theory of machinessite.iugaza.edu.ps/mawad/wp-content/uploads/file/iugaza tom2012_ch1-2.pdf · the...
TRANSCRIPT
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 1
Theory of Machines
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012
Syllabus and Course Outline
2
SAT 09:30 – 11:00 Q412
MON 09:30 – 11:00 Q412
Faculty of EngineeringDepartment of Mechanical Engineering
EMEC 3302, Theory of Machines
Instructor: Dr. Anwar Abu-ZarifaOffice: IT Building, Room: I413 Tel: 2821eMail: [email protected]: http://site.iugaza.edu.ps/abuzarifaOffice Hrs: see my website
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 3
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 4
Grading:Attendance 5%Design Project 25%Midterm 30%Final exam 40%
Course Description:
The course provides students with instruction in the fundamentals of theory ofmachines. The Theory of Machines and Mechanisms provides the foundationfor the study of displacements, velocities, accelerations, and static anddynamic forces required for the proper design of mechanical linkages, cams,and geared systems.
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 5
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 ofmechanisms such as linkages and cams.
To develop the ability to systematically design and optimizemechanisms 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 teamsin the development of mechanism designs.
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 6
Chapter 1Introduction
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012
Definitions
7
The subject Theory of Machines may be defined as that branch ofEngineering-science, which deals with the study of relative motionbetween the various parts of a machine, and forces which act onthem. The knowledge of this subject is very essential for anengineer 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.
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 8
Kinetics: The study of forces on systems in motion
A mechanism: is a device that transforms motion to some desirable patternand typically develops very low forces and transmits little power.
A machine: typically contains mechanisms that are designed to providesignificant forces and transmit significant power.
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012
Application of Kinematics
9
Any machine or device that moves contains one or more kinematic elements suchAs linkages, … gears…. belts and chains.
Bicycle is a simple example of a kinematic system that contains a chain drive to provide Torque.
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 10
An Automobile contains many more examples of kin-systems…
the transmission is full of gears….
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 11
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 12
Chapter 2DEGREES OF FREEDOM (MOBILITY)
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 13
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 14
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.
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 15
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.
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 16
Excavator
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 17
Slider-Crank Mechanism
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 18
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
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 19
1. Binary link: 2 nodes2. Ternary link: 3 nodes3. Quaternary link: 4 nodes
Joint: connection between two or more links (at theirnodes) which allows motion;
(Joints also called kinematic pairs)
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 20
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.
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 21
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
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 22
lower pair to describe joints with surface contact
The six lower pairs
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 23
The half joint is also called a roll-slide jointbecause it allows both rolling and sliding
Form closed (closed by geometry) or Force closed
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 24
A joint (also called kinematic pair) is a connection between two ormore 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 withpoint or line contact.
A full joint has one degree of freedom; a half joint has two degreesof freedom. Full joints are lower pairs; half-joints are higher pairs andallow both rotation and translation (roll-slide).
A form-closed joint is one in which the links are kept together form byits geometry; a force-closed joint requires some external force tokeep the links together.
Joint order is the number of links joined minus one (e.g. 1st ordermeans two links).
Terminology of Joints
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 25
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 withrespect 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
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 26
Elements:0: Ground (Casing, Frame)1: Rocker2: Coupler3: Crank
crank mechanism
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 27
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.
The “Ground” Link
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 28
Drawing kinematic Diagrams
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 29
Determining Degrees of Freedom
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 30
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-3GWhere:L: number of linksJ: number of full jointsG: number of grounded links
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 31
Determining DOF’s
• Gruebler’s equation for planar mechanisms
• WhereM = degree of freedom or mobilityL = number of linksJ = number of full joints (half joints count as 0.5)G = number of grounded links =1
3 1 2M L J Kutzbach’s modification of Gruebler’s equation
M= 3L-2J-3G
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 32
The Cylindrical (cylindric) joint - two degrees of freedomIt permits both angular rotation and an independent sliding motion (C joint)
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 33
The Spherical (spheric) - Three degree of freedomIt permits rotational motion about all three axes, a ball-and-socket joint (S joint)
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 34
Example
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 35
Example
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012
Gruebler’s Equation
Gruebler’s Equation
DOF = mobilityL = number of linksJ = number of revolute joints or
prismatic jointsG = number of grounded links
DOF (M) = 3*L – 2* J – 3 *G= 3 (L-1) – 2 * J
L = 2J = 1G = 1
DOF = 1
Gruebler’s equation can be used to determine the mobility of planar mechanisms.
Link 13 DOF
Link 23 DOF
1 DOF
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012
Mobility of Vise Grip Pliers
L = 5J = 4 (revolute)J = 1 (screw)G = 1 (your hand)
DOF = 3*5 - 2*5 - 1*3 = 2
1
23
4
1
2
3
4
This example applies Gruebler’s equation to the determine the mobility of a vise grip plier.
5
Each revolute joint removes two DOF.The screw joint removes two DOF.
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.
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 38
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 Joint type
1 Link 4 and Link 1 Revolute (or Pin)
2 Link 1 and Link 2 Revolute (or Pin)
3 Link 2 and Link 3 Revolute (or Pin)
4 Link 3 and Link 4Translatio
nal or (Slider)
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 39
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.
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 40
Paradoxes
• Greubler criterion does not include geometry, so it can give wrong prediction
• We must use inspection
E-quintetL=5J=6G=1M=3*5-2*6-3*1=0
Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 41
Rolling cylinders even without slip (The joint between the two wheels can bepostulated to allow no slip, provided that sufficient friction is available) is anexample in which the ground link is exactly the same length as the sum of twoother 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 designermust not apply the equation blindly.