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Four-bar linkage step by step
From a blank sheet to a rotatable four-bar linkage with bearing forces and friction – the whole process in ASOMmini.
Knowledge · Four-bar linkage
Four-bar linkage design
The four-bar linkage is the simplest and most common linkage: four links, four revolute joints. You find it in hinges, flaps, seat adjusters and windshield wipers. Here you can read which types exist, what matters in the design and how ASOM and ASOMmini support you.
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The structure
Four links, four joints
A four-bar linkage consists of the frame, two links pivoted on the frame and the coupler, which connects the two. When one link is driven, the motion of all the others is uniquely determined. Which motion results depends on the four lengths alone.
What a four-bar linkage is used for- Guiding a part: flaps, hoods, lids and doors that have to clear an obstacle when opening.
- Converting a rotation into a rocking motion, as in a windshield wiper.
- Guiding a point along a specific path, for example approximately in a straight line.
- Multiplying forces: toggle mechanisms, clamps and latches.
Basics
The lengths determine the type
Depending on which link is the shortest and how the lengths relate to each other, a link turns fully or only rocks. The Grashof condition tells you whether any link can turn fully at all.
Crank-rocker
The input link turns fully, the output link rocks back and forth. The most common type when a motor is to produce a rocking motion. See the example
Double-crank
The frame is the shortest link: input and output both turn fully, the output non-uniformly. See the example
Double-rocker
Both links pivoted on the frame only rock. Typical of hinges and flaps with a limited opening angle. See the example
Turquoise: the shortest link in each case. Dotted: the paths of the joints.
What else matters
- Transmission angle: The angle between the coupler and the output link is the usual measure of the quality of force transmission. Its smallest value over the entire motion should not fall below about 40°. More
- Dead points and extended positions: When two links lie in one line, the linkage can jam or snap through. Near such positions the forces become large. More
- Coupler curve: Every point of the coupler traces its own path. It can be used to approximate straight-line motion and dwells. More
- Special cases: In parallelogram and isosceles linkages, all links lie in one line at times. Parallelogram linkage, isosceles linkages
Try it out
Drag a joint.
Move the joints with your mouse or finger: as the lengths change, so does the type. Coupler curve, transmission angle and diagram are recalculated with every movement.
- Choose a linkage, switch the drive from A₀ to B₀
- The type is shown above the values, with the four link lengths below
- Transmission angles outside 40° to 140° are highlighted
Drag A₀, B₀, A, B or K
Linkage
Drive
- Crank-rocker
- Drive
- at A₀, fully rotating
- Drive angle φ
- 120°
- Transmission angle μ
- –
- μ min … max
- –
- Link lengths in mm
- a 80 · b 250 · c 200 · d 270
Beyond the type
The motion is only the beginning
Whether a four-bar linkage works in practice is decided by the conditions of the application. They change frequently during a project, and every change affects everything else.
What also counts
- Installation space and adjacent parts that no link may collide with.
- Forces and torques: weight, springs, gas springs, manual force and drive.
- Friction in the joints and manufacturing tolerances.
- Specified positions that the guided part must reach exactly. More on linkage synthesis
With ASOM and ASOMmini
Four-bar linkages in conceptual design
You move a joint and immediately see the complete motion sequence including forces and torques.
Built in a few clicks
In ASOMmini, you connect links and joints into a chain and see trajectories, angles and diagrams in real time. About ASOMmini
Generated from requirements
ASOM generates the four-bar linkage by synthesis from specified points or positions and maintains the requirements while you optimize. About ASOM
Forces from the start
Manual forces, drive forces and joint forces with friction appear alongside the motion, in ASOM for all scenarios at once.
Examples
All videos on the basicsFour-bar linkages in ASOMmini
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Crank-rocker
Four-bar linkage series, part 1: the crank turns fully while the rocker swings. The Grashof condition and the choice of frame tell you when this is the case.
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Double-rocker
Four-bar linkage series, part 3: if the Grashof condition is met and the frame is opposite the shortest link, both rockers swing and only the coupler turns fully.
Questions and answers
Frequently asked questions about the four-bar linkage
What is a four-bar linkage?
A planar linkage of four links connected by four revolute joints. One link is the frame; when one of the others is driven, the motion of the rest is uniquely determined.
When does a link turn fully?
When the Grashof condition is met: the shortest and the longest link together are no longer than the other two together. Which link then turns fully depends on where the shortest link is located.
What transmission angle is still acceptable?
As a guideline, the minimum transmission angle should not fall below about 40°. Below that, the joint forces rise sharply and the linkage becomes stiff to move.
Is ASOMmini enough for a four-bar linkage?
For setup, motion, forces and torques, yes. If the four-bar linkage is to be generated from specified points or positions or checked in many scenarios, ASOM is the right choice.
Can I use an existing drawing?
Yes. DXF drawings can be placed as a template or attached to a link so that they move with it.
Are you designing a four-bar linkage right now?
Tell us about your application. In an online demo, we will show you ASOM or ASOMmini using your own example.