MYP Design Levers and Linkages Notes

A Lever Is Only Three Things

1. A lever is a rigid bar that turns about a fixed pivot, and that pivot has its own name, the fulcrum.
2. The effort is the force you put in and the load is the force the bar delivers to whatever you are moving.
3. The distance from the fulcrum to the effort is the effort arm, and the distance from the fulcrum to the load is the load arm.
4. Force times distance from the fulcrum is called a moment, measured in newton metres, and a lever balances when the two moments are equal.
5. Push with 20 N at 0.5 m from the fulcrum and you make a moment of 10 Nm, which exactly balances a 100 N load sitting 0.1 m on the other side.
6. Long arm in with short arm out buys you force, and short arm in with long arm out buys you speed and distance instead.

The Three Classes: Read What Sits in the Middle

1. In a class 1 lever the fulcrum sits between the effort and the load, as in a seesaw, a pair of scissors or a claw hammer pulling a nail.
2. Class 1 is the only class that reverses direction, so pushing one end down lifts the other end up.
3. In a class 2 lever the load sits between the fulcrum and the effort, as in a wheelbarrow, a nutcracker or a bottle opener.
4. Class 2 always multiplies force, because the effort arm is always longer than the load arm.
5. In a class 3 lever the effort sits between the fulcrum and the load, as in tweezers, a fishing rod or your forearm lifting a mug.
6. Class 3 always loses force and gains speed and range, which is exactly what you want when the output has to move fast or far.

Mechanical Advantage: Trading Distance for Force

1. Mechanical advantage is the load divided by the effort, and it tells you how many times the machine multiplies what you put in.
2. You can get the same answer from the geometry alone, because mechanical advantage also equals the effort arm divided by the load arm.
3. Wheelbarrow worked example: a 400 N load sits 0.4 m from the wheel and the handles are 1.2 m from the wheel, so the effort is 400 x 0.4 divided by 1.2, which is 133 N.
   1. The mechanical advantage there is 400 divided by 133, which is 3, so the barrow triples your push.
4. Forearm worked example: your biceps pulls 40 mm from the elbow while a 20 N mug sits 320 mm away, so the muscle has to pull 20 x 320 divided by 40, which is 160 N.
   1. That gives a mechanical advantage of 0.125, a bad deal for force but it lets your hand move eight times faster than your muscle does.
5. Nothing is free, because the effort always travels further than the load by the same factor, so an advantage of 3 means your hand moves three times as far.

Linkages Carry Movement Somewhere Else

1. A linkage is a set of rigid bars joined by pivots that carries movement from an input to an output, changing its direction or size on the way.
2. The bars are called links, and a pivot screwed to the frame is a fixed pivot while the rest move with the mechanism.
3. A reverse motion linkage is a single bar on a central fixed pivot, so pushing the input end left drives the output end right.
4. Worked number: a 120 mm bar with its fixed pivot 40 mm from the input end leaves 80 mm on the output side, so the output moves twice as far as the input, the opposite way.
5. A push pull linkage uses two arms on separate fixed pivots joined by a connecting rod, so input and output move the same way at the same time.
6. That is how a model railway signal, a car bonnet catch and a pedal bin lid are all worked from somewhere other than where they sit.

Bell Cranks Turn Corners, Parallel Motion Stays Level

1. A bell crank is an L shaped lever with its fixed pivot at the corner, and it turns a movement through 90 degrees.
2. Rim brakes on a bike use bell cranks so a cable pulling upwards squeezes the pads inwards onto the wheel.
3. Make the two arms different lengths and the crank changes force and travel as well as direction.
4. Worked number: a bell crank with a 60 mm input arm and a 20 mm output arm has a mechanical advantage of 3, so a 30 N cable pull becomes 90 N at the pad while the pad moves only a third as far.
5. A parallel motion linkage uses two equal length links between two bars so the output stays parallel to the input all the way through its travel.
6. Anglepoise lamps, cantilever toolbox trays and hospital bed tables all use it so the top surface stays level as it swings out.

Building a Linkage That Does Not Bind

1. Prove the geometry in card with paper fasteners before you cut a single piece of 3 mm acrylic.
2. Drill pivot holes about 0.5 mm larger than the pin, because a hole the same size seizes up and a hole 2 mm larger gives slop you can feel.
3. Most of the wobble in a school mechanism comes from the links flexing rather than the pivots, so use 3 mm plywood instead of card for anything carrying real force.
4. Draw the linkage in both end positions, since a mechanism that fits neatly at rest can hit the frame at full travel.
5. Watch for a toggle position, where three pivots line up and the linkage either locks solid or flips to the wrong side.
6. Slip a nylon washer between moving links so they do not rub, and the mechanism still works after a hundred cycles of testing.
7. Record input and output travel in millimetres for your design folder, because 40 mm in and 110 mm out is testable while moves smoothly is not.