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.

Please Let Me Know How Much You Like This (1 is very Bad - 10 is Excellent)

Anand Domkundwar
24 Dec 2012

It is very useful for teaching purposes.

Anand Domkundwar
24 Dec 2012

As the student of engineering can have better understanding about the subject.

11 Jan 2013

i found these kind of animation for my project.thank you. i want animation for 1st inversion of 4 bar mechanism

sanjay patil
20 Feb 2013

this kind of mechanism clear the concept very well

26 Mar 2013

Better than the Best. Very useful to teach the 4bar mechanism. Thanx a lot for this. I will use for my students.

alan cheng
10 May 2013

amazing find....wanted to refresh my design theory. haven't touched it in 5 yrs and this helped a lot.

25 May 2013

this type of examples clears the basic concepts of imagination...............................i highly appriceated from it.thanks.........................

03 Jun 2013

Very well done.

Is it possible to know the angular position of the rocker as a function of the crank angle?

Chuck sapienza
07 Jul 2013

I would be interested in seeing your 4-bar linkage model.
I have read others comments, but I cannot seem to find the marvelous animation tool everyone has been commenting on.
Please send me instructions on how to access the tool.

13 Jul 2013

Please send me instructions on how to access the tool.

yarlagadda triyatha
04 Nov 2013

this mechanism is very useful for understanding.......thanks.

14 Nov 2013

having seen this , i got the basic idia about four bar chain mechanism,, and it will help me to understand other mechanism.Thanks

Black Person
25 Nov 2013

I'm Black.

Black Person
25 Nov 2013

My Darkness will Rule the World.

26 Nov 2013

it,s great job done by any one.. it,s clear my all concept.. appreciated sir and a lot of respect

17 Dec 2013

very good

09 Feb 2014

thanks a lot... very interesting

10 Mar 2014

what is the diameter of the disc and length of the levers used crank and rocker mechanism?????

parth chandravadia
12 Mar 2014

its amazing...thnx

05 Apr 2014

thank u so much .... this is very useful ..

09 Apr 2014

its very use full for project work

29 Apr 2014

with four bar mechanism, what kind of product we can make?
Great work for teaching

08 Sep 2014

how to change the dmension of the black bar? thank you for making things much easier for analysis!

20 Sep 2014

its good thanx
where is located a point for this trajectory?

30 Sep 2014

Thanks for the animation. Excellent. I am interested in animation of four bar mechanism in different planes. Please advise.

29 Oct 2014

This is very useful to design machines.

K.Sai priya
29 Oct 2014

This is very useful to understanding four bar mechanism.thanQ......

29 Oct 2014

VERY NICE it is useful

C Charmichael
06 Nov 2014

This was very helpful in designing a 4 bar articulation lever for a swing gate in a launder system. Thank you.

pranav lawhale
12 Mar 2015

I am using mechanisms as two wheels on which shaft from centre
end of wheel iof both are connected by small shaft using bearing connected to plate shaft (E shape)s

Mir Nazmul
31 Jul 2015

good but its have increasing

Anil aditya
07 Sep 2015

This tool is very useful for teaching purpose.

Saumitra Mishra
05 Apr 2016

It is not working with parallelogram linkage WHY?
Rocker is not having a full rotation.

05 Apr 2016

It is not working, because there is inflection point in that case, and it can go either way. I recommend y

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