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Four Bar Mechanisms

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Four Bar Mechanisms

All dynamics texts contain four bar mechanism and four bar slider problems, but few take time to introduce the student to these fascinating and useful mechanisms, nor do they call these by name. Four bar mechanisms and their variations (for example, a four bar slider) are found in many different types of machines, and it is the opinion of this author that the student should learn to recognize these and appreciate these. Mechanical engineering students study four bar (and five bar, six bar, etc.) mechanisms in their dynamics of machinery classes.

Questions and Answers about Four Bar Mechanisms

1. Why is it called a “four bar mechanism” when I can see only three links moving? That’s right, there are usually only three moving links; the fourth link is the “ground link” which extends between the pins A and D. Position vectors drawn along the lengths of the four links form a vector loop whose sum is zero.

2. The three moving links each have a name: Link AB is called the “input link” because we are normally given its angular velocity and acceleration. It undergoes fixed axis rotation about the pin at A.

3. Link CD is called the “output link”; like AB it undergoes fixed axis rotation, but its motion is usually oscillatory because it is the third link in the chain.

4. Link BC is called the “coupler link” because it couples links AB and CD together. Link BC undergoes general plane motion.

5. A four bar mechanism is a single degree of freedom device. This means that if we know the angular velocity of just the input link, we can determine the angular velocities of the remaining two links (if all of the geometry is known, i.e. lengths and angles of the links).

6. A “four bar slider” mechanism replaces either link AB or CD with a slider. With respect to velocities, the slider offers the same constraint as does a link. For example, in the figure at left, the slider constrains point C to move horizontally. At the position shown, the imaginary link CD would likewise constrain point C to move horizontally.

7. It is important to understand “constrained” versus “unconstrained” motion: Unconstrained motion occurs when a body moves freely in space, without being constrained to follow a particular path. Constrained motion, on the other hand, occurs when a body is forced to follow a particular path. For a rigid body, usually one or two points on it are constrained. Virtually all motion that we will study in this class is constrained motion. It is very important for a student of dynamics to be able to visualize the constraints existing in a problem. The constraints give us velocity directions. Since the relative velocity equation is a vector equation, knowing directions of vectors is a valuable “piece” of information that helps lead us to a solution of a problem.

8. The accomplished dynamics student should learn to look at a four bar mechanism and visualize the operative constraints. In the figure at right, there are three links, all with constraints. Link AB is constrained to rotate about a fixed pin at A. Link CD is constrained to rotate about a fixed pin at D. Because they are fixed, the velocities of pins A and D are zero. The velocity directions of points B and C act perpendicular to links AB and CD, respectively, tangent to the circular paths traced by points B and C. Points B and C on link BC are therefore constrained to follow circular paths.

9. Though a four bar mechanism looks complicated, visualizing these constraints reduces it to a simpler problem. We already worked a “generalized slider” in example problem ______. The approach we used there is virtually the same as is used for the link BC in a four bar mechanism. Given below is a comparison of a generalized slider with its “four bar” analog. Can you see that the (velocity) constraints on AB are exactly the same in both problems?

In the generalized slider problem, vA is given as 3 m/s. In the four bar analog, vA usually is not given. You would normally be given the length of AD and its angular velocity AD. In this figure, the rADAD product must be 3 m/s. For example, if link AD is 1.5 m in length, then its  would be 1.5 rad/sec. The rADAD product would thus give vA = 3 m/s in the direction shown (perpendicular to AD).

In this example, use of the relative velocity equation gives vB = 2.05 m/s at the angle shown. If link BC is 1 m in length, then the angular velocity of BC would be BC = 2.05 rad/sec.


0. Many students ask to see real life examples of four bar mechanisms. The figures below show a pair of locking jaw pliers and a “mechanism” formed by a door frame, the door itself, and the closing mechanism. Other examples can be found in exercise equipment, in automobiles, on the buckets of front end loaders, and in many other applications. Four bar sliders, especially the slider-crank mechanism, are found, for example, in the piston and crank mechanisms in engines.

Below is shown a slider crank (a four bar slider in which the line of action of the slider pass through the pin A of the “crank” AB).

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