Four bar linkage

A four bar linkage or simply a 4-bar or four-bar is the simplest movable linkage. It consists of 4 rigid bodies (called bars or links), each attached to two others by single joints or pivots to form a closed loop.

Four-bars are simple mechanisms common in mechanical engineering machine design and fall under the study of kinematics.

If each joint has one rotational degree of freedom (i.e., it is a pivot), then the mechanism is usually planar, and the 4-bar is determinate if the positions of any two bodies are known (although there may be two solutions). One body typically does not move (called the ground link, fixed link, or the frame), so the position of only one other body is needed to find all positions. The two links connected to the ground link are called grounded links. The remaining link, not directly connected to the ground link, is called the coupler link. In terms of mechanical action, one of the grounded links is selected to be the input link, i.e., the link to which an external force is applied to rotate it. The second grounded link is called the follower link, since its motion is completely determined by the motion of the input link.

Planar four-bar linkages perform a wide variety of motions with a few simple parts. They were also popular in the past due to the ease of calculations, prior to computers, compared to more complicated mechanisms.

Grashof's law is applied to pinned linkages and states; 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. Below are the possible types of pinned, four-bar linkages;

Types of four bar linkages, s = shortest link, l = longest link

Notable four-bar linkages

• If the input link may rotate full 360 degrees, it is called a crank. The linkage is called a crank-rocker if the input link is a crank and the opposite link is a rocker. If the opposite link is also a crank the linkage is called a double-crank.
• Pantograph (four-bar, two degrees of freedom, i.e., only one pivot joint is fixed.)
• Crank-slider, (four bar, one degree of freedom)
• Double wishbone suspension
• Chebyshev linkage (straight-line four-bar linkage)

Biological four-bar linkages

Four-bar linkages also occur in biological systems, most notably in the jaws of wrasses, a highly diverse group of marine fish. One link, typically taken as the reference, is the neurocranium (braincase). Attached to this are the nasal bone and mandible (lower jaw), the tips of which are joined to the maxilla (upper jaw). When the lower jaw is pulled down, this results in movement of the nasal and maxilla. As in mechanical four-bar linkages, the relative proportion of the link lengths determines the resulting movement. Fish which feed by biting hard-shelled organisms or biting off chunks of coral have four-bar linkages that optimize force output, but those which prey on smaller, faster fish have linkages that increase the speed of jaw protrusion for suction feeding. Furthermore, multiple combinations of link-lengths can have the same resultant force or speed, and as a result, not all wrasse species which feed on the same prey will have the same jaws. This results in a phenomenon called 'many-to-one mapping', in which there are multiple morphological solutions to the same ecological problem, which in turn fosters great morphological diversity. ^[1]

See also

• Cognate linkages

References

External links

• mechanisms101.com- Flash Four-bar Linkages simulator
• softintegration.com- Animated GIF Four-bar linkage with triangular coupler link
• Kinematic Models for Design Digital Library (KMODDL)
  Movies and photos of hundreds of working mechanical-systems models at Cornell University. Also includes an e-book library of classic texts on mechanical design and engineering.