Four-bar Mechanism

Four bar-shaped members connected to each other in one plane.

Usually:

• 1 fixed link + 3 moving links
• 4 pin joints
• 2 moving pivots + 2 fixed pivots
• 4 turning pairs

• input link - usually denoted in the left.
• output link - usually denoted in the right.
• coupler - intermediate link
• frame - fixed link

Grashof’s law

A four bar mechanism has at least one revolving link if $l_0+l_3 \le l_1+l_2$. $$

Here: $l_0,l_1,l_2,l_3$ are the length of four bars from shortest to longest. $$

Modes of motions

Mechanism	Shortest link	Criteria
Crank rocker	Input link	$s+l<p+q$
Double crank	Fixed link	$s+l<p+q$
Double rocker	Coupler link	$s+l<p+q$
Change point	Any	$s+l=p+q$
Triple rocker	Any	$s+l>p+q$

crank means a link that makes a full revolution. rocker means a link that doesn’t make a full revolution.

Crank rocker mechanism

Shortest link rotates a full revolution. Output link oscillates.

Double crank mechanism

Shortest link is fixed. Both input and output links rotates a full revolution.

Double rocker mechanism

Shortest link make full resolution. Input and output links makes a full revolution.

Special cases

$l_0+l_3 = l_1+l_2$. $$

Mechanism	Orientation
Parallelogram linkage or anti-parallelogram linkage	Equal links are opposite to each other
Deltoid linkage	Equal links are adjacent to each other

Parallelogram linkage

Double crank mechanism. Opposite links are equal and parallel. Angular velocity of input crank & output crank is same. Orientation of the coupler doesn’t change during the motion.

Anti-parallelogram linkage

Double crank mechanism. Angular velocity of input crank is different to output crank.

Deltoid linkage

• Longest link is fixed: crank rocker mechanism
• Shortest link is fixed: double crank mechanism

Non-Grashof’s condition

A four bar mechanism with the property if $l_0+l_3 \gt l_1+l_2$. $$

Here: $l_0,l_1,l_2,l_3$ are the length of four bars from shortest to longest. $$

Three links are in oscillation.