1. Sugar Milling Research Institute
Theory of Machines
Dr. Richard C. Loubser
Sugar Milling Research Institute
Contact:

2. Make an appointment before going to SMRI
Important
Make an appointment before going to SMRI
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

3. Lecture 1
Definitions
Degrees of Freedom
Conventions
Angles
Symbols

4. Definitions
Theory of machines: Kinematics and dynamics of multi-body systems
Kinematics: Description of position, velocity and acceleration
Dynamics:
Forward problem: response of system under influence of given forces
Inverse problem: forces required to give specific response

5. Definitions Rigid body Kinematic pair
System of particles where the relative position between particles does not change
Link, element, member
Large motions
Kinematic pair
Two links joined together by a joint
Revolute joint
Slider

6. Definitions
Mechanism: series of links joined together to produce a specific motion
Kinematic chains
Open chains
Closed chains
Machine: assemblage of mechanisms

7. Definitions
Planar mechanism: Mechanism which moves in plane or parallel planes
Spatial mechanism: Mechanism moving in space

8. Coordinate systems Cartesian Generalised [x,y,z]’
[q1, q2, q3, q4, q5,… qN]’

9. Symbols  constraint equation  angle (time dependant)
L length of link (fixed)
S variable distance
   fixed angles

10. Angles Angles are measure counter clockwise from +ve X axis B B q L q
AB=[Lcosq,Lsinq]T A A

11. Degrees of Freedom Y q X
[X,Y,]’
f=3

12. Degrees of Freedom
Pin joint p Y q X
[X,Y,]’
f=3-2

13. Degrees of Freedom
Slider s Y q X
[X,Y,]’
f=3-1=2

14. Degrees of Freedom
Guide g Y q X
[X,Y,]’
f=3-2

15. Four bar mechanism 3 2 4 f=3(n-1)-2p-s-2g 1 n=4 p=4 s=0 g=0

16. Four bar mechanism A 3 B 2 4 C e O d
OA=OC+CB+BA
non-linear

17. Four bar mechanism A 3 B 2 4 C e O d

18. Four bar mechanism A 3 B 2 4 C e O d

19. Grashoff’s Rule A 3 B 2 4 C e O d L+S≤P+Q L=Longest link
S=Shortest Link
P,Q = other links
S is fully rotatable