1. Slider Crank and Grashof1 2 3 4
Equivalent Linkage 1 2 3 4

2. Slider Crank and Grashof1 2 3 4 1 2 3
Infinite radius 4
e = l1 - l4
l1= inf
l4= inf
Equivalent Linkage

3. Slider Crank and Grashof1 2 3 4
Schematic 1 2 3
Infinite radius 4
e = l1 - l4
l1= inf
l4= inf

4. Grashof’s criteria for Slider Cranks
Now substitute in Grashof’s criteria for RRRR linkages.
Here 1 is definitely longest.
Let 2 be less than 3 making it shortest
Shortest + longest < sum of other two
Hence
l2+ l1 < l3+ l4
Or l2+ l1 - l4 < l3
Or l2+ ( l1 - l4 ) < l3
Or l2+ e < l3
Or s + e < L

5. Grashof ‘s criteria for RRRR linkages
l + s < p + q where s (link 1) is the shortest link
All other links rotate fully about s.
Hence if the shortest link is grounded
Both 2 and 4 rotate fully about the ground
making it a Double Crank
l + s < p + q where s (link 1) is the shortest link
Link 3 does not rotate fully about either 2 or 4.
Hence if link 3 is grounded
i.e. if the shortest link is made the coupler
Neither 2 nor 4 will rotate fully about the ground making it a Double Rocker
l + s < p + q where s (link 1) is the shortest link
If link 2 (or 4) is grounded
1 rotates fully about 2 (or 4)
3 rotates partially about 2 (or 4)
making it a Crank Rocker

6. Grashof’s criteria for Slider Cranks
Analyze using same logic as used for RRRR linkages, remembering that link 2 is the shortest here. 1 2 3 4
s+ e < L where s (link 2) is the shortest link
All other links rotate fully about s (link 2) .
If link 2 is grounded, i.e. shortest link is the ground,
Both 1 and 3 rotate fully about 2, i.e. the ground.
Since link 1 is not grounded ,
We have an Inverted Slider Crank (RRPR)
with a fully rotating crank (link 2)and a fully rotating slider. 1
s+ e < L where s is the shortest link
All other links rotate fully about s (link 2).
If the shortest link is the driver or crank,
1 rotates fully about 2 and vice versa.
3 and 4 rotate partially about 2.
If 3 is grounded ,
We have an Inverted Slider Rocker (RPRR)
with a partially rotating crank (link 2) and a fixed slider. 2

7. Grashof’s criteria for Slider Cranks1 2 3 4
Link 2 is the shortest.
s+ e < L where s is the shortest link
All other links rotate fully about s.
If the shortest link is the driver,
1 rotates fully about 2.
3 and 4 rotate partially about 1.
If 1 is grounded ,
We have a Slider Crank (RRRP)
with a fully rotating crank (link 2) and a fixed slider 3
s+ e < L where s is the shortest link
All other links rotate fully about s.
If link 4 is grounded.
Neither 1 nor 3 rotate fully about 4.
We have a Slider Rocker (RRRP)
with a partially rotating crank (link 3) and a fixed slider. 4
All these linkages are Grashofian.

8. Grashof’s criteria for Slider Cranks
Consider the other possibility
where 3 is shorter than 2.
2 is the shortest link, 1 is the longest. We substitute in Grashof’s criteria for RRRR linkages.
Shortest + longest < sum of other two
Hence
l3+ l1 < l2+ l4
Or l3+ l1 - l4 < l2
Or l3+ ( l1 - l4 ) < l2
Or l3+ e < l2
Or s + e < L

9. Grashof’s criteria for Slider Cranks
Analyze using same logic as used for RRRR linkages, considering that link 3 is the shortest here. 1 2 3 4
s+ e < L where s is the shortest link
All other links rotate fully about s (link 3) .
If link 3 is grounded,
i.e. shortest link is the ground,
Both 2 and 4 rotate fully about 3, i.e. the ground.
Since link 1 is not grounded ,
We have an Inverted Slider Crank (RRPR)
with a fully rotating crank (link 2) and a fully rotating slider. 5
s+ e < L where s is the shortest link
All other links rotate fully about s (link 3) .
If link 1 is grounded,
i.e. shortest link is the coupler
2 does not rotate fully about 1.
We have a Slider Rocker (RRRP)
with a partially rotating crank (link 2) and a fixed slider. 6

10. Grashof’s criteria for Slider Cranks
Analyze using same logic as used for RRRR linkages, considering that link 3 is the shortest here. 1 2 3 4
s+ e < L where s is the shortest link
All other links rotate fully about s (link 3) .
If link 2 is grounded,
i.e. shortest link (link 3) is the crank,
3 rotates fully about 2, i.e. the ground.
1 rotates partially about 2, i.e. the ground.
We have an Inverted Slider Rocker (RRPR)
with a fully rotating crank and a partially rotating slider. 7
s+ e < L where s is the shortest link
All other links rotate fully about s (link 3) .
If link 4 is grounded,
3 rotates fully about 4, i.e. the ground.
2 does not rotate fully about 4.
We have a Slider Crank (RRRP)
with a fully rotating crank and a fixed slider. 8

11. Grashof’s criteria for Slider Cranks : Summary
s+ e < L where s is the shortest link
Shortest link is Ground
Inverted Slider Crank
with fully rotating crank 1 5
s+ e < L where s is the shortest link
Shortest link is Crank (driver)
Inverted Slider Rocker
with fully rotating crank and partially rotating slider Or
Slider Crank
with fully rotating crank 2 7 8 3
s+ e < L where s is the shortest link
Shortest link is Coupler
Slider Rocker
with a partially rotating crank 4 6
s+ e > L where s is the shortest link
Non Grashofian Slider Rocker
with a partially rotating crank and fixed slider. Or
Non Grashofian Inverted Slider Rocker
with a partially rotating crank
and partially rotating slider.