Levers, Linkages, Gears and Other Mechanisms

Introduction

Mechanisms power every single piece of moving, operating machinery on the planet. They are literally everywhere. No matter how complicated the mechanism, all mechanical systems can be simplified into a handful of key components. The most important ones that you need to know are:

Levers

Linkages

Gears

More interesting mechanism animations

The engineering science of mechanisms

Levers

Linkages

Gears

Gears are created for transmitting rotational motion, changing direction, slowing rotation down and increasing or decreasing torque (rotational force).

Gear Theory.pdf

Spur Gears

Worm Gears

Bevel Gears

Spur gears are the most common type of gears. They have straight teeth, and are mounted on parallel shafts. Sometimes, many spur gears are used at once to create very large gear reductions.

Worm gears are used for either increasing the torque (rotational force) in a gear system or more commonly to significantly reduce the speed of an output gear.

Bevel gears are conical in shape and are used most commonly to change the direction of an output gear, usually at 90° to the original axis of rotation.

Planetary Gears

Gear Train

Rack and Pinion

Planetary gears are used when very high torque is needed along with very large speed reductions but when there is not much space available to fit the gear train in.

A gear train is simply the name given to the whole assembly of gears.

A rack and pinion is used to convert rotary motion into linear (straight line) motion. It is the same system that is used to steer car wheels for directional control.

Gear Terminology

This image shows the most common types of gear and their axis of rotation (the imaginary line they rotate around).

Use this tool to help quickly calculate the reduction ratio and the rotational speed of a single gear pair.

Calculating gear velocities and ratios

Find the 'gear ratio' of a two gear 'train'.

Find the 'rotational speed' of a gear in a two-gear 'train'.

Step 1 - Count the number of teeth on the 'drive gear'.

The drive gear is the one that is 'powered', i.e. the one that is forcing the other one to turn. It is your starting point. Let's say out drive gear has 20 teeth.

Step 1 - Take the rotational speed of your drive gear

This is normally given in revolutions per minute (rpm). This property is independent of units so imperial or metric units are irrelevant. Other units are sometimes used too.

Step 2 - Count the number of teeth on the 'driven gear'.

The driven gear is the one that is being forced to turn by the drive gear. It is rarely referred to as the 'pinion'. Let's say our driven gear has 30 teeth.

Step 2 - Use the formula S1 x T1 = S2 x T2

'S' stands for speed, whilst 'T' stands for 'teeth'. Let's say our original drive wheel has 20 teeth, rotating at a speed of 70rpm and our driven wheel has 30 teeth:

S1 x T1 = S2 x T2

Therefore:

70 x 20 = 30 x ?

Step 3 - Divide the first number by the second number.

Divide the driven gear number of teeth by the drive gear number of teeth. In our example the driven gear had 30 teeth whilst the drive gear had 20 teeth. Therefore 30/20 = 3/2 = 1.5.

The gear ratio in this case is 1.5:1, or:

(driven) 1.5:1 (drive)

Step 3 - Transpose (reorganise) the formula to make S2 the subject.

(S1 x T1) / T2 = S2

(70 x 20) / 30 = S2

Therefore:

1400 / 30 = 46.67 rpm

Gear Generator

Use this tool, to design a quick gear ratio using the same maths as you did above.

Differential Gears

How can we get a vehicles wheels to turn at different speeds when turning round corners? The secret is a differential gear. Don't be put off by how old the black and white video is. It is literally the best explanation of a differential gear on the internet.

Same Gear, Different Name: A Round-up of Gear Terms - Gear MotionsThere are many terms that can be used to describe different types of gears. We've rounded up some gear terms we've heard used to describe the gears we make.

507 Mechanical Movements

The website 507 Mechanical Movements is a lovely compilation of animated versions of a list of weird and wonderful mechanisms as detailed by the Engineer Henry T Brown all the way back in 1868.

What is amazing is that the ideas inside are still used today in all sorts of mechanical machinery.

Here is a link to the original book on Amazon.

Animated Engines

The website 'Animated Engines' is another visually interesting site which aims to show how many of the worlds engines work by animating their 'insides' - an animated 'section' view.

Have a browse - they are mesmerising to watch.