Machines and Mechanisms: Applied Kinematic Analysis, 4/e Chapter 1

Machines and Mechanisms: Applied

Kinematic Analysis, 4/e

Chapter 1

Chap 1 Introduction

Machines and Mechanisms: Applied Kinematic Analysis, 4/e

David Myszka 2

© 2012, 2005, 2002, 1999 Pearson Higher Education,

Upper Saddle River, NJ 07458. • All Rights Reserved.

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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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


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Machines and Mechanisms: Applied Kinematic Analysis,

4/e

Chapter 4 Displacement Analysis

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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4.1 Vector Analysis of Displacement

Y

Y1 r2 r3 r3 r4 r5

X1 r1 r4

X

(1)

(2) r

1 r

2 r

3 r

4

0





 r

1



 r s

1 1 r c





1 1

 

  r c

2 2 r s





2 2







 



 r c r s



3 3



3 3









 

5.3









3.2





3,



1

30, r

2

4.9, r

3

3.3

2 equations for 2 unknows

 

2

,



3



0





 r

3 r

4 r

5



 r c

3 r s





3

3 3

0



 

 

 r c r s



4 4



4 4



 

 x

1

0.8









0 r

1



10.1

2 equations for 2 unknows



4

 

1


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Y r2 r1 r3 r4 r

1 r

2 r

3 r

4

0









1.6

1.5











3 c

3 s





2

2









 r c r s



3 3



3







 

2.3







0





0

 

3

(3.9

2



1.2 )

 

2 and

 

3

X


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Analysis of Mechanism Position


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r2 r3 r1 r

1 r

2 r

3

0





50

50 c s



1



1

40 c

40

 s



2

2 d

1 

0



240 , solve for

 and d

1

15 ,



1

255







50

50 c s



1



1

40 c

40

 s



2

2

  

2 d



0

  d

1

 d

2

Y


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X




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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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Y r1 r2 r4 r3 r

1 r

2 r

3 r

4

0





12

12 c s



1



1

20 c

20

 s



2

2







 





15

15 c s



3



3







 

25







0





0



1

90 , .

  

2 and

 

3



1

60 , .

  

2 and

 

3

Calculate the differenc e of



2 and



X


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Y r1 r3 r2

X r

1 r

2 r

3

0





0.5

c



1

0.5

s



1

1.75

c



1.75

s



2

2



1



0 for

 

1 2

,

 solve for



1 and y max

 for

  

1 2 solve for



1 and y min


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4.7 LIMITING POSITIONS:


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Y r1 r4 r2 r3

X r

1 r

2 r

3 r

4

0 for

 

2

,


 and

 

)

3 max

 for

  

2

, solve for

 and

 

)

3 min


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Y r1 r4 r2 r3

X r

1 r r

3 r for for

4

0

 

3

,


 and



  

, solve for




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4.9 TRANSMISSION ANGLE


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Y r3 r1 r2

X


David Myszka 58 r

1 r

2 r

3 r

4

0





0.5

c

0.5

s



1



1

  lc ls





2

2









2.0



0







0 given



1

   

2



r2 r3 r1

Y

X r

1 r r

3

0 r

1



30, r

2

70, r

  x





 

30







0 given



1

 

2

 


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Machines and Mechanisms: Applied Kinematic Analysis,

4/e

Chapter 6 Velocity Analysis

6.2 LINEAR AND ANGULAR VELOCITY

6.2.2 Linear Velocity of a General Point


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V

A cos

 w

AB



V

A

 

 

)



Y r1 r2 r4 r3 r

1 r

2 r

3 r

4

0

 r

2



3 r

3



4 r

4

0

2

   unknowns



3 and

 

4

X


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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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Y r1 r4

X r3 r2


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1 r

2 r

3

0

 r

1 1



2 r

2

0

5



0

  

1 and

 

2 r

 

1 r r

4

  r

1 1



2 r

4




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Y r1

X r3 r2

66 r

1 r

2 r

3



0

  and

 

 r

1 1



2 r r

2 2

0



1 rad min , r



 vc vs





2

2





   unknowns



2

 



r1 r2 r3

Y

X


David Myszka 67 r

1 r

2 r

3



1 r

1



0 r

2 r

2

0 r

2

   unknowns



1 and



2




David Myszka 68 r2 r1

Y r3

X r

1 r

2 r

3

0 r

2

6,



2

340

 r

    

1

 

1

 r

1 1



2 r

2 r

2



0 r

2





8 c

8 s





2

2





   unknowns



1 and

 

2



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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Y r4 r3 r1 r2

X


David Myszka 74 r

1 r

2 r

3 r

4

0

 r

1 1



2 r

2



3 r

3

0 given



3 solve for



1 and



2



Y r2 r1 r3 r4 r4

X r6 r5 r

1 r

2 r

3 r

4



2

0 r

2

 r

3 3



4 r

4

0



2

 

.

  

3 and

 

 r

4 r

5 r

6

0



4 r

4

 r

5 5

0



0

   unknowns



5




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r2 r1

Y


David Myszka 76 r4 r3

X r

1 r

2 r

3 r

4

 r

1 1



2 r

2

0



3 r

3

0 given



1 find



2 and



3



Machines and Mechanisms: Applied Kinematic Analysis, 4/e

Chapter 7 Acceleration Analysis

7.2 LINEAR ACCELERATION

7.2.1 Linear Acceleration of Rectilinear Points


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Y

X r1 r3 r2 r4


David Myszka r

1 r

2 r

3 r

4

 r

1 1



2 r

2

0



3 r

3

0 given



1 find



2 and

 

3



1

  

1

 r

1

   

2 2

 

2

 r

2

   

3 3

 

3

 r

3

 

 

2 and

 

3

0

79



r5 r p r p r

1 r

2 r

3 r

5 r p

0

  r

1 1

 r

2 2



3

 r

3

 r

5

 r p




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Y r1 r2 r3

X


David Myszka r

1 r

2 r

3

0



1 r

1



2 r

2

0



0

 

2



 

1

 

1

 r

1

   

2

 

2

 r

2

  

0

 

2



81




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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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Y

X

85



7.10 ACCELERATION IMAGE ( Useless! )


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7.11 CORIOLIS ACCELERATION


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David Myszka r2 r3

Y

X r1

88 r

1 r r



1 r

1 r

3

  and

 

2



0

2 r

2

0



1



400, r





 vc vs





2

2





 ,

   



1

  

1

 r

1

   

2

 

2

 r

2

 





 ac as





2

2







  



0



7.12 EQUIVALENT LINKAGES


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Chapter 9 Cams

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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Chapter 13 STATIC FORCE ANALYSIS

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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Machines and Mechanisms: Applied Kinematic Analysis, 4/e Chapter 1

Machines and Mechanisms: Applied

Kinematic Analysis, 4/e

Chapter 1

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Machines and Mechanisms: Applied Kinematic Analysis, 4/e Chapter 1