four bar linkages

The reason that mechanisms which appear to have three links are called four bar linkages is rooted in the theory of kinematic chains. A chain of four links is the minimum basis for a useful mechanism. (A three link chain might make good structure, but it makes useless machinery.) The classification of kinematic chains is based on a study of the mechanism function (function usually described by associating inputs and outputs with elements of the chain) as it is related to its form (form usually described by the relative lengths of its members and the relative position of the link that is selected to act as the fixed or foundation link.) Kinematic linkages that are identical except in the choice of the foundation link are called "inversions." In describing the functional characteristics of inversions of four bar linkages it is usual to consider one pivoting link as the "input" or "driver" member and the other pivoted member as the "output" or the "driven" member. The remaining moving link has various names, but "connecting link" is descriptive enough.
The example animations here show three inversions of a four-bar chain made up of links AB, BC, CD, DA with lengths of 122, 110, 167, and 40 respectively. The forms of the three inversions are distinguished by the position of the shortest link DA with respect to the link selected as the foundation link, and their functions are distinguished by whether or not the driver and driven links can make full rotations about their pivots.
In the first inversion, called a "drag link mechanism" (animated on this page) the shortest link DA is the foundation link, and both driver and driven links AB and CD can make full revolutions. In the second inversion, called a "crank-rocker mechanism," a link (here AB) adjacent to the shortest is the foundation link, the shortest link DA can make a full revolution, and the opposite link BC oscillates. In the third inversion, called a "double rocker mechanism," a link (here BC) opposite the shortest is the foundation link. Although the shortest link DA can make a full revolution, both of the pivoting members CD and AB are constrained to oscillatory motions.
If there are four links, there must be four inversions. Where's the last one? The fourth inversion is a crank-rocker mechanism with link CD as the foundation link. It's behavior is qualitatively the same as the crank rocker shown in this set, so it was left out.
The four link chain selected to demonstrate the inversions resulted in a particularly tame drag link mechanism, and that should be fixed. The drag link is traditionally used to produce from a uniform input rotation rate a non-uniform output. The second drag link mechanism shows an extreme example.


One important application of four bar linkages is the generation of functions - relating the output of a mechanism with some functional relationship of the input. In the example shown here, the input (X) is proportional to the angular position of link AC with a travel of 60 degree of arc. The output (Y) is the angular position of link BD with a travel of 70 degrees of arc. The desired functional relationship between Y and X is Y = X^2. While X ranges from 1 to 6, Y ranges from 1 to 36. The graph in the lower left hand corner shows the positions of Y vs. X, compared to the desired functional relationship.

Category:

Education

Tags:

• four
• bar
• linkages

[TutorialsSAM]

Try SAM 6.1 !

[smithraymond09029]

Need to refresh on Dynamics 201 !

[yamanoorsai87]

Hi, I am going to use your video for a post at my blog. Thanks.

[vacuum20]

is that mobility=2?

[ebutuou123]

thanks for post! helped me with my homework/exam