1. ME 202 Mechanical Engineering for Civil Engineers
ME 201 Mechanics of Machines
11/22/2018
ME 202 Mechanical Engineering for Civil Engineers
Kinematics of Simple Machines
Asanga Ratnaweera
Dept of Mechanical Engineering

2. ME 201: Mechanics of Machines I
11/22/2018
ME 201: Mechanics of Machines I
Kinematics of Simple Machines
Asanga Ratnaweera
Dept of Mechanical Engineering

3. Kinematics of Simple Machines
What is mechanics:
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

4. Kinematics of Simple Machines
What is Kinematics:
Kinematics deals with the study of motion without the reference to the forces which cause or are developed by the motion.
[Deals with the relative motion between the parts of the machine]
What is Kinetics:
Kinetics deals with the forces that produce motion
[deals with both motion and the forces]
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

5. Kinematics of Simple Machines
What is a machine:
Machines are used to convert energy into different forms and transmit energy. Machines are composed of different types of mechanisms. 
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

6. Kinematics of Simple Machines
Simple mechanisms:
A mechanism is a mechanical device used to transfer motion, force and power from a source to an output.
Ex: cams, gears, and pulleys & belts, Linkages.
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

7. Kinematics of Simple Machines
Link:
A rigid body having two or more pairing elements which connect to other bodies for the purpose of transmitting force or motion
Link
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

8. Kinematics of Simple Machines
Common types of links
Binary link: two nodes
Ternary link: thee nodes
quaternary link: four nodes
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

9. Kinematics of Simple Machines
Kinematic link
A resistant body or an assembly which goes to make a part of a machine connecting other parts which have motion relative to it.
Rigid link
Kinematic link
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

10. Kinematics of Simple Machines
Kinematic chain
A combination of links and pairs without a fixed link.
No element is fixed to the ground or frame
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

11. Kinematics of Simple Machines
Joint
In general called a kinematic pair, providing the connection between links that permit constrained relative motion. There are two types of kinematic pairs: Lower pair, Higher pair.
Joints
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

12. Kinematics of Simple Machines
Lower pair
Have surface contact between the elemental surfaces.
prismatic joints
Revolute (pin) joints
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

13. Kinematics of Simple Machines
Lower pair
Cylindrical joint
Helical joints
Spherical joint
Universal joint
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

14. Kinematics of Simple Machines
Higher pair
Have line and point contact between the pairing elements.
CAM Follower
Gears
Pin and slot
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

15. Kinematics of Simple Machines
Linkages
Refer to kinematic chains joined by only lower pairs.
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

16. Kinematics of Simple Machines
Mechanism
A set of moving parts in a machine that performs a task. Mechanism consists of linkages and joints
Fixed
No fixed link: not a mechanism
Does not perform a task
Mechanisms
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

17. Asanga Ratnaweera, Department of Mechanical Engineering
Linkages
Some examples
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

18. Asanga Ratnaweera, Department of Mechanical Engineering
Linkages
Kinematic (skeleton) diagram
It is used to represent the essential skeleton (structure) of a mechanism, (similar to electrical circuit diagram).
Basic symbols
Lines or simple shapes are used to represent links, which are labeled by numbers.
Circles or blocks are used to represent joints, which are labeled by letters (capital).
The terms such as space diagram and configuration diagram are also used for kinemtaic diagram
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

19. Asanga Ratnaweera, Department of Mechanical Engineering
Linkages
Kinematic (Skeleton) diagram
Fixed A B C 4
Piston 3 2
Connecting rod
Skeleton diagram 1
Crank
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

20. Asanga Ratnaweera, Department of Mechanical Engineering
Linkages
Kinematic (Skeleton) diagram
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

21. Asanga Ratnaweera, Department of Mechanical Engineering
Linkages
Kinematic (Skeleton) diagram
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

22. Asanga Ratnaweera, Department of Mechanical Engineering
Linkages
Kinematic (Skeleton) diagram
Stewart platform
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

23. Asanga Ratnaweera, Department of Mechanical Engineering
Linkages
Degree of Freedom (DOF)
Number of independent movements a rigid body has
In 2D plane
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

24. Asanga Ratnaweera, Department of Mechanical Engineering
Linkages
Degree of freedom
Revolute Joint
1 DOF
(2 DOF restricted)
Slider Joint
1 DOF
(2 DOF restricted)
Pin in slot
2 DOF
(1 DOF restricted)
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

25. Asanga Ratnaweera, Department of Mechanical Engineering
Linkages
Degree of Freedom (DOF) of a linkage
Gruebler’s Equation
where
n : Total number of links (including a fixed or single ground link)
P1 : Total number of lower pairs
P2 : Total number of higher pairs
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

26. Asanga Ratnaweera, Department of Mechanical Engineering
Linkages
Degree of Freedom (DOF) of a linkage
Ex: three bar linkage
Ex: Four bar linkage A B C D
n = 4
P1 = 4
P2 = 0
DOF = 1 B C A
Ex: Five bar linkage A B C D E
n = 5
P1 = 5
P2 = 0
DOF = 2
n = 3
P1 = 3
P2 = 0
DOF = 0
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

27. Asanga Ratnaweera, Department of Mechanical Engineering
Four bar mechanism
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

28. Asanga Ratnaweera, Department of Mechanical Engineering
Four bar linkages
Slider crank mechanism
Fixed A B C 4
Piston 3
Frame 2
Connecting rod 1
Crank
This is a four bar mechanism
Skeleton diagram
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

29. Asanga Ratnaweera, Department of Mechanical Engineering
Four bar linkages
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

30. Asanga Ratnaweera, Department of Mechanical Engineering
Four bar linkages
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

31. Asanga Ratnaweera, Department of Mechanical Engineering
Four bar linkages
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

32. Asanga Ratnaweera, Department of Mechanical Engineering
Four bar linkages
Linkage geometry
Class I :
Shortest member can complete a full revolution
Class II :
No link can make a full revolution
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

33. Asanga Ratnaweera, Department of Mechanical Engineering
Four bar linkages
Linkage geometry
Class I: a – b < c – d
Class II: a – b > c – d a c d b
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering

34. Kinematic Analysis of Mechanisms
Analytical methods
Difficult when the motion is complicated
Graphical Methods
Major concern of this course
Computer methods
Beyond the scope
22 November 2018
Asanga Ratnaweera, Department of Mechanical Engineering