and the pedal cranks turn round and round.

Changing the plane of motion

Imagine the flat surface that a motion happens in. That is its plane.

  • A Ferris wheel turns in an upright plane, like a door.
  • A merry-go-round turns in a flat, level plane, like a tabletop.

Some mechanisms change the plane:

  • Bevel gears have slanted teeth and mesh at a right angle. In a hand egg beater, you turn the crank wheel in an upright plane. Bevel-type gears make the beaters spin around in a level plane in the bowl.
  • A worm gear is shaped like a screw. When the worm turns, it slowly turns a regular gear set at a right angle. Worm gears change the plane and slow the motion down a lot. The tuning pegs on many guitars use a worm gear: you turn the peg, and the post that the string winds around turns slowly, so you can tune carefully.
MechanismMotion inMotion outExample
rack and pinionrotarylinearcar steering, microscope focus knob
cam and followerrotaryreciprocating (up and down)engine valves, bobbing toys
crank and sliderrotary or reciprocatingreciprocating or rotarysewing machine needle; engine pistons
bevel gearsrotaryrotary in a different planehand egg beater, hand drill
worm gearrotaryslow rotary in a different planeguitar tuning pegs
Mechanisms that transform motion
Worked example

Let's analyse a hand egg beater

Describe how motion changes in a hand egg beater, from the crank to the beaters.

  1. Input: you turn the crank. Rotary motion in an upright plane.
  2. The crank's big gear meshes at a right angle with the small gears on the beaters. This changes the plane.
  3. Output: the beaters spin in a level plane inside the bowl. They also spin faster (big gear, small gears).
  4. The two beaters spin in opposite directions, so they mix the eggs well.

The egg beater transforms rotary motion: it changes its plane (upright to level), its speed (faster) and, for the two beaters, its direction.

Worked example

Let's choose a mechanism

An engineer wants a turning motor to open and close a sliding gate in a straight line. Which mechanism could she use?

  1. The motor gives rotary motion.
  2. The gate must move in a straight line (linear).
  3. Rotary to linear: a rack and pinion. The motor turns the pinion; the rack is fixed along the bottom of the gate.
  4. Turning the motor one way slides the gate open; turning it the other way slides it closed.

A rack and pinion. Many sliding gate openers really work this way.

Just for fun

What did the rack say to the pinion?

"Every time you turn around, I get pushed aside!"

Hands-on activity

Build a cam toy

You need: a small cardboard box (like a tissue or cereal box), a pencil or wooden skewer (the axle), thick cardboard, a straw, a paper figure or animal you draw and cut out, tape, and glue.

  1. A grown-up pokes a hole in the middle of each long side of the box, near the bottom, so the pencil can go straight through. Poke a third hole in the top of the box, right above the middle.
  2. Cut an egg-shaped cam from thick cardboard (about 6 cm long). A grown-up pokes a hole near its wide end.
  3. Slide the pencil through one side hole, through the cam, and out the other side. Tape the cam to the pencil so they turn together.
  4. Push the straw down through the top hole so it rests on the cam. This is the follower. Tape your paper figure to the top of the straw.
  5. Turn the pencil (the crank). Watch your figure bob up and down!
  6. Improve: make a cam with two bumps. How does the motion change? What happens with a perfectly round cam with the hole in the centre?

What to look for: rotary motion of the pencil becomes up-and-down (reciprocating) motion of the straw. A two-bump cam makes the figure bob twice per turn. A round, centred cam does not move the follower at all. Safety: a grown-up does all poking and cutting with sharp tools.

Your turn

1

What does a rack and pinion do?

2

What kind of motion does a cam make its follower do?

3

What is a plane of motion?

4

Which gears mesh at a right angle and change the plane of motion?

5

Name one place a rack and pinion is used.

6

How does a sewing machine get an up-and-down needle from a turning motor?

7

What two things does a worm gear change?

More practice: warm-up

1

What is a pinion?

2

What is a rack?

3

A Ferris wheel turns in an upright plane or a level plane?

4

What part rests on a cam?

5

Name a musical instrument part that uses a worm gear.

More practice: on your own

1

Explain the difference between transmitting motion and transforming motion.

2

In a car engine, pistons move up and down and turn the crankshaft. What kind of change is this?

3

Your cam toy's figure goes up and down twice for each turn of the pencil. What shape is your cam?

4

Why is a worm gear good for tuning a guitar?

5

In a hand egg beater, the crank turns in an upright plane. What plane do the beaters turn in, and which gears do this?

Challenge

1

Design a mechanism for a toy where turning a crank makes a bird's wings flap up and down AND a wheel spin. Describe the mechanisms you'd use.

2

A round cam with its axle exactly in the centre doesn't move the follower at all. Why?

3

A car's steering wheel turns 3 times to move the front wheels from all the way left to all the way right. Which mechanism is inside, and what does it transform?

Check your understanding

Quiz

1.

A rack and pinion changes...

2.

A cam and follower changes rotary motion into...

3.

Bevel gears are used to...

4.

Which mechanism slows motion a lot and changes its plane?

5.

A sewing machine needle goes up and down. Its motor turns round and round. This is a change from...

6.

A merry-go-round turns in...

7.

Which mechanism would best turn a motor's rotation into a gate sliding open in a straight line?

For parents and teachers

Big idea (D2.4, D2.3): Mechanisms can transform motion: change its kind (rotary ↔ linear or reciprocating), its plane (upright ↔ level, using bevel or worm gears), its speed and its direction. Building and improving the cam toy uses the engineering design process (A1.3).

About "plane": It may help to hold a paper plate upright and spin it (like a Ferris wheel), then lay it flat and spin it (like a merry-go-round). Same turning, different plane.

Common difficulties:

  • Confusing transmit and transform. Transmit = pass along; transform = change.
  • Thinking any wheel is a cam. A cam must be off-centre or not round.
  • Safety: poking holes in boxes and cutting thick cardboard need a grown-up with proper tools.