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# MENG 372 Mechanical Systems Spring 2011

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MENG 372 Mechanical Systems Spring 2011
Dr. Mustafa Arafa American University in Cairo Mechanical Engineering Department

Course Information Course goals: Analyze & design planar mechanisms
Analyze forces, velocities & accelerations in machines Use computers for the above Textbook: Design of Machinery, R.Norton, McGraw-Hill, 3rd ed., 2004. Computer usage: Working Model, MATLAB Grading: attendance 5%; homework 10%; quizzes 5%; mid-term exams 30%; projects 25%; final exam 25% Lecture notes: will be posted my website. I will communicate with you on BlackBoard. Additional material will also be covered on the board. Please print out the notes beforehand & bring them to class.

MENG 372 Chapter 2 Kinematics Fundamentals
All figures taken from Design of Machinery, 3rd ed. Robert Norton 2003

2.1 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. Rigid body in a plane has 3 DOF: x,y,q Rigid body in space has 6 DOF (3 translations & 3 rotations)

2.2 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.

Backhoe Excavator

Slider-Crank Mechanism

2.3 Links, joints, and kinematic chains
Links: rigid member having nodes Node: attachment points Binary link: 2 nodes Ternary link: 3 nodes Quaternary link: 4 nodes Joint: connection between two or more links (at their nodes) which allows motion Classified by type of contact, number of DOF, type of physical closure, or number of links joined

Joint Classification 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 = number of links-1

Types 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: fixed w.r.t. 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

Determining Degrees of Freedom
For simple mechanisms calculating DOF is simple Open Mechanism DOF=3 Closed Mechanism DOF=1

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

2.4 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

Example

Example

2.5 Mechanisms and Structures
Mechanism: DOF>0 Structure: DOF=0 Preloaded Structure – DOF<0, may require force to assemble

2.7 Paradoxes Greubler criterion does not include geometry, so it can give wrong prediction We must use inspection E-quintet

2.10 Intermittent Motion Series of Motions and Dwells
Dwell: no output motion with input motion Examples: Geneva Mechanism, Linear Geneva Mechanism, Ratchet and Pawl

Geneva Mechanism

Linear Geneva Mechanism

Ratchet and Pawl

Fourbar Mechanism 1 -1 Twobar has -1 degrees of freedom (preloads structure) Threebar has 0 degrees of freedom (structure) Fourbar has 1 degree of freedom The fourbar linkage is the simplest possible pin-jointed mechanism for single degree of freedom controlled motion

4-Bar Nomenclature Ground Link Links pivoted to ground: Coupler Crank
Rocker Coupler Link 3, length b B Coupler Link 4, length c A Link 2, length a Rocker Crank Link 1, length d Ground Link Pivot 02 Pivot 04

Where would you see 4-bar mechanisms?

Sheet Metal Shear (Mechanical Workshop)

Sheet Metal Shear (Mechanical Workshop)

Door Mechanism (ACMV Lab)

Door Mechanism (ACMV Lab)

Backhoe Excavator

Brake of a Wheelchair Folding sofa

Honda Accord trunk Chevy Cobalt Garage door Desk Lamp

Inversions Created by attaching different links to ground
Different behavior for different inversions

Inversions of a 4-Bar Mechanism
Crank-rocker Crank-rocker Crank-crank Rocker-rocker

2.12 The Grashof Condition Grashof condition predicts behavior of linkage based only on length of links S=length of shortest link L=length of longest link P,Q=length of two remaining links If S+L ≤ P+Q the linkage is Grashof :at least one link is capable of making a complete revolution Otherwise the linkage is non-Grashof : no link is capable of making a complete revolution

For S+L<P+Q Crank-rocker if either link adjacent to shortest is grounded Double crank if shortest link is grounded Double rocker if link opposite to shortest is grounded

For S+L>P+Q All inversions will be double rockers
No link can fully rotate

For S+L=P+Q (Special case Grashof)
All inversions will be double cranks or crank rockers Linkage can form parallelogram or antiparallelogram Often used to keep coupler parallel (drafting machine) Parallelogram form Deltoid form Anti parallelogram form

Problems with Special Grashof
All inversions have change points twice per revolution of input crank when all links become collinear Behavior at change points is indeterminate If used in continuous machine, must have some mechanism to “carry through”

2.13 Linkages of more than 4 bars
5-bar 2DOF Geared 5-bar 1DOF Provide more complex motion See Watt’s sixbar and Stephenson’s sixbar mechanisms in the textbook

Linkages of more than 4 bars
Volvo 740 Hood

Volvo 740 Hood

Animation using Working Model ®

Cabinet Hinge

2.15 Compliant Mechanisms Compliant “link” capable of significant deflection acts like a joint Also called a “living hinge” Advantage: simplicity, no assembly, little friction

More Examples: Front End Loader

Drum Brake

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