nonGrashof

NonGrashof, often written as non-Grashof, refers to a class of planar four-bar linkages whose link lengths do not satisfy Grashof’s inequality. In a four-bar linkage with link lengths arranged in nondecreasing order a ≤ b ≤ c ≤ d, Grashof’s criterion states that a + d ≤ b + c. When this inequality is not satisfied, i.e., a + d > b + c, the mechanism is classified as non-Grashof.

In a non-Grashof linkage, no single link can complete a full 360-degree rotation about its joint. As a result, the motion is typically restricted to oscillations, and the mechanism tends to behave as a double-rocker, where both the input and output joints rock back and forth within a limited range. The coupler link also exhibits constrained travel, and certain configurations may have dead-center positions where movement stalls.

Non-Grashof linkages are chosen when a design requires limited, predictable motion rather than continuous rotation. They can be used to convert small input displacements into nonlinear output motion, provide mechanical advantage variation within a restricted range, or serve as reciprocating drives in compact mechanisms. The non-Grashof classification contrasts with Grashof linkages, where a + d ≤ b + c guarantees that at least one link can rotate fully, enabling crank-rocker, double-crank, or related motion types. A related, intermediate case is semi-Grashof (a + d = b + c), which yields specific configurations where crank-like motion may exist depending on the setup.