mecn 4110 - mechanisms design - fall 2012_lecture 01

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LectureLecture

11Mechanisms DesignMechanisms Design

MECN 4110 MECN 4110

Professor: Dr. Omar E. Meza CastilloProfessor: Dr. Omar E. Meza [email protected]

http://facultad.bayamon.inter.edu/omezaDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringInter American University of Puerto RicoInter American University of Puerto Rico

Bayamon CampusBayamon Campus

mailto:[email protected]

http://www.bc.inter.edu/facultad/omeza

Lecture 1Lecture 1MEC

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Catalog DescriptionCatalog Description: : Analysis of mobility and Analysis of mobility and kinematics of mechanisms. Application of the kinematics of mechanisms. Application of the graphical and computerized techniques of position graphical and computerized techniques of position analysis, speed, and acceleration in mechanisms. analysis, speed, and acceleration in mechanisms. Design of levies and gears. Introduction to the Design of levies and gears. Introduction to the synthesis of mechanismssynthesis of mechanisms..

Prerequisites: Prerequisites: ENGR 2220 – Computerized ENGR 2220 – Computerized Engineering Graphics, MECN 3120 – Vector Engineering Graphics, MECN 3120 – Vector Mechanics for Engineers: Dynamics.Mechanics for Engineers: Dynamics.

Course Text: Course Text: Norton, Robert L., Norton, Robert L., Design of Design of Machinery: An Introduction to the Synthesis and Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and MachinesAnalysis of Mechanisms and Machines, 3, 3rdrd. Ed., . Ed., McGraw-Hill, 2004.McGraw-Hill, 2004.

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SyllabusSyllabus


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Absences:Absences: On those days when you will be absent, On those days when you will be absent, find a friend or an acquaintance to take notes for find a friend or an acquaintance to take notes for you or visit the web page. you or visit the web page. Do not call or send an Do not call or send an e-mail the instructor and ask what went on in e-mail the instructor and ask what went on in class, and what the homework assignment is.class, and what the homework assignment is.

Homework assignments:Homework assignments: Homework problems will Homework problems will be assigned on a regular basis. Problems will be be assigned on a regular basis. Problems will be solved using the Problem-Solving Technique on solved using the Problem-Solving Technique on any white paper with no more than one problem any white paper with no more than one problem written on one sheet of paper. Homework will be written on one sheet of paper. Homework will be collected when due, with your name written collected when due, with your name written legibly on the front of the title page. It is graded legibly on the front of the title page. It is graded on a 0 to 100 points scale. Late homework (any on a 0 to 100 points scale. Late homework (any reason) reason) will not be acceptedwill not be accepted..

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Problem-Solving Technique:Problem-Solving Technique:A.A. KnownKnownB.B. FindFindC.C. AssumptionsAssumptionsD.D. SchematicSchematicE.E. Analysis, andAnalysis, andF.F. ResultsResults

Quiz : Quiz : There are several partial quizzes during the There are several partial quizzes during the semester.semester.

Partial Exams and Final Exam: Partial Exams and Final Exam: There are three There are three partial exams during the semester, and a final partial exams during the semester, and a final exam at the end of the semester.exam at the end of the semester.

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Laboratory Reports: Laboratory Reports: There seven or eight There seven or eight experimental laboratories throughout the experimental laboratories throughout the semester. Laboratory reports must be submitted semester. Laboratory reports must be submitted by each group, one week after the experiment is by each group, one week after the experiment is done. The report must be written in English, in a done. The report must be written in English, in a professional format.professional format.

Final Project: Final Project: There is a final project, it will consist There is a final project, it will consist in the design of a mechanism with application of in the design of a mechanism with application of course knowledge. course knowledge.

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The total course grade is comprised of homework The total course grade is comprised of homework assignments, quizzes, partial exams, final exam, and assignments, quizzes, partial exams, final exam, and a project as follows:a project as follows: HomeworkHomework 15%15% QuizQuiz 15%15% Laboratory ReportsLaboratory Reports 20%20% Partial ExamsPartial Exams 20%20% Final ExamFinal Exam 20%20% Final ProjectFinal Project10%10% 100%100%

Cheating: Cheating: You are allowed to cooperate on You are allowed to cooperate on homework by sharing ideas and methods. Copying homework by sharing ideas and methods. Copying will not be tolerated. Submitted work copied from will not be tolerated. Submitted work copied from others will be considered academic misconduct and others will be considered academic misconduct and will get no pointswill get no points..

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Most Course Material (Course Notes, Handouts, Most Course Material (Course Notes, Handouts, Homework, Final Project, and Communications) on Homework, Final Project, and Communications) on Web PageWeb Page

Power Point Lectures will posted every week or Power Point Lectures will posted every week or two.two.

Office Hours: Tuesday and Thursday @ 5:50 to 7:20 Office Hours: Tuesday and Thursday @ 5:50 to 7:20 PMPM

Email: Email: [email protected]

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Course MaterialsCourse Materials

mailto:[email protected]


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Tentative Lectures ScheduleTentative Lectures Schedule

TopicTopic LectureLectureIntroduction of Mechanism and KinematicsIntroduction of Mechanism and Kinematics 1, 2 and 31, 2 and 3


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ReferenceReference

Myska, David H. Myska, David H. Machines & Mechanisms: applied Machines & Mechanisms: applied kinematic analysiskinematic analysis, 2, 2ndnd Ed., Prentice Hall, 2002 Ed., Prentice Hall, 2002

Sandor, G. N., and Erdman A. G., Sandor, G. N., and Erdman A. G., Mechanism Design: Mechanism Design: Analysis and SynthesisAnalysis and Synthesis, 4, 4thth. Ed., Prentice Hall, 2001. Ed., Prentice Hall, 2001

Waldron, Kenneth J. and Kinzel, Gary L., Waldron, Kenneth J. and Kinzel, Gary L., Kinematics, Kinematics, Dynamics, and Design of MachineryDynamics, and Design of Machinery, John Wiley & Sons, , John Wiley & Sons, Inc, 2004.Inc, 2004.


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Introduction and Basic ConceptsIntroduction and Basic Concepts

Topic 1: Mechanism and Topic 1: Mechanism and KinematicsKinematics

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One thing you learn in science is that One thing you learn in science is that there is no perfect answer, no perfect there is no perfect answer, no perfect measure.measure.

A. O. BeckmanA. O. Beckman


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Up on completion of this chapter, the Up on completion of this chapter, the student will be able tostudent will be able to Explain the need for kinematic analysis of Explain the need for kinematic analysis of

mechanism.mechanism. Define the basic components that comprise a Define the basic components that comprise a

mechanism.mechanism. Draw the kinematic diagram from a view of a Draw the kinematic diagram from a view of a

complex mechanism.complex mechanism. Compute the number of degrees of freedom of Compute the number of degrees of freedom of

a mechanism.a mechanism. Identify a four bar mechanism and classify it Identify a four bar mechanism and classify it

according to its possible motion.according to its possible motion. Identify a slider crank mechanism.Identify a slider crank mechanism.

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mon 1.1 ANALYSIS AND SYSTHESIS1.1 ANALYSIS AND SYSTHESIS

Analysis:Analysis: the techniques that allow the the techniques that allow the designer to critically examine an already designer to critically examine an already existing or proposed design in order to existing or proposed design in order to judge its suitability for task.judge its suitability for task.

Synthesis (or Design): Synthesis (or Design): the process of the process of prescribing the sizes, shapes, material prescribing the sizes, shapes, material compositions, and arrangements of parts compositions, and arrangements of parts so that the resulting machine will perform so that the resulting machine will perform the prescribed task.the prescribed task.

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mon 1.2 DESIGN PROCESS1.2 DESIGN PROCESS

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mon 1.3 THE ENGINEERING REPORT1.3 THE ENGINEERING REPORT

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

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mon 1.4 UNITS1.4 UNITS

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

andand The System International (SI)The System International (SI)

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mon 1.5 THE SCIENCE OF MECHANICS1.5 THE SCIENCE OF MECHANICS

Statics: Statics: deals with analysis of stationary deals with analysis of stationary systems, that is, those in which time is not systems, that is, those in which time is not a factor.a factor.

Dynamics: Dynamics: deals with systems that change deals with systems that change with time.with time.

Kinematics: Kinematics: the study of motion, quite the study of motion, quite apart from the forces which produce that apart from the forces which produce that motion. More particularly kinematics is motion. More particularly kinematics is the study of position, displacement the study of position, displacement rotation, speed, velocity, and acceleration.rotation, speed, velocity, and acceleration.

Kinetics: Kinetics: the study of force on system in the study of force on system in motion.motion.

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Reuleaux’ Definition:Reuleaux’ Definition: Machine:Machine: a combination of resistant bodies so a combination of resistant bodies so

arranged that their means the mechanical arranged that their means the mechanical forces of nature can be compelled to do work forces of nature can be compelled to do work accompanied by certain determinate motion.accompanied by certain determinate motion.

Mechanism: Mechanism: an assemblage of resistant bodies, an assemblage of resistant bodies, connected by movable joints, to form a closed connected by movable joints, to form a closed kinematic chain with one link fixed and having kinematic chain with one link fixed and having the purpose of transforming motion.the purpose of transforming motion.

Structure: Structure: also a combination of resistant also a combination of resistant bodies connected by joints, but its purpose is bodies connected by joints, but its purpose is not to d work or to transform motion. A not to d work or to transform motion. A structure is intended to be rigid.structure is intended to be rigid.


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mon 1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY

A mechanical system’s A mechanical system’s mobility (M)mobility (M) can be can be classified according to the number of degrees of classified according to the number of degrees of freedom (DOF) that it possesses. The system’s freedom (DOF) that it possesses. The system’s DOF is equal to the DOF is equal to the number of independent number of independent parameters (measurements) that are needed parameters (measurements) that are needed uniquely define its position in space and at any uniquely define its position in space and at any instant of timeinstant of time. .

This system of the pencil in the plane has three This system of the pencil in the plane has three DOFDOF

The pencil in the this example represents a rigid The pencil in the this example represents a rigid body, or link, which for purposes of kinematics body, or link, which for purposes of kinematics analysis we will assume to be incapable of analysis we will assume to be incapable of deformation.deformation.

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DOF of rigid body in SpaceDOF of rigid body in Space DOF of Rigid body in DOF of Rigid body in PlanePlane


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mon 1.7 TYPES OF MOTION1.7 TYPES OF MOTION

Pure rotationPure rotation

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Reference line

Reference line


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Pure translationPure translation

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Complex Motion : Complex Motion : Rotation + TranslationRotation + Translation

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q


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mon 1.7 LINKS, JONTS AND KINEMATIC CHAINS1.7 LINKS, JONTS AND KINEMATIC CHAINS

LinkagesLinkages are the basic building blocks of are the basic building blocks of all mechanisms. A all mechanisms. A linkagelinkage consist of links consist of links (or bars), generally considered rigid, (or bars), generally considered rigid, which are connected by joints, such as which are connected by joints, such as pins (or revolutes), or prismatic joints to pins (or revolutes), or prismatic joints to form open or closed chains (or loops). form open or closed chains (or loops). Such Such kinematic chainskinematic chains, with at least one , with at least one link fixed, become (1) link fixed, become (1) mechanismsmechanisms if at if at least two other links retain mobility, or (2) least two other links retain mobility, or (2) structuresstructures if no mobility remains. if no mobility remains.

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A A linklink is an rigid body that possesses at is an rigid body that possesses at least two nodes that are points for least two nodes that are points for attachment to other links.attachment to other links.

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Link of different order:Link of different order:

Binary link : one of 2 nodesBinary link : one of 2 nodes

Ternary link : one of 3 nodesTernary link : one of 3 nodes

Quaternary link : one of 4 nodesQuaternary link : one of 4 nodes

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A A jointjoint is an connection between two or is an connection between two or more links (at their nodes), which allows more links (at their nodes), which allows some motion, or potential motion, some motion, or potential motion, between the connected links. Joints (between the connected links. Joints (also also called kinematic pairscalled kinematic pairs) can be classified in ) can be classified in several ways:several ways:1.1. By the type of contact between the elements, By the type of contact between the elements,

line, point or surface.line, point or surface.2.2. By the number of degrees of freedom allowed By the number of degrees of freedom allowed

at the joint.at the joint.3.3. By the type of physical closure of the joint: By the type of physical closure of the joint:

either force or form closed.either force or form closed.4.4. By the number of links joined (order of the By the number of links joined (order of the

joint).joint).

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The kinematic pairs can be:The kinematic pairs can be:

Lower pairLower pair (surface contact): are the (surface contact): are the joints with surface contact between the joints with surface contact between the pair elements.pair elements.

Higher pair Higher pair (point or line contact): are (point or line contact): are the joints with point or line contact the joints with point or line contact between the pair elements.between the pair elements.

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mon 1.8 JOINT PAIRS: THE SIX LOWER PAIRS1.8 JOINT PAIRS: THE SIX LOWER PAIRS

Lower Pair:Lower Pair:

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3-D Mechanism3-D Mechanism

Name (symbol)Name (symbol) DOFDOF ContainsContainsRevolute (R)Revolute (R) 11 RRPrismatic (P)Prismatic (P) 11 PPScrew or Helical (H)Screw or Helical (H) 11 R + PR + PCylindric (C)Cylindric (C) 22 R+PR+PSpherical (S)Spherical (S) 33 R+R+RR+R+RPlanar or Flat (F)Planar or Flat (F) 33 R+P+PR+P+P

Planar MechanismPlanar Mechanism

DOF: Degree of FreedomDOF: Degree of Freedom


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Revolute (R): Revolute (R): Rotating full pin jointRotating full pin joint

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Dq


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Prismatic (P): Prismatic (P): Translating full slider jointTranslating full slider joint

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Helical (H):Helical (H):


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Cylindric (C)Cylindric (C) ::


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Spherical (S):Spherical (S):


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Flat (F) :Flat (F) :


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mon 1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT

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Roll-slide (Half or RP) jointRoll-slide (Half or RP) joint

DX

Dq

Linkage against Plane (Force close)Linkage against Plane (Force close)


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mon 1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT

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Higher Pair: Higher Pair: 2 DOF2 DOF

Pin in Slot Pin in Slot ((Form Close)Form Close)

Dq

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Lower pair orLower pair or Full joint Full joint : 1 DOF joint: 1 DOF joint Higher pair, Higher pair, half joint : > 1 DOF, roll-sliderhalf joint : > 1 DOF, roll-slider Joint order = Joint order = number ofnumber of link joinedlink joined - 1 - 1

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Second order pin jointFirst order pin jointFirst order pin jointFirst order pin joint

Second order pin jointSecond order pin joint


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mon 1.9 PLANAR MOTION1.9 PLANAR MOTION

KINEMATIC CHAIN: KINEMATIC CHAIN: An assemblage of links and An assemblage of links and joints, interconnected in a way to provide a joints, interconnected in a way to provide a controlled output motion in response to a controlled output motion in response to a supplied input motion.supplied input motion.

CRANK: CRANK: Link that makes a complete Link that makes a complete revolution and is pivoted to ground.revolution and is pivoted to ground.

ROCKET: ROCKET: Link that has oscillatory (back and Link that has oscillatory (back and forth) rotation and is pivoted to ground.forth) rotation and is pivoted to ground.

COUPLER (or connecting rod): COUPLER (or connecting rod): Link that has Link that has complex motion and is not pivoted to ground.complex motion and is not pivoted to ground.

GROUND: GROUND: defined as any link or links that are defined as any link or links that are fixed (nonmoving) with respect to the fixed (nonmoving) with respect to the reference frame.reference frame.

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mon 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

Degree of Freedom (DOF): Degree of Freedom (DOF): Number or Number or inputs that need to be provided in order o inputs that need to be provided in order o create a predictable output. Also: number create a predictable output. Also: number of independent coordinates required to of independent coordinates required to define its position.define its position.

In Planar Mechanisms:In Planar Mechanisms: 1 link in the plane has 3 DOF1 link in the plane has 3 DOF

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2 links in the plane have 6 DOF2 links in the plane have 6 DOF

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Dx2

Dy2Dy1

Dx1Dq1 Dq2


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2 links connected by a full joint have 4 DOF2 links connected by a full joint have 4 DOF

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2 links connected by a roll-slide (half) have 2 links connected by a roll-slide (half) have 5 DOF5 DOF

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Dy

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Gruebler’s equationGruebler’s equation

DOF orDOF or M = 3L – 2J – 3GM = 3L – 2J – 3G

Where:Where:M=degree of freedom or mobilityM=degree of freedom or mobilityL= number of linksL= number of linksJ=number of jointsJ=number of jointsG=number of grounded links (always G=number of grounded links (always

1)1)

M = 3(L - 1) – 2JM = 3(L - 1) – 2J

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Kutzbatch’s modification of Gruebler’s equationKutzbatch’s modification of Gruebler’s equation

M = 3(L – 1)– 2JM = 3(L – 1)– 2J11 – J – J22

Where:Where:M= degree of freedom or mobilityM= degree of freedom or mobilityL= number of linksL= number of linksJJ11= number of DOF (full) joints= number of DOF (full) jointsJJ22= number of DOF (half) joints= number of DOF (half) joints

Full Joint = 1Full Joint = 1Half Joint = 0.5Half Joint = 0.5

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mon 1.11 MECHANISMS AND STRUCTURES1.11 MECHANISMS AND STRUCTURES

If the DOF is If the DOF is positivepositive, it will be a , it will be a mechanismmechanism, and , and the links will have relative motion. If the DOF is the links will have relative motion. If the DOF is exactly exactly zerozero, then it will be a , then it will be a structurestructure, and no , and no motion is possible. If the DOF is motion is possible. If the DOF is negativenegative, then it , then it is a is a preloaded structurepreloaded structure, which means that no , which means that no motion is possible and some stresses may also be motion is possible and some stresses may also be present at the time of assembly.present at the time of assembly.

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1.1. Number or links L = 4Number or links L = 42.2. Number of (full joint) 4 joints J=4Number of (full joint) 4 joints J=43.3. Number of ground link G=1Number of ground link G=1

M = 3(4 - 1) – 2x4M = 3(4 - 1) – 2x4M = 1M = 1

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1.1. Number or links L = 9Number or links L = 92.2. Number of full joints 10 and half joints 2 Number of full joints 10 and half joints 2

J=12J=123.3. Number of ground link G=1Number of ground link G=1

M = 3(9 - 1) – 2x12M = 3(9 - 1) – 2x12M = 0M = 0

5858


N 4

110

Int

er -

Baya

mon

MEC

N 4

110

Int

er -

Baya

mon

Homework1 Homework1 http://facultad. bayamon.inter.edu/omeza/

Omar E. Meza Castillo Ph.D.Omar E. Meza Castillo Ph.D.

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mecn 4110 - mechanisms design - fall 2012_lecture 01

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