Theory of Machines - Semantic Scholar

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


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


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.


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.


Chapter 1Introduction


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.


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.


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.


An Automobile contains many more examples of kin-systems…

the transmission is full of gears….


Chapter 2DEGREES OF FREEDOM (MOBILITY)


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).


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.


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.


Excavator


Slider-Crank Mechanism


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


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)


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.


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


lower pair to describe joints with surface contact

The six lower pairs


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

Form closed (closed by geometry) or Force closed


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


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


Elements:0: Ground (Casing, Frame)1: Rocker2: Coupler3: Crank

crank mechanism


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


Drawing kinematic Diagrams


Determining Degrees of Freedom


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


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


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


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


Example


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


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.


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)



4 Link 3 and Link 4Translatio

nal or (Slider)


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.


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


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.

Theory of Machines - Semantic Scholar

Documents

Transcript of Theory of Machines - Semantic Scholar