Theory of Machines

Theory of Machines

Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012

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Syllabus and Course Outline

Faculty of Engineering Department of Mechanical Engineering EMEC 3302, Theory of Machines Instructor: Dr. Anwar Abu-Zarifa Office: IT Building, Room: I413 Tel: 2821 eMail: [email protected] Website: http://site.iugaza.edu.ps/abuzarifa Office Hrs: see my website SAT

09:30 – 11:00

Q412

MON

09:30 – 11:00

Q412


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Text Book: R. L. Norton, Design of Machinery “An Introduction to the Synthesis and Analysis of Mechanisms and Machines”, McGraw Hill Higher Education; 3rd edition

Reference Books:  John J. Uicker, Gordon R. Pennock, Joseph E. Shigley, Theory of Machines and Mechanisms  R.S. Khurmi, J.K. Gupta,Theory of Machines  Thomas Bevan, The Theory of Machines  The Theory of Machines by Robert Ferrier McKay  Engineering Drawing And Design, Jensen ect., McGraw-Hill Science, 7th Edition, 2007  Mechanical Design of Machine Elements and Machines, Collins ect., Wiley, 2 Edition, 2009 Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012

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Grading: Attendance Design Project Midterm Final exam

5% 25% 30% 40%

Course Description: The course provides students with instruction in the fundamentals of theory of machines. The Theory of Machines and Mechanisms provides the foundation for the study of displacements, velocities, accelerations, and static and dynamic forces required for the proper design of mechanical linkages, cams, and geared systems.


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Course Objectives: Students combine theory, graphical and analytical skills to understand the Engineering Design. Upon successful completion of the course, the student will be able:    

To develop the ability to analyze and understand the dynamic (position, velocity, acceleration, force and torque) characteristics of mechanisms such as linkages and cams. To develop the ability to systematically design and optimize mechanisms to perform a specified task. To increase the ability of students to effectively present written, oral, and graphical solutions to design problems. To increase the ability of students to work cooperatively on teams in the development of mechanism designs.


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Chapter 1 Introduction


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Definitions The subject Theory of Machines may be defined as that branch of Engineering-science, which deals with the study of relative motion between the various parts of a machine, and forces which act on them. The knowledge of this subject is very essential for an engineer in designing the various parts of a machine. Kinematics: The study of motion without regard to forces More particularly, kinematics is the study of position, displacement, rotation, speed, velocity, and acceleration.


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Kinetics: The study of forces on systems in motion A mechanism: is a device that transforms motion to some desirable pattern and typically develops very low forces and transmits little power. A machine: typically contains mechanisms that are designed to provide significant forces and transmit significant power.


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Application of Kinematics

Any machine or device that moves contains one or more kinematic elements such As linkages, … gears…. belts and chains. Bicycle is a simple example of a kinematic system that contains a chain drive to provide Torque.


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An Automobile contains many more examples of kin-systems… the transmission is full of gears….


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Chapter 2 DEGREES OF FREEDOM (MOBILITY)


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Degrees of Freedom (DOF) or Mobility • DOF: Number of independent parameters (measurements) needed to uniquely define position of a system in space at any instant of time. • A mechanical system’s mobility (M) can be classified according to the number of degrees of freedom (DOF). • DOF is defined with respect to a selected frame of reference (ground). Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012

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 Rigid body in a plane has 3 DOF: x,y,z  Rigid body in 3D-space has 6 DOF, 3 translations & 3 rotations three lengths (x, y, z), plus three angles (θ, φ, ρ).  The pencil in these examples represents a rigid body, or link.


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Types of Motion • Pure rotation: the body possesses one point (center of rotation) that has no motion with respect to the “stationary” frame of reference. All other points move in circular arcs. • Pure translation: all points on the body describe parallel (curvilinear or rectilinear) paths. • Complex motion: a simultaneous combination of rotation and translation.


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Excavator


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Slider-Crank Mechanism


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Links, joints, and kinematic chains Linkage design:  Linkages are the basic building blocks of all mechanisms  All common forms of mechanisms (cams, gears, belts, chains) are in fact variations on a common theme of linkages. • Linkages are made up of links and joints.

• Links: rigid member having nodes • Node: attachment points


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1. Binary link: 2 nodes 2. Ternary link: 3 nodes 3. Quaternary link: 4 nodes Joint: connection between two or more links (at their nodes) which allows motion; (Joints also called kinematic pairs)


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Joint Classification Joints 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). A more useful means to classify joints (pairs) is by the number of degrees of freedom that they allow between the two elements joined.


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A joint with more than one freedom may also be a higher pair

• • • •

Type of contact: line, point, surface Number of DOF: full joint=1DOF, half joint=2DOF Form closed (closed by geometry) or Force closed (needs an external force to keep it closed) Joint order

Joint order = number of links-1


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lower pair to describe joints with surface contact

The six lower pairs


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The half joint is also called a roll-slide joint because it allows both rolling and sliding

Form closed (closed by geometry) or Force closed


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Terminology of Joints  A joint (also called kinematic pair) is a connection between two or more links at their nodes, which may allow motion between the links.  A lower pair is a joint with surface contact; a higher pair is a joint with point or line contact.  A full joint has one degree of freedom; a half joint has two degrees of freedom. Full joints are lower pairs; half-joints are higher pairs and allow both rotation and translation (roll-slide).  A form-closed joint is one in which the links are kept together form by its geometry; a force-closed joint requires some external force to keep the links together.  Joint order is the number of links joined minus one (e.g. 1st order means two links).


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Kinematic chains, mechanisms, machines, link classification • • • •

Kinematic chain: links joined together for motion Mechanism: grounded kinematic chain Machine: mechanism designed to do work Link classification:  Ground: any link or links that are fixed, nonmoving with respect to the reference frame  Crank: pivoted to ground, makes complete revolutions  Rocker: pivoted to ground, has oscillatory motion  Coupler: link has complex motion, not attached to ground


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crank mechanism Elements: 0: Ground (Casing, Frame) 1: Rocker 2: Coupler 3: Crank


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The “Ground” Link

 When studying mechanisms it is very helpful to establish a fixed reference frame by assigning one of the links as “ground”.  The motion of all other links are described with respect to the ground link.  For example, a fourbar mechanism often looks like a 3-bar mechanism, where the first “bar” is simply the ground link.


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Drawing kinematic Diagrams


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Determining Degrees of Freedom


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Determining Degrees of Freedom Two unconnected links: 6 DOF (each link has 3 DOF)

When connected by a full joint: 4 DOF (each full joint eliminates 2 DOF)

Gruebler’s equation for planar mechanisms: DOF = 3L-2J-3G Where: L: number of links J: number of full joints G: number of grounded links Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012

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Determining DOF’s • Gruebler’s equation for planar mechanisms M= 3L-2J-3G

• Where M = degree of freedom or mobility L = number of links J = number of full joints (half joints count as 0.5) G = number of grounded links =1

M  3  L  1  2 J Kutzbach’s modification of Gruebler’s equation Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012

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The Cylindrical (cylindric) joint - two degrees of freedom It permits both angular rotation and an independent sliding motion (C joint)


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The Spherical (spheric) - Three degree of freedom It permits rotational motion about all three axes, a ball-and-socket joint (S joint)


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Example


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Example


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Gruebler’s Equation Gruebler’s equation can be used to determine the mobility of planar mechanisms.

L = 2 J = 1 G = 1 DOF = 1

Link 1 3 DOF

Gruebler’s Equation DOF L J G

= mobility = number of links = number of revolute joints or prismatic joints = number of grounded links

DOF (M) = 3*L – 2* J – 3 *G = 3 (L-1) – 2 * J

1 DOF

Link 2 3 DOF


Mobility of Vise Grip Pliers This example applies Gruebler’s equation to the determine the mobility of a vise grip plier.

1

4

5 1

4

3 3

2

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Each revolute joint removes two DOF. The screw joint removes two DOF. L=5 J = 4 (revolute) J = 1 (screw) G = 1 (your hand) DOF = 3*5 - 2*5 - 1*3 = 2

The mobility of the plier is two. Link 3 can be moved relative link1 when you squeeze your hand and the jaw opening is controlled by rotating link 5.


Punch Press

Slider-Crank Mechanism

As designated in the figure, there are four links link 1, link 2, link 3 and link 4. Link 1 acts as a crank. Link 2 acts as connecting link, link 3 is the slider and link 4 is ground.

Joint Number

Formed between links

1

Link 4 and Link 1

2

Link 1 and Link 2

3

Link 2 and Link 3

4

Link 3 and Link 4

Joint type

Revolute (or Pin) Revolute (or Pin) Revolute (or Pin) Translatio nal or (Slider)


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Mechanisms and Structures

 If DOF > 0, the assembly of links is a mechanism and will exhibit relative motion  If DOF = 0, the assembly of links is a structure and no motion is possible.  If DOF < 0,then the assembly is a preloaded structure, no motion is possible, and in general stresses are present.


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Paradoxes • Greubler criterion does not include geometry, so it can give wrong prediction • We must use inspection

L=5 J=6 G=1 M=3*5-2*6-3*1=0

E-quintet


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Rolling cylinders even without slip (The joint between the two wheels can be postulated to allow no slip, provided that sufficient friction is available) is an example in which the ground link is exactly the same length as the sum of two other links. If no slip occurs, then this is a one-freedom, or full, joint that allows only relative angular motion (Δθ) between the wheels. With that assumption, there are 3 links and 3 full joints, The equation predicts DOF = 0 (L=3, J1=3), but the mechanism has DOF = 1. Others paradoxes exist, so the designer must not apply the equation blindly.


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Theory of Machines

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