MECN 4110: Mechanisms Design
Mechanisms Design
MECN 4110
Professor: Dr. Omar E. Meza Castillo
omeza@bayamon.inter.edu
http://facultad.bayamon.inter.edu/omeza
Department of Mechanical Engineering
MSP21
4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
BIENVENIDOS
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4110: Mechanisms
MECN
Design- Bayamón
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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.
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4110: Mechanisms
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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 e-mail 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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4110: Mechanisms
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Syllabus
 Problem-Solving Technique:
A.
B.
C.
D.
E.
F.
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.
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4110: Mechanisms
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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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4110: Mechanisms
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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
10%
 Quiz
15%
 Laboratory Reports
20%
 Partial Exams
20%
 Final Exam
20%
 Final Project
15%

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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4110: Mechanisms
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Course Materials
 Most Course Material (Course Notes, Handouts, Homework,
Final Project, and Communications) on Web Page:
http://facultad.bayamon.inter.edu/omeza/MECN4110a.htm
 Power Point Lectures will posted every week or two via
Edmodo o the web page.
 Office Hours: Tuesday and Thursday @ 10:30 to 12:00 AM
 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
 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
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.
 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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4110: Mechanisms
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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:
 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.
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 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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4110: Mechanisms
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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,
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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
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
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
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
 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.
 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
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DOF: Degree of Freedom
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Planar Mechanism
3-D Mechanism
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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
DX
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Linkage against Plane (Force close)
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1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT
 Higher Pair: 2 DOF
DX
Dq
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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
joint
Firs
t oorder
rder ppin
in jo
int
Seco
nd orderorder
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:
 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
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
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
Dx2
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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
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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
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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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Homework1  http://facultad. bayamon.inter.edu/omeza/
Omar E. Meza Castillo Ph.D.
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GRACIAS
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