Can anyone explain the Grashof Criterion ?

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The Grashof Criterion determines the conditions for continuous relative motion in a planar four-bar linkage. It states that the sum of the lengths of the shortest and longest links must not exceed the sum of the lengths of the other two links. This relationship ensures that the mechanism can achieve full rotation without locking up. The criterion is derived from the geometric properties of linkages, and various mathematical proofs exist to validate it. Understanding this concept is crucial for analyzing and designing mechanical systems involving four-bar linkages.
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Hi, I'm a university second year Mechanical Engineering student and I'm new to this module of Kinematics and Dynamics of Machinery and I've just learned the concept of the Grashof Criterion where "The sum of the shortest and longest link of a planar four-bar linkage cannot be greater than the sum of remaining two links if there is to be continuous relative motion between the links."

L_{max}+L_{min}\leqL_{a}+L_{b}

Can anyone explain to me why is it so? Why must the sum of the max and min linkages be longer than the other 2?? Is there a mathematical equation to prove this? Thanks for the assistance :)
 
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