1:17
Crank-rocker
Four-bar linkage series, part 1: one crank turns fully while the rocker swings. The Grashof condition tells you when this is the case.
Four-bar linkage series · Part 4 · ASOMmini
Parallelogram and antiparallelogram linkage
If opposite links are of equal length, the Grashof condition becomes an equation. Depending on the arrangement, the result is a parallelogram linkage (parallel crank) or an antiparallelogram linkage (antiparallel crank).
1:01
The principle
The limit case of the Grashof condition
If there are two shortest and two longest links, the shortest and longest links together are exactly as long as the other two: the inequality of the Grashof condition becomes an equation. If the links of equal length are opposite each other, both links pivoted on the frame are cranks, no matter which link is the frame.
Twice per revolution, all links lie in one line. At this change point, the linkage can flip into the other type; starting from this position is particularly critical. In practice, only the range in which it cannot flip is therefore usually used.
Two types
- Parallelogram linkage: The links form a parallelogram. Both cranks are always parallel and turn at the same speed, and the coupler moves parallel to itself.
- Antiparallelogram linkage: The two long links cross like an hourglass. The cranks turn in opposite directions with a strongly varying ratio, and the coupler turns twice relative to the frame for each revolution of the cranks.
The videos
Every type in motion
1:01Parallelogram linkage
a = c = 32, b = d = 50, so a + b = 82 = c + d. Used, for example, in windshield wipers, as the double arm of desk lamps or in drafting machines.
1:04Antiparallelogram linkage
a = c = 100, b = d = 223, with the long links crossed: a + b = 323 = c + d. Occasionally used in mechanical switches.
In ASOMmini
From the textbook straight into the model
In ASOMmini, you build every type in this series with just a few clicks and immediately see how it moves.
Change lengths, see the effect
Move a joint, and ASOMmini recalculates the motion in real time – so you can see when a link no longer turns fully.
Paths and diagrams
Trajectories show the paths of the joints, and diagrams show angles, velocities and accelerations over the entire motion sequence. More on analysis
Forces and torques as well
With masses, springs and friction, the basic type becomes a concept whose forces and torques you know. More on force calculation
Four-bar linkage series
All example videos
More parts of the series
1:17
1:22
Double-crank
Four-bar linkage series, part 2: if the shortest link is the frame, both links pivoted on the frame turn fully.
1:11
Isosceles four-bar linkages
Four-bar linkage series, part 5: links of equal length are next to each other. Plus the rhombus linkage, in which all links are of equal length.
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