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Machines and Mechanisms: Applied

Kinematic Analysis, 4/e

Chapter 1

Machines and Mechanisms: Applied Kinematic Analysis, 4/e

David Myszka

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Chap 1 Introduction

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1.1 INTRODUCTION

Determine appropriate movement

of the wipers

View range

Tandem or opposite

Wipe angle

Location of pivots

Timing of wipers

Wiping velocity

The force acting on the machine

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1.2 MACHINES AND MECHANISMS

Machine

Devices used to alter,

transmit, and direct forces

to accomplish a specific

objective

Mechanism

Mechanical portion of a

machine that has the

function of transferring

motion and forces from a

power source to an output

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1.3 KINEMATICS

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Dynamics

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Kinematics

Kinematics

Deal with the way things move

Kinematic analysis

Determine

Position, displacement, rotation, speed, velocity, acceleration

Provide

Geometry dimensions of the mechanism

Operation range

Dynamic analysis

Power capacity, stability, member load

Planar mechanism – motion in 2D space

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1.4 MECHANISM TERMINOLOGY Mechanism

Synthesis is the process of developing mechanism to satisfy a set of performance requirements

for the machine.

Analysis ensures that the mechanism will exhibit motion to accomplish the requirements.

Linkage

Frame

Links– rigid body

Joint

Primary joint (full joint)

Revolute joint (pin or hinge joint)– pure

rotation

Sliding joint (piston or prism joint)– linear

sliding

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Higher-order joint (half joint)

Allow rotation and sliding

Cam joint

Gear connection

Simple link

A rigid body contains only two joints

Crank

Rocker

Complex link

A rigid body contains more than two joints

Rocker arm

Bellcrank

Point of interest

Actuator

A power source link

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1.5 Kinematic Diagram

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Kinematic Diagram

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Machines and Mechanisms: Applied Kinematic Analysis, 4/e

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Machines and Mechanisms: Applied Kinematic Analysis, 4/e

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1.7 MOBILITY

1.7.1 Gruebler’s Equation

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Constrained mechanism

one degree of freedom

Locked mechanism

Zero or negative degrees of freedom

Unconstrained mechanism

More than one degree of freedom

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Actuators and Drivers

Electric motors (AC)

Electric motors (DC)

Engines

Servomotors

Air or hydraulic motors

Hydraulic or pneumatic cylinders

Screw actuators

Manual

1.7.2 Actuators and Drivers

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1.8 COMMONLY USED LINKS AND JOINTS

1.8.1 Eccentric Crank

1.8.2 Pin-in-a-Slot Joint

1.8.3 Screw Joint

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1.9 SPECLAL CASES OF THE MOBILITY EQUATION

1.9.1 Coincident Joints

1.9.2

• One degree of freedom actually if pivoted links are the same size

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1.10 THE FOUR-BAR MECHANISM

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1.10.1 Degree-of-Freedom

s : short link

l : long link

p , q : intermediate link

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1.11 SLIDER-CRANK MECHANISM

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1.12 SPECIAL PURPOSE MECHANISMS

1.12.1 Straight-Line Mechanisms

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1.12.2 Parallelogram Mechanisms

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1.12.3 Quick-Return Mechanisms

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1.12.4 Scotch Yoke Mechanism

Machines and Mechanisms: Applied Kinematic Analysis,

4/e Chapter 4 Displacement Analysis

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4.2 POSITION 4.2.1 Position of a Point

4.3 DISPLACEMENT 4.3.1 Linear Displacement

4.3.2 Angular Displacement

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4.4 DISPLACEMENT ANALYSIS

Locate the positions of all

links as driver link is

displaced

Configuration

Positions of all the links

One degree of freedom

Moving one link will

precisely position all

other links

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4.5 DISPLACEMENT:GRAPHICAL ANALYSIS

4.5.1 Displacement of a Single Driving Link

4.5.2 Displacement of the Remaining Slave Links

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4.5.2 Displacement of the Remaining Slave Links

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r1

r2

r4

r3 r3 r5

r4

Y

X

X1

Y1

1 2 3 4

3 31 1 2 2

1 1 2 2 3 3

1 1 2 3

3 4 5

3 3 4 4 1

3 3 4 4

1

0

5.30

3.2

3, 30, 4.9, 3.3

0

00.8

10.1

r r r r

r cr s r c

rc r s r s

r r r

r r r

r c r c x

r s r s

r

2 equations for 2 unknows

2 equations for 2 unknows

(1)

(2) 2 3,

4 1and x

4.1 Vector Analysis of Displacement

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1 2 3 4

3 32

2 3 3

2 2 1/2

3

2 3

0

31.6 2.30

1.5 3 0

(3.9 1.2 )

r r r r

r cc

s r s

r

solve for and

X

Y

r1

r4

r3

r2

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Analysis of Mechanism Position

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1 2 3

1 2 1

1 2

1 2 1

1

1 2 2

1 2

2 2

1 2

0

50 400

50 40 0

240 ,

15 , 255

50 400

50 40 0

r r r

c c d

s s

solve for and d

when rotate

c c d

s s

solve for and d

d d d

r3

r1

Y

r2

X

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Machines and Mechanisms: Applied Kinematic Analysis, 4/e

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4.6.1 Closed-Form Position Analysis Equations for an In-Line

Slider-Crank

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4.6.2 Closed-Form Position Analysis Equations for an Offset

Slider-Crank

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Machines and Mechanisms: Applied Kinematic Analysis, 4/e

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1 2 3 4

31 2

1 2 3

1 2 3

1 2 3

0

1512 20 250

12 20 15 0

90 , .

60 , .

r r r r

cc c

s s s

eqs solve for and

eqs solve for and

Calculate the differenc

2 e of in and

r3

r2

Y

X r4

r1

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Machines and Mechanisms: Applied Kinematic Analysis, 4/e

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1 2 3

1 2

1 2

1 2 1 max

1 2 1 min

0

0.5 1.75 10

0.5 1.75

,

,

r r r

c c

s s y

for solve for and y

for solve for and y

r1

r3 r2

X

Y

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4.7 LIMITING POSITIONS:

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1 2 3 4

1 2 1 3 max

1 2 1 3 min

0

, )

, )

r r r r

for solve for and

for solve for and

Y

X

r2

r4

r3

r1

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1 2 3 4

2 3 1 max 2

2 3 1 min

0

,

,

r r r r

for solve for and

for solve for

r1

r2 r4

Y

r3

X

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4.9 TRANSMISSION ANGLE

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1 2 3 4

1 2

1 2

1 2

0

0.5 2.00

0.5 0

r r r r

c lc

s ls

given solve for l and

r2

r1

r3

Y

X

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1 2 3

1 2 3

1 2

0

30, 70, 030

r r r

xr r r

given solve for and x

Y

r1

r2 X

r3

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4/e

Chapter 6 Velocity Analysis

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6.2 LINEAR AND ANGULAR VELOCITY

6.2.2 Linear Velocity of a General Point

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cos

sin /( )

A B

AB A

V V along AB link

w V link length

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1 2 3 4

2 2 3 3 4 4

3 4

0

0

r r r r

r r r

eqs for unknowns and

r2 r1

r3

r4

X

Y

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6.6 GRAPHICAL VELOCITY ANALYSIS:RELATIVE VELOCITY METHOD

6.6.1 Points on Links Limited to Pure Rotation or Rectilinear Translation

6.6.2 General Points on a Floating Link

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1 2 3

1 1 2 2

1 2

1 4

1 1 2 4

0

00

5

r r r

r r

eqs for and

r r r

r r r

r1

r2

r3

r4

X

Y

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1 2 3

1 1 2 2 2

2

1 2

2

2

0

0

5 min ,

r r r

solve for and

r r r

vcrad r

vs

eqs for unknowns and v

Y

X

r3

r2

r1

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1 2 3

1 1 2 2 2

2

1 2

0

0

0

50

r r r

r r r

r

eqs for unknowns and

r2

r1

r3

X

Y

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1 2 3

2 2 3

1 1

1 1 2 2 2

2

2

2

1 2

0

16, 340

3

0

8

8

r r r

r r

eqs for unknowns r and

r r r

cr

s

eqs for unknowns and

r1

r3

r2

Y

X

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6.9 ALGEBRAIC SOLUTIONS

6.9.1 Slider-Crank Mechanism

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6.9.2 Four-Bar Mechanism

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6.10 INSTANTANEOUS CENTER OF ROTATION

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6.11 LOCATING INSTANT CENTERS

6.11.1 Primary Centers

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6.12 GRAPHICAL VELOCITY ANALYSIS:

INSTANT CENTER METHOD

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1 2 3 4

1 1 2 2 3 3

3 1 2

0

0

r r r r

r r r

given solve for and

r1

r2 r4

Y

r3

X

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1 2 3 4

2 2 3 3 4 4

2 3

4 5 6

4 4 5 5

5

0

0

60 .

0

00

r r r r

r r r

rpm solve for and

r r r

r rv

eqs for unknowns and v

r1

r2 r4

r3

r5

r4 X

r6

Y

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1 2 3 4

1 1 2 2 3 3

1 2 3

0

0

r r r r

r r r

given find and

r1 r2

r3

r4

X

Y

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Chapter 7 Acceleration Analysis

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7.2 LINEAR ACCELERATION

7.2.1 Linear Acceleration of Rectilinear Points

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1 2 3 4

1 1 2 2 3 3

1 2 3

1 1 1 2 2 2 2 3 3 3 3

2 3

0

0

0

r r r r

r r r

given find and

r r r

solve for and

r2 r1

r3

Y

r4

X

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pr

r5

1 2 3 5

1 1 2 2 3 3 5

0p

p

p

r r r r r

r r r r r

r

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1 2 3

1 1 2 2

2

1 1 1 1 2 2 2 2

2

0

00

00

r r r

r rv

solve for and v

r ra

solve for and a

r2 r3

r1 X

Y

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7.8 ALGEBRAIC SOLUTIONS

7.8.1 Slider-Crank Mechanism

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7.8.2 Four-Bar Mechanism

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r1

Y

r3

r2 X

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7.10 ACCELERATION IMAGE ( Useless! )

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7.11 CORIOLIS ACCELERATION

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1 2 3

1 2

1 1 2 2 2

2

1 2 2

2

2

1 1 1 2 2 2 2

2

2

0

0

400, ,

0

r r r

solve for and

r r r

vcr solve for and v

vs

acr r

as

solve for and a

r3 r2

r1

Y

X

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7.12 EQUIVALENT LINKAGES

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Chapter 9 Cams

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9.1 INTRODUCTION

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Plate cam

Cylindrical cam

Linear cam

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9.2 TYPES OF CAMS

Follower motion

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Follower position

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9.3 TYPES OF FOLLOWERS

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9.11 THE 4-STATION GENEVA MECHANISM

Constant rotation producing index motion

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13.3 MOMENTS AND TORQUES

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13.5 FREE-BODY DIAGRAMS

13.5.1 Drawing a Free-Body Diagram

13.5.2 Characterizing Contact Forces

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13.6 STATIC EQUILIBRIUM

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13.7 ANALYSIS OF A TWO-FORCE MEMBER

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Chapter 14 DYNAMIC FORCE ANALYSIS

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