Mechanism of Machinery

MEng 3071

Esmael Adem

Department of Mechanical and Vehicle Engineering

School of Mechanical, Chemical & Materials Engineering

Adama Science and Technology University

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Chapter One

Introduction

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One thing you learn in science is thatthere is no perfect answer, no perfectmeasure.

A. O. Beckman

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Course Objectives

Up on completion of this chapter, the student will be able to

Explain the need for kinematic analysis ofmechanism.

Define the basic components that comprise amechanism.

Draw the kinematic diagram from a view of acomplex mechanism.

Compute the number of degrees of freedom of amechanism.

Identify a four bar mechanism and classify itaccording to its possible motion.

Identify a slider crank mechanism.

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1.1 ANALYSIS AND SYSTHESIS

Analysis: the techniques that allow thedesigner to critically examine an alreadyexisting or proposed design in order tojudge its suitability for task.

Synthesis (or Design): the process ofprescribing the sizes, shapes, materialcompositions, and arrangements of partsso that the resulting machine will performthe prescribed task.

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1.2 DESIGN PROCESS

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1.5 THE SCIENCE OF MECHANICS

Statics: deals with analysis of stationarysystems, that is, those in which time isnot a factor.

Dynamics: deals with systems that changewith time.

Kinematics: the study of motion, quiteapart from the forces which produce thatmotion. More particularly kinematics isthe study of position, displacementrotation, speed, velocity, and acceleration.

Kinetics: the study of force on system inmotion.

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1.5 THE SCIENCE OF MECHANICS

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1.5 THE SCIENCE OF MECHANICS

Reuleaux’ Definition:

Machine: a combination of resistant bodies soarranged that their means the mechanical forcesof nature can be compelled to do workaccompanied by certain determinate motion.

Mechanism: an assemblage of resistant bodies,connected by movable joints, to form a closedkinematic chain with one link fixed and havingthe purpose of transforming motion.

Structure: also a combination of resistant bodiesconnected by joints, but its purpose is not to dwork or to transform motion. A structure isintended to be rigid.

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1.5 THE SCIENCE OF MECHANICS

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1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY

A mechanical system’s mobility (M) can beclassified according to the number of degrees offreedom (DOF) that it possesses. The system’sDOF is equal to the number of independentparameters (measurements) that are neededuniquely define its position in space and at anyinstant of time.

This system of the pencil in the plane has threeDOF

The pencil in the this example represents a rigidbody, or link, which for purposes of kinematicsanalysis we will assume to be incapable ofdeformation.

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1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY

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DOF of rigid body in Space DOF of Rigid body in Plane

1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY

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1.7 TYPES OF MOTION

Pure rotation

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Reference line

Reference line

1.7 TYPES OF MOTION

Pure translation

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1.7 TYPES OF MOTION

Complex Motion : Rotation + Translation

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1.7 LINKS, JONTS AND KINEMATIC CHAINS

Linkages are the basic building blocks ofall mechanisms. A linkage consist of links(or bars), generally considered rigid,which are connected by joints, such aspins (or revolutes), or prismatic joints toform open or closed chains (or loops).Such kinematic chains, with at least onelink fixed, become (1) mechanisms if atleast two other links retain mobility, or(2) structures if no mobility remains.

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1.7 LINKS, JONTS AND KINEMATIC CHAINS

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1.7 LINKS, JONTS AND KINEMATIC CHAINS

A link is an rigid body that possesses atleast two nodes that are points forattachment to other links.

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1.7 LINKS, JONTS AND KINEMATIC CHAINS

Link of different order:

Binary link : one of 2 nodes

Ternary link : one of 3 nodes

Quaternary link : one of 4 nodes

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1.7 LINKS, JONTS AND KINEMATIC CHAINS

A joint is an connection between two ormore links (at their nodes), which allowssome motion, or potential motion,between the connected links. Joints (alsocalled kinematic pairs) can be classified inseveral ways:

1. By the type of contact between the elements,line, point or surface.

2. By the number of degrees of freedom allowedat 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 thejoint).

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1.7 LINKS, JONTS AND KINEMATIC CHAINS

The kinematic pairs can be:

Lower pair (surface contact): are thejoints with surface contact between thepair elements.

Higher pair (point or line contact): arethe joints with point or line contactbetween the pair elements.

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1.8 JOINT PAIRS: THE SIX LOWER PAIRS

Lower Pair:

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3-D Mechanism

Name (symbol) DOF Contains

Revolute (R) 1 R

Prismatic (P) 1 P

Screw or Helical (H) 1 R + P

Cylindric (C) 2 R+P

Spherical (S) 3 R+R+R

Planar or Flat (F) 3 R+P+P

Planar Mechanism

DOF: Degree of Freedom

1.8 JOINT PAIRS: THE SIX LOWER PAIRS

Revolute (R): Rotating full pin joint

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Dq

1.8 JOINT PAIRS: THE SIX LOWER PAIRS

Prismatic (P): Translating full slider joint

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DX

1.8 JOINT PAIRS: THE SIX LOWER PAIRS

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Helical (H):

1.8 JOINT PAIRS: THE SIX LOWER PAIRS

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Cylindric (C) :

1.8 JOINT PAIRS: THE SIX LOWER PAIRS

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Spherical (S):

1.8 JOINT PAIRS: THE SIX LOWER PAIRS

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Flat (F) :

1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT

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Roll-slide (Half or RP) joint

DX

Dq

Linkage against Plane (Force close)

1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT

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Higher Pair: 2 DOF

Pin in Slot (Form Close)

Dq

DX

1.9 PLANAR MOTION

Lower pair or Full joint : 1 DOF joint

Higher pair, half joint : > 1 DOF, roll-slider

Joint order = number of link joined - 1

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Second order pin joint

First order pin jointFirst order pin joint

Second order pin joint

1.9 PLANAR MOTION

KINEMATIC CHAIN: An assemblage of linksand joints, interconnected in a way to providea controlled output motion in response to asupplied input motion.

CRANK: Link that makes a complete revolutionand is pivoted to ground.

ROCKET: Link that has oscillatory (back andforth) rotation and is pivoted to ground.

COUPLER (or connecting rod): Link that hascomplex motion and is not pivoted to ground.

GROUND: defined as any link or links that arefixed (nonmoving) with respect to thereference frame.

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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

Degree of Freedom (DOF): Number orinputs that need to be provided in order ocreate a predictable output. Also: numberof independent coordinates required todefine its position.

In Planar Mechanisms:

1 link in the plane has 3 DOF

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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

2 links in the plane have 6 DOF

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Dx2

Dy2Dy1

Dx1Dq1 Dq2

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

2 links connected by a full joint have 4 DOF

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Dx

Dy

Dq1 Dq2

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

2 links connected by a roll-slide (half) have5 DOF

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Dy

Dq1

Dq2

Dx2

Dx1

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

Gruebler’s equation

DOF or M = 3L – 2J – 3G

Where:

M=degree of freedom or mobility

L= number of links

J=number of joints

G=number of grounded links (always 1)

M = 3(L - 1) – 2J

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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

Kutzbatch’s modification of Gruebler’sequation

M = 3(L – 1)– 2J1 – J2

Where:M= degree of freedom or mobilityL= number of linksJ1= number of DOF (full) jointsJ2= number of DOF (half) joints

Full Joint = 1

Half Joint = 0.5

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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

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1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

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1.11 MECHANISMS AND STRUCTURES

If the DOF is positive, it will be a mechanism, andthe links will have relative motion. If the DOF isexactly zero, then it will be a structure, and nomotion is possible. If the DOF is negative, then it isa preloaded structure, which means that no motionis possible and some stresses may also be presentat the time of assembly.

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1.12 EXAMPLES

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1.12 EXAMPLES

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1.12 EXAMPLES

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1.12 EXAMPLES

1. Number or links L = 4

2. Number of (full joint) 4 joints J=4

3. Number of ground link G=1

M = 3(4 - 1) – 2x4

M = 1

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1.12 EXAMPLES

1. Number or links L = 9

2. Number of full joints 10 and half joints 2J=12

3. Number of ground link G=1

M = 3(9 - 1) – 2x12

M = 0

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Classification of Mechanism

According to the types of motion of the output link

1. Swinging or rocking mechanism

Examples

a) Crank-Rocker four bar linkage

See attached video

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Cont’d

b) Rack and Pinion joint

c) Crank and slotted lever mechanism (see attached video for shaper mechanism)

d) Cam-Follower mechanism

2. Reciprocating mechanisms

a) Slider-crank mechanism see figure

b) Scotch-Yoke mechanism

c) Shaping Mechanism

d) Quick-return mechanism

3. Curve generators

a) Straight line mechanism

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Cont’d

4. Other mechanisms

a. Toggle mechanism

b. Parallel mechanisms

c. Intermittent motion mechanisms

d. Steering gear mechanisms

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INTERMITENT MOTION

Is a sequence of motions and dwells.Dwell; is a period in which the output linkremains stationary while the input linkcontinues to move.

INTERMITENT MOTION

INVERSION

An inversion is created by grounding adifferent link in the kinematic chain. Thusthere are as many inversions of a givenlinkage as it has links.

INVERSION

INVERSION – All inversions of the Grashof fourbar linkage

THE GRASHOF CONDITION

2.- Input Link

1.- Fixed Link

3.- Coupler Link

4.- Follower Link

THE GRASHOF CONDITION

The four bar linkage, shown in previousslide, is a basic mechanism which is quitecommon. Further, the vast majority ofplanar one degree-of-freedom (DOF)mechanisms have "equivalent" four barmechanisms. The four bar has tworotating links ("levers") which have fixedpivots, (bodies 2 and 4 above). One of thelevers would be an input rotation, whilethe other would be the output rotation.The two levers have their fixed pivots withthe "ground link"(body 1) and areconnected by the "coupler link" (body 3).

THE GRASHOF CONDITION - Definitions

Crank- a ground pivoted link which iscontinuously rotatable.

Rocker- a ground pivoted link that is onlycapable of oscillating between two limitpositions and cannot rotate continuously.

THE GRASHOF CONDITION - Definitions

Grashof Condition- is a very simplerelationship which predicts the rotationbehavior or rotability of a fourbarlinkage's inversions based only on the linklengths

Let:

S=length of shortest link

L=length of longest link

P=length of one remaining link

Q=length of other remaining link

Then if: S+L<=P+Q

THE GRASHOF CONDITION

The linkage is Grashof and at least onelink will be capable of making a fullrevolution with respect to the groundplane. This is called a Class I kinematicchain.

If the inequality is not true, then thelinkage is non-Grashof and no link will becapable of a complete revolution relativeto any other link. This is a Class IIkinematic chain.

The order of the assemble in thekinematic chain in S, L, P, Q, or S, P, L, Qor any other order, will not change theGrashof condition.

THE GRASHOF CONDITION

The motions possible from a fourbarlinkage will depend on both the Grashofcondition and the inversion chosen. Theinversions will be defined with respect tothe shortest link. The motions are:

For the Class I case, S + L < P + Q:

Ground either link adjacent to theshortest and you get a crank-rocker, inwhich the shortest link will fully rotateand the other link pivoted to groundwill oscillate.

THE GRASHOF CONDITION

THE GRASHOF CONDITION

Ground the shortest link and you willget a double-crank, in which both linkspivoted to ground make completeevolutions as does the coupler.

Ground the link opposite the shortestand you will get a Grashof double-rocker, in which both links pivoted toground oscillate and only the couplermakes a full revolution.

THE GRASHOF CONDITION

THE GRASHOF CONDITION

For the Class II case, S + L > P + Q:

All inversions will be triple-rockers inwhich no link can fully rotate.

THE GRASHOF CONDITION

THE GRASHOF CONDITION

For Class III case, S+L = P+Q

All inversion will be either double-cranks, or crank-rocker

THE GRASHOF CONDITION

For Class III case, S+L = P+Q

All inversion will be either double-cranks, or crank-rocker

THE GRASHOF CONDITION

For Class III case, Special Grashof Case

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