mecn 4110: mechanisms design mechanisms design mecn 4110 professor: dr. omar e. meza castillo...

Mechanisms DesignMECN 4110

Professor: Dr. Omar E. Meza Castilloomeza@bayamon.inter.edu

http://facultad.bayamon.inter.edu/omezaDepartment of Mechanical Engineering

BIENVENIDOS

gn 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.

Syllabus

gn 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.

Syllabus

gn Problem-Solving Technique:

A. KnownB. FindC. AssumptionsD. SchematicE. Analysis, andF. 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.

Syllabus

gn 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.

Syllabus

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

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.

gn 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

Course Materials

Tentative Lectures Schedule

Topic Lecture

Introduction of Mechanism and Kinematics 1, 2 and 3

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.

Introduction and Basic Concepts

Topic 1: Mechanism and Kinematics

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

A. O. Beckman

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.

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.

1.2 DESIGN PROCESS

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)

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)

1.4 UNITS

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

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.18

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.

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. 22

DOF of rigid body in Space DOF of Rigid body in Plane

1.7 TYPES OF MOTION

Pure rotation

Reference line

1.7 TYPES OF MOTION

Pure translation

1.7 TYPES OF MOTION

Complex Motion : Rotation + Translation

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.

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

Link of different order:

Binary link: one of 2 nodes

Ternary link: one of 3 nodes

Quaternary link: one of 4 nodes

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).

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.

1.8 JOINT PAIRS: THE SIX LOWER PAIRS

Lower Pair:

3-D Mechanism

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

DOF: Degree of Freedom

Revolute (R): Rotating full pin joint

Prismatic (P): Translating full slider joint

Helical (H):

Cylindric (C):

Spherical (S):

Flat (F):

1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT

Roll-slide (Half or RP) joint:

Linkage against Plane (Force close)

1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT

Higher Pair: 2 DOF

Pin in Slot (Form Close)

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

Second order pin joint

First order pin jointFirst order pin joint

Second order pin joint

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.

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

2 links in the plane have 6 DOF

Dy2Dy1

Dx1Dq1 Dq2

2 links connected by a full joint have 4 DOF

Dq1 Dq2

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

Gruebler’s equation

DOF or M = 3L – 2J – 3G

Where:M=degree of freedom or mobilityL= number of linksJ=number of jointsG=number of grounded links (always 1)

M = 3(L - 1) – 2J

Kutzbatch’s modification of Gruebler’s equation

M = 3(L – 1)– 2J1 – J2

Where:M= degree of freedom or mobilityL= number of linksJ1= number of DOF (full) jointsJ2= number of DOF (half) joints

Full Joint = 1Half Joint = 0.5

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.

1.12 EXAMPLES

1. Number or links L = 42. Number of (full joint) 4 joints J=43. Number of ground link G=1

M = 3(4 - 1) – 2x4M = 1

1.12 EXAMPLES

1. Number or links L = 92. Number of full joints 10 and half joints 2 J=123. Number of ground link G=1

M = 3(9 - 1) – 2x12M = 0

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

Omar E. Meza Castillo Ph.D.

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