Frequently, a designer would like to predict that the input to a fourbar can rotate continuously.
Grashof's Criterion (sometimes called Grashof's Law, Grashof' Rule, or Grashof's Criterion) helps us to predict whether one Part can rotate continuously, or not. We apply the criterion to fourbar kinematicchains that are joined with PinJoints. A Grashof mechanism has at least one part that rotates continuously. A simple CrankRocker is the best known Grashof mechanism.
We start by making the frame as the shortest Part, designated 'S'. The part we choose as the shortest part does not change the following analysis. Review the schematics images below. They show a fourbar in two positions  the 'Stretched' and the 'Overlapping' positions. Each Part is designated a letter. S and L, are the Shortest [Frame] and Longest links, respectively. The other two Parts are designated P and Q. If L can reach the Stretched and the Overlapping positions [see schematics below], then the mechanism, can also rotate fully, because [sort of proof!]
If L can reach these positions it can also move to all of the intermediate positions[needs proof]. If this is agreed, then we want to know the lengths of P and Q that do not prevent L moving the two extreme positions. 

Stretched Condition  Grashof Proof 1 
Stretched position  top image  a triangle gives one inequality:
If P+Q < L+S, [or L+S > P+Q) then the joints would break. Overlapping position  bottom image  gives two more inequalities, and can exist when:
If Q were to increase in length to become equal to the inequality, P rotates clockwise to become horizontal, and if greater, it would break the mechanism.
If P were to increase in length to become equal to the inequality, then Q rotates counterclockwise to become horizontal, and if greater, it would break the mechanism. The Grashof Conditions: From 1, 2 and 3 above, we can say 'L' can rotate fully when these conditions, call them 'Conditions {A}', are met: Conditions {A} : S + L ≤ P + Q: Condition 1 S + P ≤ Q + L: Condition 2 S + Q ≤ L + P: Condition 3 {We can derive the same conditions if we move Q that is adjacent to S to the other side of the mechanism (S adjacent to P). We can also prove  not here  that the coupler can also rotate fully  see Motion Geometry of Mechanism, Dijksman}. 

Overalpping Condition  Grashof Proof 2 

If S, is the shortest Part, one of the remaining Parts must be the longest Part. Eventually, we can prove  but we have not proved fully in this analysis  if the total lengths of the shortest and longest Part is equal or shorter than the sum of the lengths of the other two parts, then the shortest link can make a complete revolution, with respect to the others, and vice versa. This is the Grashof Criterion (also called the Grashof Rule, or even the Grashof Classification) by Franz Grashof in 1883. So, stated as an inequality: (L + S) < (P + Q) : Grashof (L + S) = (P + Q) : then it is a special condition  see below  Parallelogram and Kite. (L + S) > (P + Q) : Non Grashof 

Generally, if the the Grashof condition is met, the Parts other than the shortest can only oscillate with respect to the others. If two parts can make a complete rotation, the two parts must be the shortest at the same time, and therefore have equal length. This is true if two of the three Grashof Conditions are met we can get a Kite, or a Parallelogram  see below. 

GRASHOF : DoubleCrank The Shortest Part is the Frame (BasePart) = then the mechanism is a DoubleCrank Also called a DragLine. Both Parts that are joined to the BasePart will rotate fully. 


GRASHOF: Crankrocker The Shortest Part is joined to the Frame (BasePart) = then the mechanism is a CrankRocker This is the most common fourbar maechanism. 

Grashof Double Rocker Rotating Coupler 
GRASHOF: DoubleRocker with Rotating Coupler The Shortest Part is the Coupler = then the linkage is a DoubleRocker, but the Coupler can rotate fully. To model this: Add a MotionPath FB to a Circle at the end of one of the Parts. Then add a LinearMotion FB to the MotionPath FB to rotate the MotionPoint. Joint the MotionPoint to, one of the rocking Parts.
Then join the MotionPoint to the other Rocking Link. 

Grashof Double Rocker Rotating Coupler 
GRASHOF SPECIAL CASE 1 'Parallelogram' / 'Antiparallelogram'. Here, the Length of the:
The Shortest and Longest parts are opposite to each other. It is not possible to predict kinematically what the position of the Dyad will be after the links become 'flat', or inline. The inertia of a part may make the mechanism move in one way, but it is not advisable to operate in the flat position, unless you transmit motion from the input to the output with gears or a belt. If you want to model, and build this mechanism and to make the rotations predictable, then it is best to add two Cranks  with a belt between them, or a GearPair with idler gear between the input and the output Parts. 

Grashof Double Rocker Rotating Coupler 
GRASHOF SPECIAL CASE 2 'Kite', or 'Deltoid'. Here, the Length of the:
The Shortest and Longest parts are adjacent to each other. You will notice that the crank must rotate two times while the output rotates one time. 