Question

If you have a four-bar linkage system, what must be true about the relationship between the lengths of the bars to ensure the system does not jam during rotation?

Accepted Answer

To ensure a four-bar linkage rotates without jamming, it must satisfy Grashof’s Law, which states that the sum of the lengths of the shortest and longest bars must be less than or equal to the sum of the lengths of the other two bars. For a linkage to achieve continuous full rotation, the shortest link must be either the input crank or the ground link. If the sum of the shortest and longest links is exactly equal to the sum of the other two, the linkage will reach a &#x27;toggle position&#x27;—a state where all bars align in a straight line, causing the mechanism to momentarily lock or change its direction of motion. An analogy for this is a bicycle pedal, where if the crank and the rod aligned perfectly flat, the force would pass directly through the pivot point, leaving the system unable to rotate further without external momentum. If the sum of the shortest and longest links exceeds the sum of the remaining two, the system is classified as a non-Grashof linkage, meaning no bar can complete a full 360-degree rotation and the mechanism will inevitably jam.

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If you have a four-bar linkage system, what must be true about the relationship between the lengths of the bars to ensure the system does not jam during rotation?