Inter - Bayamon
Lecture
MECN 4110
1
Mechanisms Design
MECN 4110
Professor: Dr. Omar E. Meza Castillo
omeza@bayamon.inter.edu
http://facultad.bayamon.inter.edu/omeza
Department of Mechanical Engineering
Inter American University of Puerto Rico
Bayamon Campus
Inter - Bayamon
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.
MECN 4110
 Course
Text:
Norton, Robert L., Design of
Machinery: An Introduction to the Synthesis and
Analysis of Mechanisms and Machines, 3rd. Ed.,
McGraw-Hill, 2004.
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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 email 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.
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Syllabus
 Problem-Solving Technique:
A. Known
B. Find
C. Assumptions
D. Schematic
E. Analysis, and
F. 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.
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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.
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Course Grading
 The total course grade is comprised of homework
assignments, quizzes, partial exams, final exam,
and a project as follows:
 Homework
15%
 Quiz
15%
 Laboratory Reports
20%
 Partial Exams
20%
 Final Exam
20%
 Final Project
10%

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.
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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.
 Office Hours: Tuesday and Thursday @ 5:50 to 7:20
PM
 Email: mezacoe@gmail.com
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Tentative Lectures Schedule
Topic
Lecture
Introduction of Mechanism and Kinematics
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1, 2 and 3
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Reference


MECN 4110

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.
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One thing you learn in science is that
there is no perfect answer, no perfect
measure.
A. O. Beckman
Topic 1: Mechanism and
Kinematics
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Introduction and Basic Concepts
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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.
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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.
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 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.
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1.2 DESIGN PROCESS
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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)
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1.4 UNITS
 There are several systems of units used in
engineering. The most common in the
United States are:
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 The U.S. foot-pound-second (fps) system,
 The U.S. inch-pound-second (ips) system,
and
 The System International (SI)
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1.4 UNITS
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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.
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1.5 THE SCIENCE OF MECHANICS
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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.
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1.5 THE SCIENCE OF MECHANICS
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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.
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1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY
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DOF of rigid body in Space
DOF of Rigid body in Plane
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1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY
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1.7 TYPES OF MOTION
 Pure rotation
Reference line
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Reference line
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1.7 TYPES OF MOTION
 Pure translation
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1.7 TYPES OF MOTION
 Complex Motion : Rotation + Translation
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q
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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.
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1.7 LINKS, JONTS AND KINEMATIC CHAINS
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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.
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1.7 LINKS, JONTS AND KINEMATIC CHAINS
 Link of different order:
 Binary link : one of 2 nodes
 Ternary link : one of 3 nodes
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 Quaternary link : one of 4 nodes
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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:
1. By the type of contact between the elements,
line, point or surface.
2. By the number of degrees of freedom allowed
at the joint.
3. By the type of physical closure of the joint:
either force or form closed.
4. By the number of links joined (order of the
joint).
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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.
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 Higher pair (point or line contact): are
the joints with point or line contact
between the pair elements.
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1.8 JOINT PAIRS: THE SIX LOWER PAIRS
 Lower Pair:
Name (symbol)
DOF Contains
Revolute (R)
1
R
Prismatic (P)
1
P
Screw or Helical (H)
1
R+P
Cylindric (C)
2
R+P
Spherical (S)
3
R+R+R
Planar or Flat (F)
3
R+P+P
Planar Mechanism
3-D Mechanism
DOF: Degree of Freedom
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1.8 JOINT PAIRS: THE SIX LOWER PAIRS
 Revolute (R): Rotating full pin joint
Dq
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1.8 JOINT PAIRS: THE SIX LOWER PAIRS
 Prismatic (P): Translating full slider joint
DX
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1.8 JOINT PAIRS: THE SIX LOWER PAIRS
 Helical (H):
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1.8 JOINT PAIRS: THE SIX LOWER PAIRS
 Cylindric (C) :
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1.8 JOINT PAIRS: THE SIX LOWER PAIRS
 Spherical (S):
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1.8 JOINT PAIRS: THE SIX LOWER PAIRS
 Flat (F) :
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1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT
 Roll-slide (Half or RP) joint
Dq
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DX
Linkage against Plane (Force close)
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1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT
 Higher Pair: 2 DOF
DX
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Dq
Pin in Slot (Form Close)
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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
First o
rder pin
join
t
S
econd ordorder
er pin jopin
int joint
Second
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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.
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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:
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 1 link in the plane has 3 DOF
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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
 2 links in the plane have 6 DOF
Dy1
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Dq1
Dy2
Dx1
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Dx2
Dq2
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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
 2 links connected by a full joint have 4 DOF
Dy
Dx
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Dq1
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Dq2
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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
 2 links connected by a roll-slide (half) have
5 DOF
Dq2
Dx1
Dy
Dq1
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Dx2
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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
 Gruebler’s equation
DOF or M = 3L – 2J – 3G
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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
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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
 Kutzbatch’s
equation
modification
of
Gruebler’s
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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
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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY
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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.
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1.12 EXAMPLES
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1.12 EXAMPLES
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1.12 EXAMPLES
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1.12 EXAMPLES
1. Number or links L = 4
2. Number of (full joint) 4 joints J=4
3. Number of ground link G=1
M = 3(4 - 1) – 2x4
M= 1
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1.12 EXAMPLES
1. Number or links L = 9
2. Number of full joints 10 and half joints 2
J=12
3. Number of ground link G=1
M = 3(9 - 1) – 2x12
M= 0
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MECN 4110
Homework1  http://facultad. bayamon.inter.edu/omeza/
Omar E. Meza Castillo Ph.D.
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