1. THOERY OF MECHANISMS AND MACHINES
Module-12
STATIC AND DYNAMIC BALANCING
4 BAR LINKAGES AND IC ENGINES
Instructed by:
Dr. Anupam Saxena
Associate Professor
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
FB 361
Prepared by:
Abhishek Attal & Abhishek Sharma
Final Year Dual Degree Student
Department of Mechanical Engineering
Indian Institute of Technology Kanpur
NL312, FB369

2. Balance of Multi-Cylinder EnginespA f x Q H V T Q pA N
Crank rotates with constant speed

3. Balance of Multi-Cylinder EnginesV pA H N Q H V T
Net unbalanced force is the
Horizontal force on the frame
pA - H Q pA N
This will be transferred to the
Foundation via the crank...

4. Balance of Single Cylinder Enginesx y
q = t r l f m a + m 2 m co m cr m b + m s m 1

5. Balance of Single Cylinder Enginesm a + m 2 l m b + m s m 1 r
q = t f x x

6. Balance of Multi-Cylinder Engines
What if we place another identical second
system to drive the same crank shaft y
We place the system smartly... m a + m 2 r l m b + m s m 1 + m 1 q m b s + x r x l m 2 + m a
Two centripetal forces get balanced out
Two reciprocatory inertial forces may or may not

7. Balance of Multi-Cylinder Engines
What if we place another identical second
system to drive the same crank shaft y
We place the system smartly... m a + m 2 r l m b + m s m 1 + m 1 q m b s + x r x l m 2 + m a
Two centripetal forces get balanced out
Two reciprocatory inertial forces may or may not

8. Balance of Multi-Cylinder Engines
What if we place TWO EXTRA PAIRS of the
same system ? y
Again, we place the systems smartly... r r l l q x r l r l x F R2 F R1 F R3 F R4 F R1 = F R2 = F R3 = F R4 =
Do these forces balance out?

9. Balance of Multi-Cylinder Engines
Another way of looking at the force balance... y
Primary components r r q r r x
Primary forces balance and so do their
components

10. Balance of Multi-Cylinder Engines
Another way of looking at the force balance... y
Secondary components 2q x
Secondary forces balance and so do their
components F R1 = F R2 = F R3 = F R4 =

11. Balance of Multi-Cylinder Engines
How about moments ? y
All axes PARALLEL 1
All single cylinder systems
IDENTICAL 2 r r l l
Distances between axes the
same q x r l r l x F R2 F R1 F R3 4 F R4 3 1 a 2
INLNE SYSTEM a 3 a 4

12. Balance of Multi-Cylinder Engines
How about moments ? y
All axes PARALLEL 1
All single cylinder systems
IDENTICAL 2 r r l l
Distances between axes the
same q x r l r l x F R2 F R1 F R3 4 F R4 3 1 F R1 a 2 F R2 a
INLNE SYSTEM 3 F R3 a 4 F R4

13. Balance of Multi-Cylinder Engines

14. Balance of Multi-Cylinder Engines

15. Balance of Multi-Cylinder Engines

16. Balance of Multi-Cylinder Engines
Firing in TWO STROKE cycle y
n: number of cylinders 1 2 r r l l q x r l r l x F R2 F R1 F R3 O 4 F R4 3 z 1 F R1 a 2 F R2 a 3 F R3 a 4 F R4

17. Balance of Multi-Cylinder Engines
Firing in FOUR STROKE cycle y
n: number of cylinders 1 2 r r l l q x r l r l x F R2 F R1 F R3 O 4 F R4 3 z 1 F R1 a 2 F R2 a 3 F R3 a 4 F R4

18. Balance of Multi-Cylinder Engines
Consider moment about CENTERLINE...
Consider 2 stroke cycle and firing order as y 1 2 r r l
Unbalanced and NON zero l q x r l r l x F R2
Pitching moment F R1 F R3 O 4 F R4 3 z 1 F R1 a 2 F R2 a 3 F R3 a 4 F R4

19. Balance of Multi-Cylinder Engines
What stops us from reshuffling the cylinders? ... y 1 2 r r l l q x r l r l x F R2 F R1 F R3 O 4 F R4 3 z 1 F R1 a F R2 2 a 3 F R3 a F R4 4

20. Balance of Multi-Cylinder Engines
What stops us from reshuffling the cylinders? ...
Consider 2 stroke cycle... y 1 2
Unbalanced and NON zero r r l
But lower than previous case? l q x r l r l x F R2 F R1 F R3 O 4 F R4 3 z 1 F R1 a F R4 4 a 3 F R3 a F R2 2