Grashof Condition

Is related to the Four Bar Linkage

Mechanism Inversion

Occurs when a fixed link is allowed to move and an alternate link is fixed instead. By doing so, the relative motion between the links is unchanged but the absolute motion, and function of the mechanism is not different.

The Grashof Condition

Definition

Breaks four-bar linkages down into three different classes and gives an indication of expected rotational motion. You need to consider different inversions of the mechanisms.

This predicts the rotation behaviour of a four bar linkage’s inversion based on link lengths only

Let:

• S = length of shortest link
• L = length of longest link
• P = length of one remaining link
• Q = length of the other link Then evaluate the following expression which puts you into different classes:
  $S+L\le P+Q$

Classes:

Class 1
$S+L<P+Q$
This is a Grashof linkage:

• Ground link adjacent to the shortest link is a crank-rocker
• The ground shortest link is a double-crank
• The ground link opposite to the shortest is a Grashof double-rocker

Class 2
$S+L>P+Q$
This is a non-Grashof linkage which functions as triple rockers.
None of these links can have full revolutions.

Class 3
$S+L=P+Q$
This is a special-case Grashof-linkage where depending on orientation,. the four bar linkage could be in:

• Parallelogram form
• Antiparallelogram form
• Double-parallelogram form
• Deltoid or kite form

The Barker Classification

Definition

A More detailed classification from the Grashof condition. Classifies things into 14 types.

There’s a table outlining the 14 cases and their conditions.