Four Bar Linkages in Machine Design

Four bar linkages are most preferred machine components as they have a large number of dimensions to be varied which allows for more flexibility in design and these dimensions can be varied to fit the design constraints of machines. But with flexibility in design comes the complexity, this results in complicated design techniques. The design techniques become simpler if one or more slider joints are included in the mechanisms.

The exact desired motion is very rare to be produced by using four bar linkages. By using four bar linkages synthesis techniques we can obtain approximate desired motions. With increase in the level of accuracy required for the desired motion, the complexity of computation increases greatly.

Mechanisms are required to follow the specified path and pass through the desired points as closely as possible. For some mechanisms it is more desirable that they should pass through the specified points and for some other mechanisms following the path is more important. There are two approaches to four bar linkage synthesis.

1. Precision Position Approach: In this approach the position through which the mechanism is desired to pass are selected and in the solution mechanism is compelled to exactly pass through these positions. In this approach it is difficult to control the path of mechanism between the specified points. The precision position approach generally employ graphical methods of synthesis. If the design positions are more than three than the solutions become complex and computer program is used for synthesis.
2. Path Optimization Approach: In this approach a large number of design positions are selected and the overall deviation of mechanism from these design points is minimized. For this approach numerical optimization techniques are employed using computers.

There are infinite synthesis problems. The common classes of problems with practical importance are:

1. The Double Rocker Problem: It is desired to design a four bar linkage such that if the input link moves through certain angle the output link should move through a specified angle.
2. The Motion Generation Problem: For this problem the motion of coupler is specified and a linkage mechanism is to be synthesized such that it's coupler has the desired motion.
3. The Function Generation Problem: The mechanism is to be designed such that the two cranks follow a required functional relationship, that is, for a set of angles of one crank the other crank should move to the angles specified in the other set.
4. The Rocker Amplitude Problem: In this case a crank-rocker linkage is to be designed such that for the continuous rotation of the driving crank the output link oscillates through a specified angular amplitude.
5. The Point Path Problem: A four bar linkage is to be synthesized such that a point on the coupler follows a specified path.