1. Mechanisms Design MECN 4110
Professor: Dr. Omar E. Meza Castillo
Department of Mechanical Engineering

2. BIENVENIDOS

3. Syllabus
Catalog Description: Analysis of mobility and kinematics of mechanisms. Application of the graphical and computerized techniques of position analysis, speed, and acceleration in mechanisms. Design of levies and gears. Introduction to the synthesis of mechanisms.
Prerequisites: ENGR 2220 – Computerized Engineering Graphics, MECN 3120 – Vector Mechanics for Engineers: Dynamics.
Course Text: Norton, Robert L., Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines, 3rd. Ed., McGraw-Hill, 2004.

4. Syllabus
Absences: On those days when you will be absent, find a friend or an acquaintance to take notes for you or visit the web page. Do not call or send an the instructor and ask what went on in class, and what the homework assignment is.
Homework assignments: Homework problems will be assigned on a regular basis. Problems will be solved using the Problem-Solving Technique on any white paper with no more than one problem written on one sheet of paper. Homework will be collected when due, with your name written legibly on the front of the title page. It is graded on a 0 to 100 points scale. Late homework (any reason) will not be accepted.

5. Problem-Solving Technique:
Syllabus
Problem-Solving Technique:
Known
Find
Assumptions
Schematic
Analysis, and
Results
Quiz : There are several partial quizzes during the semester.
Partial Exams and Final Exam: There are three partial exams during the semester, and a final exam at the end of the semester.

6. Syllabus
Laboratory Reports: There seven or eight experimental laboratories throughout the semester. Laboratory reports must be submitted by each group, one week after the experiment is done. The report must be written in English, in a professional format.
Final Project: There is a final project, it will consist in the design of a mechanism with application of course knowledge.

7. Course Grading
The total course grade is comprised of homework assignments, quizzes, partial exams, final exam, and a project as follows:
Homework %
Quiz %
Laboratory Reports 20%
Partial Exams %
Final Exam %
Final Project %
100%
Cheating: You are allowed to cooperate on homework by sharing ideas and methods. Copying will not be tolerated. Submitted work copied from others will be considered academic misconduct and will get no points.

8. Course Materials
Most Course Material (Course Notes, Handouts, Homework, Final Project, and Communications) on Web Page:
Power Point Lectures will posted every week or two via Edmodo o the web page.
Office Hours: Tuesday and 10:30 to 12:00 AM

9. Tentative Lectures Schedule
Topic
Lecture
Introduction of Mechanism and Kinematics
1, 2 and 3

10. Reference
Myska, David H. Machines & Mechanisms: applied kinematic analysis, 2nd Ed., Prentice Hall, 2002
Sandor, G. N., and Erdman A. G., Mechanism Design: Analysis and Synthesis, 4th. Ed., Prentice Hall, 2001
Waldron, Kenneth J. and Kinzel, Gary L., Kinematics, Dynamics, and Design of Machinery, John Wiley & Sons, Inc, 2004.

11. Introduction and Basic Concepts
One thing you learn in science is that there is no perfect answer, no perfect measure.
A. O. Beckman
Topic 1: Mechanism and Kinematics
Introduction and Basic Concepts

12. Up on completion of this chapter, the student will be able to
Course Objectives
Up on completion of this chapter, the student will be able to
Explain the need for kinematic analysis of mechanism.
Define the basic components that comprise a mechanism.
Draw the kinematic diagram from a view of a complex mechanism.
Compute the number of degrees of freedom of a mechanism.
Identify a four bar mechanism and classify it according to its possible motion.
Identify a slider crank mechanism.

13. 1.1 ANALYSIS AND SYSTHESIS
Analysis: the techniques that allow the designer to critically examine an already existing or proposed design in order to judge its suitability for task.
Synthesis (or Design): the process of prescribing the sizes, shapes, material compositions, and arrangements of parts so that the resulting machine will perform the prescribed task.

14. 1.2 DESIGN PROCESS

15. 1.3 THE ENGINEERING REPORT
LAB REPORT GUIDE
Title Page of Lab Report (2)
Table of Contents (3)
Abstract (5)
Objectives and Introduction (15)
Theory (15)
Result and Discussion (35)
Conclusions (15)
References (10)

16. The U.S. foot-pound-second (fps) system,
1.4 UNITS
There are several systems of units used in engineering. The most common in the United States are:
The U.S. foot-pound-second (fps) system,
The U.S. inch-pound-second (ips) system, and
The System International (SI)

17. 1.4 UNITS

18. 1.5 THE SCIENCE OF MECHANICS
Statics: deals with analysis of stationary systems, that is, those in which time is not a factor.
Dynamics: deals with systems that change with time.
Kinematics: the study of motion, quite apart from the forces which produce that motion. More particularly kinematics is the study of position, displacement rotation, speed, velocity, and acceleration.
Kinetics: the study of force on system in motion.

19. 1.5 THE SCIENCE OF MECHANICS

20. 1.5 THE SCIENCE OF MECHANICS
Reuleaux’ Definition:
Machine: a combination of resistant bodies so arranged that their means the mechanical forces of nature can be compelled to do work accompanied by certain determinate motion.
Mechanism: an assemblage of resistant bodies, connected by movable joints, to form a closed kinematic chain with one link fixed and having the purpose of transforming motion.
Structure: also a combination of resistant bodies connected by joints, but its purpose is not to d work or to transform motion. A structure is intended to be rigid.

21. 1.5 THE SCIENCE OF MECHANICS

22. 1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY
A mechanical system’s mobility (M) can be classified according to the number of degrees of freedom (DOF) that it possesses. The system’s DOF is equal to the number of independent parameters (measurements) that are needed uniquely define its position in space and at any instant of time.
This system of the pencil in the plane has three DOF
The pencil in the this example represents a rigid body, or link, which for purposes of kinematics analysis we will assume to be incapable of deformation.

23. 1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY
DOF of rigid body in Space DOF of Rigid body in Plane

24. 1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY

25. 1.7 TYPES OF MOTION
Pure rotation
Reference line
Reference line

26. 1.7 TYPES OF MOTION
Pure translation

27. Complex Motion : Rotation + Translation
1.7 TYPES OF MOTION
Complex Motion : Rotation + Translation

28. 1.7 LINKS, JONTS AND KINEMATIC CHAINS
Linkages are the basic building blocks of all mechanisms. A linkage consist of links (or bars), generally considered rigid, which are connected by joints, such as pins (or revolutes), or prismatic joints to form open or closed chains (or loops). Such kinematic chains, with at least one link fixed, become (1) mechanisms if at least two other links retain mobility, or (2) structures if no mobility remains.

29. 1.7 LINKS, JONTS AND KINEMATIC CHAINS

30. 1.7 LINKS, JONTS AND KINEMATIC CHAINS
A link is an rigid body that possesses at least two nodes that are points for attachment to other links.

31. 1.7 LINKS, JONTS AND KINEMATIC CHAINS
Link of different order:
Binary link: one of 2 nodes
Ternary link: one of 3 nodes
Quaternary link: one of 4 nodes

32. 1.7 LINKS, JONTS AND KINEMATIC CHAINS
A joint is an connection between two or more links (at their nodes), which allows some motion, or potential motion, between the connected links. Joints (also called kinematic pairs) can be classified in several ways:
By the type of contact between the elements, line, point or surface.
By the number of degrees of freedom allowed at the joint.
By the type of physical closure of the joint: either force or form closed.
By the number of links joined (order of the joint).

33. 1.7 LINKS, JONTS AND KINEMATIC CHAINS
The kinematic pairs can be:
Lower pair (surface contact): are the joints with surface contact between the pair elements.
Higher pair (point or line contact): are the joints with point or line contact between the pair elements.

34. 1.8 JOINT PAIRS: THE SIX LOWER PAIRS
Name (symbol)
DOF
Contains
Revolute (R) 1 R
Prismatic (P) P
Screw or Helical (H)
R + P
Cylindric (C) 2
R+P
Spherical (S) 3
R+R+R
Planar or Flat (F)
R+P+P
Planar Mechanism
3-D Mechanism
DOF: Degree of Freedom

35. 1.8 JOINT PAIRS: THE SIX LOWER PAIRS
Revolute (R): Rotating full pin joint

36. 1.8 JOINT PAIRS: THE SIX LOWER PAIRS
Prismatic (P): Translating full slider joint

37. 1.8 JOINT PAIRS: THE SIX LOWER PAIRS
Helical (H):

38. 1.8 JOINT PAIRS: THE SIX LOWER PAIRS
Cylindric (C):

39. 1.8 JOINT PAIRS: THE SIX LOWER PAIRS
Spherical (S):

40. 1.8 JOINT PAIRS: THE SIX LOWER PAIRS
Flat (F):

41. 1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT
Roll-slide (Half or RP) joint:
Linkage against Plane (Force close)

42. 1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT
Higher Pair: 2 DOF
Pin in Slot (Form Close)

43. Lower pair or Full joint : 1 DOF joint
1.9 PLANAR MOTION
Lower pair or Full joint : 1 DOF joint
Higher pair, half joint : > 1 DOF, roll-slider
Joint order = number of link joined - 1
First order pin joint
Second order pin joint

44. CRANK: Link that makes a complete revolution and is pivoted to ground.
1.9 PLANAR MOTION
KINEMATIC CHAIN: An assemblage of links and joints, interconnected in a way to provide a controlled output motion in response to a supplied input motion.
CRANK: Link that makes a complete revolution and is pivoted to ground.
ROCKET: Link that has oscillatory (back and forth) rotation and is pivoted to ground.
COUPLER (or connecting rod): Link that has complex motion and is not pivoted to ground.
GROUND: defined as any link or links that are fixed (nonmoving) with respect to the reference frame.

45. 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
Degree of Freedom (DOF): Number or inputs that need to be provided in order o create a predictable output. Also: number of independent coordinates required to define its position.
In Planar Mechanisms:
1 link in the plane has 3 DOF

46. 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
2 links in the plane have 6 DOF

47. 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
2 links connected by a full joint have 4 DOF

48. 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
2 links connected by a roll-slide (half) have 5 DOF

49. 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
Gruebler’s equation
DOF or M = 3L – 2J – 3G
Where:
M=degree of freedom or mobility
L= number of links
J=number of joints
G=number of grounded links (always 1)
M = 3(L - 1) – 2J

50. 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
Kutzbatch’s modification of Gruebler’s equation
M = 3(L – 1)– 2J1 – J2
Where:
M= degree of freedom or mobility
L= number of links
J1= number of DOF (full) joints
J2= number of DOF (half) joints
Full Joint = 1
Half Joint = 0.5

51. 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

52. 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

53. 1.11 MECHANISMS AND STRUCTURES
If the DOF is positive, it will be a mechanism, and the links will have relative motion. If the DOF is exactly zero, then it will be a structure, and no motion is possible. If the DOF is negative, then it is a preloaded structure, which means that no motion is possible and some stresses may also be present at the time of assembly.

54. Application Problems

55. 1.12 EXAMPLES

56. 1.12 EXAMPLES

57. 1.12 EXAMPLES

58. Number of (full joint) 4 joints J=4 Number of ground link G=1
1.12 EXAMPLES
Number or links L = 4
Number of (full joint) 4 joints J=4
Number of ground link G=1
M = 3(4 - 1) – 2x4
M = 1

59. Number of full joints 10 and half joints 2 J=12
1.12 EXAMPLES
Number or links L = 9
Number of full joints 10 and half joints 2 J=12
Number of ground link G=1
M = 3(9 - 1) – 2x12
M = 0

60. Homework1  http://facultad. bayamon.inter.edu/omeza/
Omar E. Meza Castillo Ph.D.

61. ¿Preguntas? Comentarios

62. GRACIAS