Linkages

Levers can be joined together to form linkages. Simple linkages change the direction of motion and the amount of force.

Reverse motion

Reverse motion linkages change the direction of input so that the output goes the opposite way. A fixed pivot forces the change in direction. These are often used on foldable clothes horses.

Showing reverse motion linkage and the direction of the moving pivots in simple linear Z shaped image and the fixed pivot. This is sat alongside a photograph of a folding clotheshorse.

Parallel or push/pull

Parallel motion or push/pull linkages use two fixed pivots to make the input and output travel in the same direction, through a link arm. Each fixed pivot has a moving pivot on either side, allowing the movement and power to go backwards and forwards. Changing the placing of the fixed pivots changes the amount of force exerted, while keeping the direction the same. For example, a toolbox with drawers opens up effectively using parallel motion linkages.

Showing parallel linkage and the direction of the push/pull moving pivots and two fixed pivots. This is sat alongside a photograph of an open toolbox with drawers.

Bell crank

Bell crank linkages change the direction of force through 90 degrees. The amount of output force can be changed by moving the fixed pivot. When used in bicycle brakes, the rider can pull the brakes from the handlebars, which changes direction through the bell crank to make the brake pads touch the wheels.

Bell crank linkage with fixed and moving pivots and arrows showing changes of direction. Alongside is a photograph of a bike where the bell crank is placed above and over the wheel.

Crank and slider

Crank and slider linkages change rotary motion into reciprocating motion. A fixed pivot is attached to a crank, which turns around and pushes and pulls a slider. When used in a car engine, the ignition of petrol by the spark plugs pushes the slider up, moving the connecting rod and turning the crank.

Showing a mechanical device called a crank slider and the moving pivot directing the movements of the other components.

Treadle

Treadle linkages use a rotary input to turn a crank on a fixed pivot. A connecting rod joins two moving pivots to another fixed pivot. This is how a pair of windscreen wipers works on a car, moving backwards and forwards together.

Showing a mechanical device called a treadle linkage and the moving pivot and connecting rod directing the movements of the other crank.

Angles in linkages

It is important when using levers to understand the angles in place for each arrangement. This way a designer can design appropriately for users’ needs.

A reverse motion linkage replicates a 'Z' angle. Z angles feature two internal angles, which will both be the same as long the input and output linkages remain parallel.

In the image below, the top internal angle is 30°, and therefore the alternate internal angle at the bottom is also 30°:

Z angle diagram showing top and alternate bottom angles at 30° each.

Where two lines intersect, the opposite angles are equal, and where two angles sit on a horizontal line the total angle together is 180°:

Two lines intersecting show opposite x and y angles as equal.X + Y = 180°

Also, corresponding angles are the same size in this 'F' arrangement:

Showing corresponding angles as the same size in an 'F' arrangement.

Example

From all of this, the angles A, B and C can be calculated for the parallel linkage below:

A parallel linkage diagram with angles A, B and C to be calculated.

A = 115° as it matches 115° on the Z angle

A and B both sit on a horizontal line, so 115° + B = 180°

180° - 115° = 65°, so angle B = 65°

B and C match on a Z angle, so B and C are both 65°.

Question

Calculate angles A, B and C in the parallel linkage below:

A parallel linkage diagram with angles A, B and C to be calculated.

C = 35°

C + A = 180° and A = B

Therefore, 35° + A = 180°

180° - 35° = 145°

A and B = 145°