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Gruebler's Equation Theory of Machines Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 1 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 Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 2 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 3 Grading: Attendance 5% Design Project 25% Midterm 30% Final exam 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. Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 4 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. Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 5 Chapter 1 Introduction Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 6 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. Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 7 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. Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 8 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. Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 9 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 10 Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 11 Chapter 2 DEGREES OF FREEDOM (MOBILITY) Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 12 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 13 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 14 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 15 Excavator Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 16 Slider-Crank Mechanism Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 17 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 18 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) Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 19 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 20 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 21 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 22 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 Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 23 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;ahigher 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;aforce-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). Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 24 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 Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 25 crank mechanism Elements: 0: Ground (Casing, Frame) 1: Rocker 2: Coupler 3: Crank Dr. Anwar Abu-Zarifa . Islamic University of Gaza . Department of Mechanical Engineering . © 2012 26 The “Ground” Link . When
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