Machines ans Mechanisms: Applied Kinematic Analysis

Machines and Mechanisms: Applied
Kinematic Analysis, 4/e
Chapter 1
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


Kinematic analysis



Determine
 Position, displacement, rotation, speed, velocity, acceleration
Provide
 Geometry dimensions of the mechanism
 Operation range
Dynamic analysis


Deal with the way things move
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)


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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)




Simple link







A rigid body contains only two joints
Crank
Rocker
Complex link


Allow rotation and sliding
Cam joint
Gear connection
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


Locked mechanism


one degree of freedom
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,
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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
Y1
Y
r4
r2
r3
r3
r5
X1
r1
r4
X
(1) r 1  r 2  r 3  r 4  0
 r1s1   r2 c 2   r3c3   5.3 
  r c    r s    r s    3.2   0

 1 1  2 2   3 3  
r1  3,1  30,r2  4.9,r3  3.3
2 equations for 2 unknows  2 ,3
(2) r 3  r 4  r 5  0
 r3c3   r4 c 4   x1 
 r s    r s      0
 3 3   4 4  0.8
r1  10.1
2 equations for 2 unknows 4 and x1
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Y
r1
r2
r4
X
r3
r 1 r 2 r 3 r 4  0
 1.6  3c 2   r3c3   2.3
 1.5   3s    r s    0   0

  2  3 3 

r3  (3.92  1.22 )1/2
solve for 2 and 3
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Analysis of Mechanism Position
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Y
r1
r2
r3
X
r 1 r 2 r 3  0
50c1   40c 2   d1 
50 s    40s      0
0 

1

2
1  240,solve for 2 and d1
whenrotate15,1  255
50c1   40c 2   d 2 
50 s    40s      0
0 

1

2
solve for 2 and d 2
d  d1  d 2
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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
r2
r3
r1
r4
X
r 1 r 2 r 3 r 4  0
12c1   20c 2  15c3   25
12s    20s   15s    0   0



1

2
3

1  90,eqs.solve for 2 and 3
1  60,eqs.solve for 2 and 3
Calculate the difference of  2 inand 
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Y
r1
X
r3
r2
r 1 r 2 r 3  0
0.5c1  1.75c 2  1 
0.5s   1.75s    y   0
 

1

2
for1   2 ,solve for1and  ymax 
for1   2   ,solve for1and  ymin
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4.7 LIMITING POSITIONS:
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Y
r1
X
r2
r4
r3
r 1 r 2 r 3 r 4  0
for1   2 ,solve for1and 3 )max 
for1   2   ,solve for1and 3 )min
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Y
r1
X
r4
r2
r3
r 1 r 2 r 3 r 4  0
for 2  3 ,solve for1 max and  2 
for 2  3   ,solve for1 min 
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4.9 TRANSMISSION ANGLE
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Y
X
r3
r1
r2
r 1 r 2 r 3 r 4  0
0.5c1  lc 2   2.0
0.5s   ls    0   0


1
 2 
given1solve forland  2 
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Y
r 1 r 2 r 3  0
r2
 x 
r1  30,r2  70,r 3  
0

30


given1 solve for 2 and x
r3
r1
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Machines and Mechanisms: Applied Kinematic Analysis,
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Chapter 6 Velocity Analysis
6.2 LINEAR AND ANGULAR VELOCITY
6.2.2 Linear Velocity of a General Point
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VA cos   VB along ABlink
wAB  VA sin  /(link length)
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Y
r1
X
r2
r4
r3
r 1 r 2 r 3 r 4  0
 2 r 2  3r 3  4 r 4  0
eqs forunknowns3 and 4
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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
X
r1
r4
r3
r2
r 1 r 2 r 3  0
0 
 1r 1  2 r 2     0
5
 
eqs for1and 2
r  r 1 r 4
r   1r 1  2 r 4
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Y
r1
r2
X
r3
r 1 r 2 r 3  0
solve forand  
 1r 1  2 r 2  r2  0
vc 2 
1  5rad min,r 2  

vs 2 
eqs forunknowns2 and v
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Y
X
r1
r2
r3
r 1 r 2 r 3  0
 1r 1  2 r 2  r2  0
0 
r 2  
50 
eqs forunknowns1and 2 
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r2
r1
Y
r3
X
r 1 r 2 r 3  0
 1
r2  6, 2  340 r 3   
 3
eqs forunknownsr1and 1
 1r 1  2 r 2  r 2  0
8c 2 
r 2 

8s 2 
eqs forunknowns1and 2
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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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Y
X
r1
r2
r4
r3
r 1 r 2 r 3 r 4  0
 1r 1  2 r 2  3r 3  0
given3 solve for1and 2 
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Y
r3
r2
r4
r 1 r 2 r 3 r 4  0
r1
r4
r6
X
 2 r 2  3r 3  4 r 4  0
2  60rpm.solve for3 and 
r 4  r 5  r 6  0
r5
0 
 4 r 4  5 r 5     0
v
 
eqs forunknowns5 and v
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Y
r2
r1
r3
X
r4
r 1 r 2 r 3 r 4  0
 1r 1  2 r 2  3r 3  0
given 1 find 2 and 3 
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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
r2
r4
r3
r 1 r 2 r 3 r 4  0
 1r 1  2 r 2  3r 3  0
given 1 find 2 and 3
 1  1r 1    2  2   2 r 2    3  3  3r 3   0
solve for2 and 3
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r5
rp
rp  r 1  r 2  r 3  r 5  0
rp   1r 1  2 r 2  3  r 3  r 5 
rp 
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Y
X
r1
r2
r3
r 1 r 2 r 3  0
0 
 1r 1  2 r 2     0
v
 
solve for2 and v
0 
 1  1  1r 1    2  2   2 r 2      0
a
 
solve for2 and a
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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
r3
r2
X
r1
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7.10 ACCELERATION IMAGE ( Useless! )
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7.11 CORIOLIS ACCELERATION
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Y
r2 r3
X
r1
r 1 r 2 r 3  0
solve for1and  2
 1r 1  r 2  2 r 2  0
vc 
1  400,r 2   2  ,solve for2 and v
vs 2 
 ac 
 1  1r 1    2  2   2 r 2    2   0
 as 2 
solve for2 and a
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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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