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Four-Bar Linkage and Coupler Curve

The four-bar mechanism, in its simplest form, has four bar-shaped links and four turning pairs, as shown in the animation. The fixed link (the black bar) may actually be bar-shaped, but more frequently it represents the frame of a machine and in that case is usually a massive casting of irregular shape. This interesting linkage system is the building block of more complicated mechanical linkage systems. Therefore it is a fundamental concept to be learned by mechanical engineering students.

In a four-bar mechanism, one of the rotating members usually is the driver and is called the crank or driver (the red bar). The other usually is called the rocker or follower (the green bar). The floating link ( the blue bar ) that connects the crank and the rocker is called the connecting rod, and the fixed link ( the black bar ) is called the frame.

Many mechanisms can be broken down into equivalent four-bar linkages. These mechanisms have many aplications in mecanical operations. Four-bar linkages are considered one of the fundamental mechanisms.

In this animation You can move either the red or green ball for different arrangements. Now you can also change the length of linkages. Note that when the ball is moved to a point that this mechanism can't handle, the rocker and connecting rod will be separated from the crank. However, the end of the connecting rod will try to reach to the tip of the crank. This is because the connecting rod and follower use forward kinematics to reach to the tip of the crank.

Grashof's law is applied to four-bar mechanisms.

How do the components of the animation work?
  • You can hide and show the grid by clicking on the Grid button
  • You can clear drawings by clicking the Clear button. This is useful when ever you move or change the length of components to discard the unwanted curves
  • Curve drawing will stop after two complete revolutions of the Crank and the animation will get faster. This will eliminate load on your CPU.
  • You can resume drawing any time by clicking the Clear button
  • You can drag the green and red circles to move the four-bar mechanism or change the length of the frame (black bar)
  • You can also change location of the green and red circles by changing their x and y coordinates. The coordinate entry text box background color corresponds to the circle color.
  • You MUST press the ENTER button after you have entered a value into the coordinate text input boxes.
  • You can change the rotation speed of the crank by changing the value in the rotation speed text box.
  • Setting the rotation speed to zero will stop the crank.
  • Negative speed values will turn the crank in the opposite direction.
  • The blue circle which draws the curve is on the same plane as the blue bar. The curve drawn by the blue circle is called the Coupler Curve.
  • The coordinate points of the blue circle are displayed in the blue input text boxes and you can change these values any time
  • The x coordinate axis of this point starts from where the blue and green bars join and extend towards where the blue and red bars join (positive direction)
  • The y coordinate axis extends upward from the corner where the blue and green bars join
  • You can also drag the blue circle when the crank is stopped, or while it is in motion if you can catch it.