Mechanical Calculations - MA, VR and Gear RPM

The maths of mechanisms

A mechanism takes an input force or motion and changes it - making a force bigger, or a speed faster, or turning one movement into another. The calculations tell you by exactly how much. This module covers the three you need: mechanical advantage (MA), velocity ratio (VR) and the output speed of a gear train. A warning up front: all three are ratios, so they have no units.

Mechanism words

Four terms run through the calculations.

Match each quantity to its formula

What is mechanical advantage?

Mechanical advantage (MA) is calculated as which of these?

• The load divided by the effort
• The effort divided by the load
• The load added to the effort
• The load multiplied by the effort

The MA formula

For any lever or mechanism: MA = load / effort If MA is greater than 1, the mechanism magnifies your effort - a small effort moves a large load. Because it divides one force by another, MA is a ratio with no units. A longer effort arm gives a bigger MA.

Find the mechanical advantage

A lever lifts a load of 200 N using an effort of 50 N. Calculate the mechanical advantage. (MA = load / effort. It has no units.)

Force ratio vs movement ratio

MA and VR look similar but measure different things - one is about force, the other about distance.

Find the velocity ratio

To raise a load, the effort moves 2 m while the load rises 0.5 m. Calculate the velocity ratio. (VR = distance moved by effort / distance moved by load. It has no units.)

Small drives large

A small driver gear turns a larger driven gear. Compared with the driver, how does the driven gear turn?

• More slowly, with greater turning force
• More quickly, with greater turning force
• At exactly the same speed and force
• It does not turn at all

Which have no units?

Select the TWO quantities that are ratios and so have NO units.

• Mechanical advantage
• Velocity ratio
• Effort
• Load

Work out a gear speed

Put the steps for finding the output speed of a driven gear into the correct order.

• Note the driver gear's number of teeth and its rpm
• Note the number of teeth on the driven gear
• Multiply the driver's teeth by the driver's rpm
• Divide that total by the driven gear's teeth
• The answer is the driven gear's rpm

Find the driven gear speed

A driver gear with 20 teeth turns at 100 rpm and meshes with a driven gear that has 40 teeth. What is the speed of the driven gear? (driven rpm = driver teeth x driver rpm / driven teeth.)

Choose the mechanism

Three mechanism decisions. Pick the correct outcome each time.

• You want a spanner to loosen a tight bolt using less effort. What gives a bigger mechanical advantage?
• A driver gear with 20 teeth drives a gear with 60 teeth. The 60-tooth gear turns...
• To make the output gear turn FASTER than the input, the driven gear should have...

Learn the three formulas cold

Learn the three formulas cold: MA = load / effort, VR = effort distance / load distance, and driven rpm = driver teeth x driver rpm / driven teeth. Then the mark-saver: MA, VR and gear ratio are all ratios, so they have no units - never write newtons after an MA. And read gears the right way round: a large driven gear turns slower with more force, a small one turns faster.