1. MENG 372 Mechanical Systems Spring 2011
Dr. Mustafa Arafa
American University in Cairo
Mechanical Engineering Department

2. Course Information Course goals: Analyze & design planar mechanisms
Analyze forces, velocities & accelerations in machines
Use computers for the above
Textbook: Design of Machinery, R.Norton, McGraw-Hill, 3rd ed., 2004.
Computer usage: Working Model, MATLAB
Grading: attendance 5%; homework 10%; quizzes 5%; mid-term exams 30%; projects 25%; final exam 25%
Lecture notes: will be posted my website. I will communicate with you on BlackBoard. Additional material will also be covered on the board. Please print out the notes beforehand & bring them to class.

3. MENG 372 Chapter 2 Kinematics Fundamentals
All figures taken from Design of Machinery, 3rd ed. Robert Norton 2003

4. 2.1 Degrees of Freedom (DOF) or Mobility
DOF: Number of independent parameters (measurements) needed to uniquely define position of a system in space at any instant of time.
Rigid body in a plane has 3 DOF: x,y,q
Rigid body in space has 6 DOF (3 translations & 3 rotations)

5. 2.2 Types of Motion
Pure rotation: the body possesses one point (center of rotation) that has no motion with respect to the “stationary” frame of reference. All other points move in circular arcs.
Pure translation: all points on the body describe parallel (curvilinear or rectilinear) paths.
Complex motion: a simultaneous combination of rotation and translation.

6. Backhoe Excavator

7. Slider-Crank Mechanism

8. 2.3 Links, joints, and kinematic chains
Links: rigid member having nodes
Node: attachment points
Binary link: 2 nodes
Ternary link: 3 nodes
Quaternary link: 4 nodes
Joint: connection between two or more links (at their nodes) which allows motion
Classified by type of contact, number of DOF, type of physical closure, or number of links joined

9. Joint Classification Type of contact: line, point, surface
Number of DOF: full joint=1DOF, half joint=2DOF
Form closed (closed by geometry) or Force closed (needs an external force to keep it closed)
Joint order = number of links-1

10. Types of joints

11. Kinematic chains, mechanisms, machines, link classification
Kinematic chain: links joined together for motion
Mechanism: grounded kinematic chain
Machine: mechanism designed to do work
Link classification:
Ground: fixed w.r.t. reference frame
Crank: pivoted to ground, makes complete revolutions
Rocker: pivoted to ground, has oscillatory motion
Coupler: link has complex motion, not attached to ground

12. Determining Degrees of Freedom
For simple mechanisms calculating DOF is simple
Open Mechanism
DOF=3
Closed Mechanism
DOF=1

13. Determining Degrees of Freedom
Two unconnected links: 6 DOF
(each link has 3 DOF)
When connected by a full joint: 4 DOF
(each full joint eliminates 2 DOF)
Gruebler’s equation for planar mechanisms: DOF = 3L-2J-3G
Where:
L: number of links
J: number of full joints
G: number of grounded links

14. 2.4 Determining DOF’s Gruebler’s equation for planar mechanisms
M=3L-2J-3G
Where
M = degree of freedom or mobility
L = number of links
J = number of full joints (half joints count as 0.5)
G = number of grounded links =1

15. Example

16. Example

17. 2.5 Mechanisms and Structures
Mechanism: DOF>0
Structure: DOF=0
Preloaded Structure – DOF<0, may require force to assemble

18. 2.7 Paradoxes
Greubler criterion does not include geometry, so it can give wrong prediction
We must use inspection
E-quintet

19. 2.10 Intermittent Motion Series of Motions and Dwells
Dwell: no output motion with input motion
Examples: Geneva Mechanism, Linear Geneva Mechanism, Ratchet and Pawl

20. Geneva Mechanism

21. Linear Geneva Mechanism

22. Ratchet and Pawl

23. Fourbar Mechanism 1 -1
Twobar has -1 degrees of freedom (preloads structure)
Threebar has 0 degrees of freedom (structure)
Fourbar has 1 degree of freedom
The fourbar linkage is the simplest possible pin-jointed mechanism for single degree of freedom controlled motion

24. 4-Bar Nomenclature Ground Link Links pivoted to ground: Coupler Crank
Rocker
Coupler
Link 3, length b B
Coupler
Link 4, length c A
Link 2, length a
Rocker
Crank
Link 1, length d
Ground Link
Pivot 02
Pivot 04

25. Where would you see 4-bar mechanisms?

26. Sheet Metal Shear (Mechanical Workshop)

27. Sheet Metal Shear (Mechanical Workshop)

28. Door Mechanism (ACMV Lab)

29. Door Mechanism (ACMV Lab)

30. Backhoe Excavator

31. Brake of a Wheelchair
Folding sofa

32. Honda Accord trunk
Chevy Cobalt
Garage door
Desk Lamp

33. Inversions Created by attaching different links to ground
Different behavior for different inversions

34. Inversions of a 4-Bar Mechanism
Crank-rocker
Crank-rocker
Crank-crank
Rocker-rocker

35. 2.12 The Grashof Condition
Grashof condition predicts behavior of linkage based only on length of links
S=length of shortest link
L=length of longest link
P,Q=length of two remaining links
If S+L ≤ P+Q the linkage is Grashof :at least one link is capable of making a complete revolution
Otherwise the linkage is non-Grashof : no link is capable of making a complete revolution

36. For S+L<P+Q
Crank-rocker if either link adjacent to shortest is grounded
Double crank if shortest link is grounded
Double rocker if link opposite to shortest is grounded

37. For S+L>P+Q All inversions will be double rockers
No link can fully rotate

38. For S+L=P+Q (Special case Grashof)
All inversions will be double cranks or crank rockers
Linkage can form parallelogram or antiparallelogram
Often used to keep coupler parallel (drafting machine)
Parallelogram form
Deltoid form
Anti parallelogram form

39. Problems with Special Grashof
All inversions have change points twice per revolution of input crank when all links become collinear
Behavior at change points is indeterminate
If used in continuous machine, must have some mechanism to “carry through”

40. 2.13 Linkages of more than 4 bars
5-bar 2DOF
Geared 5-bar 1DOF
Provide more complex motion
See Watt’s sixbar and Stephenson’s sixbar mechanisms in the textbook

41. Linkages of more than 4 bars
Volvo 740 Hood

42. Volvo 740 Hood

43. Animation using Working Model ®

44. Cabinet Hinge

45. 2.15 Compliant Mechanisms
Compliant “link” capable of significant deflection acts like a joint
Also called a “living hinge”
Advantage: simplicity, no assembly, little friction

46. More Examples: Front End Loader

47. Drum Brake