Kinematics of Machinery Through HyperWorks (History of ... - FTP ITB!

conjunctionfrictionΜηχανική

13 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

650 εμφανίσεις

Kinematics of Machinery Through HyperWorks
HIST
OR
Y
O
F
M
ECHANISM
AND
MA
CHINE
S
CIENCE
S
e
ries
Ed
ito
r
Ai
m
s
and
Scope
of
t
h
e
S
er
i
e
s
Thi
s
book
s
e
ri
es
ai
ms
t
o
es
t
a
bl
i
s
h
a
w
e
l
l
defi
n
ed
forum
for
Monographs
and
P
ro-
ceedings
on
the
H
is
tory
of
Mechanis
m
a
nd
Machine
S
cience
(MMS).
The
s
eries
publ
i
s
hes
w
orks
t
h
at
gi
v
e
an
o
v
e
rvi
e
w
o
f
t
he
hi
s
t
ori
cal
de
v
e
l
opment
s
,
from
t
he
earl
i
-
es
t
times
up
to
and
i
ncluding
the
r
ecent
p
as
t,
of
MMS
in
all
its
technical
as
pects
.
This
technical
approach
is
an
es
s
e
ntial
c
ha
r
acter
istic
o
f
th
e
s
er
ies.
By
d
iscu
ssin
g
t
echni
cal
det
a
i
l
s
and
formul
a
t
i
ons
and
e
v
e
n
reformul
a
t
i
n
g
t
hos
e
i
n
t
erms
of
modern
f
o
r
m
alism
s
th
e
p
o
ssib
ility
is
cr
eated
n
o
t
o
n
l
y
t
o
t
r
ack
th
e
h
isto
r
i
cal
tech
n
i
cal
d
e
v
e
l-
opments
b
u
t
a
ls
o
t
o
u
s
e
pas
t
e
xperiences
in
technical
teaching
a
nd
res
earch
today
.
In
order
t
o
d
o
s
o,
t
h
e
e
mphas
i
s
m
us
t
b
e
o
n
t
echni
cal
as
pect
s
rat
her
t
han
a
purel
y
hi
s
t
ori
cal
focus
,
al
t
hough
t
h
e
l
at
t
e
r
h
as
i
t
s
pl
ace
t
oo.
F
u
rt
hermore,
t
h
e
s
eri
e
s
w
i
l
l
cons
i
d
er
t
h
e
republ
i
cat
i
o
n
o
f
out
-of-pri
nt
ol
der
w
orks
with
En
g
lish
tr
a
n
s
latio
n
a
n
d
co
m
m
e
n
ts.
The
book
s
e
ri
es
i
s
i
n
t
e
nded
t
o
c
ol
l
ect
t
echni
cal
vi
e
w
s
o
n
h
i
s
t
o
ri
cal
de
v
e
l
opment
s
of
th
e
b
r
o
ad
field
o
f
MMS
in
a
u
n
i
q
u
e
f
r
a
m
e
th
at
can
b
e
seen
in
its
to
tality
as
an
En
-
c
y
cl
opaedi
a
of
t
h
e
H
i
s
t
o
ry
of
MMS
b
u
t
w
i
t
h
t
h
e
a
ddi
t
i
onal
purpos
e
o
f
a
rchi
vi
ng
and
teaching
t
he
His
t
ory
o
f
MMS
.
Therefore
th
e
book
s
e
ries
is
intended
not
only
f
or
re-
s
earchers
o
f
t
he
H
i
s
t
ory
o
f
E
ngi
neeri
n
g
b
ut
al
s
o
for
p
rofes
s
i
onal
s
and
s
t
udent
s
w
ho
are
i
nt
eres
t
e
d
i
n
obt
ai
ni
ng
a
c
l
ear
pers
pect
i
v
e
o
f
t
he
pas
t
for
t
hei
r
fut
u
re
t
echni
cal
w
o
rks
.
The
books
will
be
written
i
n
g
eneral
by
engineers
b
ut
not
only
f
or
engineers
.
about
fut
u
re
publ
i
cat
i
ons
w
i
t
h
i
n
t
h
e
s
eri
e
s
a
t
:
LA
R
M
:
L
aborat
ory
o
f
R
obot
i
c
s
a
nd
Mechat
roni
cs
V
i
a
D
i
B
i
a
s
i
o
43,
03043
C
a
s
s
i
no
(F
r)
It
al
y
F
o
r
o
the
r
title
s
publis
he
d
i
n
t
his
s
e
r
ie
s
,
go
to
Pro
s
p
ecti
v
e
a
u
t
h
o
r
s
a
n
d
ed
ito
rs
can
co
n
t
act
th
e
s
eries
e
d
ito
r
,
Pro
f
esso
r
M
.
C
eccarelli,
D
i
MS
A
T

U
ni
v
e
rs
i
t
y
of
C
a
s
s
i
no
www
.
s
pri
nger
.
com
/
seri
es/
7481
MAR
C
O
C
E
C
C
A
R
ELLI
Volume 18
E-mail:
ceccarelli@unicas.it
Kinematics of Machinery
Through HyperWorks
J.S. Rao
of being entered and e
x
ecuted on a computer system, for e
xclusi
v
e use by the purchaser of the work.
any means, electronic, mechanical, photocop
ying, microf
ilming, recording or otherwise, without written
No part of this w
ork may be reproduced, stored in a retrie
v
al system, or transmitted in an
y form or by
permission from the Publisher
, with the e
xception of an
y material supplied specif
ically for
the purpose
ISSN 1875-3442
e-ISSN 1875-3426
Springer Dordrecht Heidelberg London New York
Altair Engineering
Chief Science Officer
Outer Ring Road
560103 Bangalore
India
js.rao@altair.com
ISBN 978-94-007-1155-6
e-ISBN 978-94-007-1156-3
DOI 10.1007/978-94-007-1156-3
Every effort has been made to contact the copyright holders of the figures which have been reproduced
from other sources. Anyone with a copyright claim who has not been properly credited is requested to
contact the publishers, so that due acknowledgements may be made in subsequent editions.
© Springer Science+Business Media B.V. 2011
Printed on acid-free paper
Springer is part of Springer Science+Business Media (
www.springer.com
)
Cover design
: SPi Publisher Services
J.S. Rao
Library of Congress Control Number: 2011922909
Additional material to this book can be downloaded from http://extras.springer.com
Dedicated to the memory of my parents
Jammi Chikka Rao
Jammi Ramanamma

Contents
Pr
eface
.
.....
....
.....
.....
.....
.....
.....
.....
.....
.....
....
.....
.
x
i
1
B
eginnings
o
f
t
he
T
h
eory
of
M
a
chines
...
.....
.....
.....
....
.....
.
1
1
.
1
B
e
g
i
n
n
i
n
g
o
f
t
h
e
W
h
e
e
l
..
.....
.....
.....
.....
.....
....
.....
.
1
1.2
A
rchi
medes
(
287–212
B
C
)
.
....
.....
.....
.....
.....
....
.....
.
2
1
.
3
W
a
t
e
r
W
h
e
e
l
s
......
.....
.....
.....
.....
.....
.....
....
.....
.
3
1
.
4
W
in
d
M
ills
.
.
.
.....
.....
.....
.....
.....
.....
.....
....
.....
.
4
1
.
5
R
e
n
a
i
s
s
a
n
c
e
E
n
g
i
n
e
e
r
s
...
.....
.....
.....
.....
.....
....
.....
.
4
1.6
I
ndus
t
r
i
a
l
R
e
v
ol
ut
i
on
.
....
.....
.....
.....
.....
.....
....
.....
.
5
1
.
7
T
h
e
N
a
t
u
r
e
o
f
T
h
i
s
B
o
o
k
.
.....
.....
.....
.....
.....
....
.....
.
6
2
P
la
na
r
M
echa
n
isms
....
.....
.....
.....
.....
.....
.....
....
.....
.
9
2
.
1
B
a
s
i
c
K
i
n
e
m
a
t
i
c
C
o
n
c
e
p
t
s
.....
.....
.....
.....
.....
....
.....
.
1
0
2
.
2
E
l
e
m
e
n
t
a
r
y M
e
c
h
a
n
i
s
m
s
.
.
.....
.....
.....
.....
.....
....
.....
.
1
8
2
.
3
G
r
ü
b
l
e
r

s
C
r
i
t
e
r
i
o
n
f
o
r
P
l
a
n
a
r
M
e
c
h
a
n
i
s
m
s
.
.....
.....
....
.....
.
1
8
2
.
4
F
o
u
r
-
L
i
n
k C
h
a
i
n
s
..
.....
.....
.....
.....
.....
.....
....
.....
.
2
2
2
.
5
K
i
n
e
m
a
t
i
c
I
n
v
e
r
s
i
o
n
.....
.....
.....
.....
.....
.....
....
.....
.
2
5
2
.
6
A
d
d
i
t
i
o
n
a
l
P
r
o
b
l
e
m
s
.....
.....
.....
.....
.....
.....
....
.....
.
3
4
3
Ki
n
em
ati
c
A
n
al
ys
i
s
of
M
ech
an
i
s
m
s
.
.....
.....
.....
.....
....
.....
.
3
7
3
.
1
V
elo
c
ities
b
y
t
h
e
Cen
t
r
o
Meth
o
d
.....
.....
.....
.....
....
.....
.
4
0
3
.
2
R
e
l
a
t
i
v
e
V
e
l
o
c
i
t
y
E
q
u
a
t
i
o
n
.
....
.....
.....
.....
.....
....
.....
.
4
7
3.2.1
R
ot
at
i
o
n
o
f
a
R
i
gi
d
L
i
n
k
a
bout
a
F
i
x
ed
A
x
i
s
....
....
.....
.
4
7
3
.
2
.
2
R
elati
v
e
V
elo
c
ity
Eq
u
a
tio
n
o
f
T
w
o
Po
in
ts
o
n
a
R
ig
id
B
o
d
y
.
.....
.....
.....
.....
.....
.....
.....
....
.....
.
4
8
3.2.3
R
el
at
i
v
e
V
el
oci
t
y
Equat
i
o
n
o
f
T
w
o
C
o
i
n
ci
dent
P
o
i
n
t
s
B
e
l
ongi
ng
t
o
T
w
o
R
i
g
i
d
B
odi
es
....
.....
.....
....
.....
.
5
4
3.3
R
elati
v
e
A
cceleration
E
quation
.
.....
.....
.....
.....
....
.....
.
5
9
3.3.1
R
ot
at
i
o
n
o
f
a
R
i
gi
d
L
i
n
k
a
bout
a
F
i
x
ed
A
x
i
s
....
....
.....
.
5
9
3.3.2
R
elati
v
e
A
cceleration
o
f
T
w
o
Points
on
a
R
igid
B
ody
.....
.
6
0
vi
i
v
iii
Cont
ent
s
3.3.3
R
elati
v
e
A
cceleration
E
qua
tion
o
f
T
w
o
C
o
incident
Points
B
e
l
ongi
ng
t
o
T
w
o
R
i
g
i
d
B
odi
es
....
.....
.....
....
.....
.
6
7
3.4
A
cceleration
A
nalys
i
s
o
f
R
eci
procating
Engine
Mechanis
m
.
.....
.
7
4
3
.
4
.
1
K
l
e
i
n

s
C
o
n
s
t
r
u
c
t
i
o
n
...
.....
.....
.....
.....
....
.....
.
7
4
3
.
4
.
2
R
itter
h
au
s
C
o
n
s
tr
u
c
tio
n
.
.....
.....
.....
.....
....
.....
.
7
6
3
.
4
.
3
B
e
n
n
e
t

s
C
o
n
s
t
r
u
c
t
i
o
n
..
.....
.....
.....
.....
....
.....
.
7
7
3.5
A
nalytical
Determination
o
f
V
elocity
and
A
cceleration
o
f
t
he
P
i
s
t
o
n
..
.....
.....
.....
.....
.....
.....
.....
.....
....
.....
.
7
7
3.5.1
H
armonic
A
nalys
i
s
f
or
V
e
locity
and
A
cceleration
o
f
t
he
P
i
s
t
o
n
.
.....
.....
.....
.....
.....
.....
.....
....
.....
.
7
9
3
.
6
A
d
d
i
t
i
o
n
a
l
P
r
o
b
l
e
m
s
.....
.....
.....
.....
.....
.....
....
.....
.
8
0
4
S
trai
gh
t
L
i
n
e
M
oti
o
n
a
n
d
U
n
i
v
ers
al
C
o
u
p
l
i
n
g
.
.....
.....
....
.....
.
8
5
4
.
1
C
o
n
d
itio
n
f
o
r
Ex
act
Str
a
ig
h
t
Lin
e
Mo
tio
n
.
.
.....
.....
....
.....
.
8
6
4
.
2
E
x
a
c
t
S
t
r
a
i
g
h
t
L
i
n
e
M
o
t
i
o
n
M
e
c
h
a
n
i
s
m
s
...
.....
.....
....
.....
.
8
7
4
.
2
.
1
P
au
cellier
M
ech
an
ism
.
.
.....
.....
.....
.....
....
.....
.
8
7
4
.
2
.
2
H
a
r
t
M
e
c
h
a
n
i
s
m
..
.....
.....
.....
.....
.....
....
.....
.
8
7
4
.
2
.
3
S
c
o
t
t

R
u
s
s
e
l
M
e
c
h
a
n
i
s
m
.
....
.....
.....
.....
....
.....
.
8
9
4
.
3
A
p
p
r
o
x
i
m
a
t
e
S
t
r
a
i
g
h
t
L
i
n
e
M
o
t
i
o
n
M
e
c
h
a
n
i
s
m
s
.
.
.....
....
.....
.
8
9
4.3.1
M
odi

e
d
S
cot
t

R
u
s
s
e
l
(G
ras
s
hopper)
Mechani
s
m
.
.
.
.....
.
8
9
4
.
3
.
2
W
a
t
t
M
e
c
h
a
n
i
s
m
.
.
.....
.....
.....
.....
.....
....
.....
.
9
0
4
.
3
.
3
T
c
h
e
b
i
c
h
e
f
f
M
e
c
h
a
n
i
s
m
.....
.....
.....
.....
....
.....
.
9
1
4
.
3
.
4
R
o
b
e
r
t
S
t
r
a
i
g
h
t
L
i
n
e
M
e
c
h
a
n
i
s
m
...
.....
.....
....
.....
.
9
3
4
.
3
.
5
P
a
n
t
o
g
r
a
p
h
.
.....
.....
.....
.....
.....
.....
....
.....
.
9
5
4
.
3
.
6
B
e
a
m
E
n
g
i
n
e
.
....
.....
.....
.....
.....
.....
....
.....
.
9
5
4
.
3
.
7
R
i
c
h
a
r
d
s
I
n
d
i
c
a
t
o
r
.....
.....
.....
.....
.....
....
.....
.
9
5
4
.
3
.
8
C
r
o
s
b
y
I
n
d
i
c
a
t
o
r
.
.
.....
.....
.....
.....
.....
....
.....
.
9
6
4.3.9
D
obbi
e–McInnes
M
echani
s
m
.
.....
.....
.....
....
.....
.
9
7
4
.
4
S
t
e
e
r
i
n
g
G
e
a
r
M
e
c
h
a
n
i
s
m
.....
.....
.....
.....
.....
....
.....
.
9
7
4
.
4
.
1
D
a
v
i
s
S
t
e
e
r
i
n
g
G
e
a
r
M
e
c
h
a
n
i
s
m
.
...
.....
.....
....
.....
.
9
7
4
.
4
.
2
A
c
k
e
r
m
a
n
n
S
t
e
e
r
i
n
g
G
e
a
r
M
e
c
h
a
n
i
s
m
.
...
.....
....
.....
.
1
0
1
4
.
5
H
o
o
k
e

s
(
C
a
r
d
a
n
,U
n
i
v
e
r
s
a
l
)
J
o
i
n
t
o
r
[
U
n
i
v
e
r
s
a
l
C
o
u
p
l
i
n
g
]
.
.
.....
.
1
0
1
4.5.1
D
oubl
e
H
ook
e’
s
J
oi
nt
.
.
.
.....
.....
.....
.....
....
.....
.
1
0
4
4
.
6
S
o
l
v
e
d
P
r
o
b
l
e
m
s
...
.....
.....
.....
.....
.....
.....
....
.....
.
1
0
5
4
.
7
A
d
d
i
t
i
o
n
a
l
P
r
o
b
l
e
m
s
.....
.....
.....
.....
.....
.....
....
.....
.
1
1
6
5 C
a
m
s
...
....
.....
.....
.....
.....
.....
.....
.....
.....
....
.....
.
1
1
7
5
.
1
T
y
p
e
s
o
f
C
a
m
s
a
n
d
F
o
l
l
o
w
e
r
s
..
.....
.....
.....
.....
....
.....
.
1
1
7
5.2
D
is
placement
D
iagrams
.
.
.....
.....
.....
.....
.....
....
.....
.
1
2
1
5
.
3
D
i
s
k
C
a
m
w
i
t
h
K
n
i
f
e
-
E
d
g
e
F
o
l
l
o
w
e
r
.
.....
.....
.....
....
.....
.
1
4
0
5
.
4
T
r
a
n
s
l
a
t
i
n
g
R
o
l
l
e
r
F
o
l
l
o
w
e
r
....
.....
.....
.....
.....
....
.....
.
1
4
1
5
.
5
T
r
a
n
s
l
a
t
i
n
g
F
l
a
t
F
o
l
l
o
w
e
r
.
.....
.....
.....
.....
.....
....
.....
.
1
5
1
5
.
6
O
scillatin
g
F
lat
F
o
llo
wer
.
.....
.....
.....
.....
.....
....
.....
.
1
5
5
5
.
7
C
a
m
s
o
f
S
p
e
c
i

e
d
C
o
n
t
o
u
r
.
....
.....
.....
.....
.....
....
.....
.
1
5
7
5
.
8
S
o
l
v
e
d
P
r
o
b
l
e
m
s
...
.....
.....
.....
.....
.....
.....
....
.....
.
1
6
3
Cont
ent
s
ix
5
.
9
A
d
d
i
t
i
o
n
a
l
P
r
o
b
l
e
m
s
.....
.....
.....
.....
.....
.....
....
.....
.
1
8
5
6
Spur
G
e
a
r
s
.
.
.....
.....
.....
.....
.....
.....
.....
.....
....
.....
.
1
8
7
6
.
1
C
l
a
s
s
i

c
a
t
i
o
n
o
f
G
e
a
r
s
...
.....
.....
.....
.....
.....
....
.....
.
1
8
7
6
.
2
T
y
p
e
s
o
f
M
o
t
i
o
n
...
.....
.....
.....
.....
.....
.....
....
.....
.
1
9
2
6
.
3
N
o
m
e
n
c
l
a
t
u
r
e
.....
.....
.....
.....
.....
.....
.....
....
.....
.
1
9
4
6
.
4
L
a
w
o
f
G
e
a
r
T
o
o
t
h
A
c
t
i
o
n
.....
.....
.....
.....
.....
....
.....
.
1
9
8
6
.
5
I
n
v
o
l
u
t
e a
s
a
G
e
a
r
T
o
o
t
h
P
r
o

l
e
......
.....
.....
.....
....
.....
.
1
9
9
6.6
L
ayout
of
an
In
v
o
l
u
t
e
G
ear
S
e
t
.
.....
.....
.....
.....
....
.....
.
2
0
1
6.7
P
roduci
n
g
G
ear
T
eet
h
....
.....
.....
.....
.....
.....
....
.....
.
2
0
5
6
.
8
M
e
s
h
i
n
g
G
e
a
r
s
a
n
d
L
i
n
e
o
f
C
o
n
t
a
c
t
..
.....
.....
.....
....
.....
.
2
0
7
6
.
9
I
n
t
e
r
f
e
r
e
n
c
e o
f
I
n
v
o
l
u
t
e G
e
a
r
s
..
.....
.....
.....
.....
....
.....
.
2
0
7
6
.
1
0
M
i
n
i
m
u
m
N
u
m
b
e
r
o
f
T
e
e
t
h
t
o
A
v
o
i
d
I
n
t
e
r
f
e
r
e
n
c
e
.
.....
....
.....
.
2
1
0
6
.
1
1
C
o
n
t
a
c
t
R
a
t
i
o
......
.....
.....
.....
.....
.....
.....
....
.....
.
2
1
2
6
.
1
2
C
y
c
l
o
i
d
a
l
T
o
o
t
h
P
r
o

l
e
s
..
.....
.....
.....
.....
.....
....
.....
.
2
1
5
6
.
1
3
C
y
c
l
o
i
d
a
l
a
n
d
I
n
v
o
l
u
t
e
T
o
o
t
h
F
o
r
m
s
..
.....
.....
.....
....
.....
.
2
1
8
6
.
1
4
S
o
l
v
e
d
P
r
o
b
l
e
m
s
...
.....
.....
.....
.....
.....
.....
....
.....
.
2
1
8
6
.
1
5
A
d
d
i
t
i
o
n
a
l
P
r
o
b
l
e
m
s
.....
.....
.....
.....
.....
.....
....
.....
.
2
2
7
7
H
elical,
Spiral,
W
o
rm
and
B
e
v
el
Gears
..
.....
.....
.....
....
.....
.
2
2
9
7
.
1
I
n
v
o
l
u
t
e H
e
l
i
c
o
i
d
.
..
.....
.....
.....
.....
.....
.....
....
.....
.
2
2
9
7
.
2
H
e
l
i
c
a
l
G
e
a
r
T
o
o
t
h
R
e
l
a
t
i
o
n
s
...
.....
.....
.....
.....
....
.....
.
2
2
9
7
.
3
C
o
n
t
a
c
t
o
f
H
e
l
i
c
a
l
G
e
a
r
T
e
e
t
h
..
.....
.....
.....
.....
....
.....
.
2
3
3
7
.
4
H
e
l
i
c
a
l
G
e
a
r
C
a
l
c
u
l
a
t
i
o
n
s
......
.....
.....
.....
.....
....
.....
.
2
3
5
7
.
5
S
p
i
r
a
l
[
C
r
o
s
s
e
d
H
e
l
i
c
a
l
]
G
e
a
r
s
.
.
.....
.....
.....
.....
....
.....
.
2
3
5
7
.
6
W
o
r
m
G
e
a
r
i
n
g
.....
.....
.....
.....
.....
.....
.....
....
.....
.
2
3
6
7
.
7
B
e
v
e
l
G
e
a
r
s
..
.....
.....
.....
.....
.....
.....
.....
....
.....
.
2
3
9
7
.
8
F
o
r
m
a
t
i
o
n o
f
B
e
v
e
l
G
e
a
r
s
.
.....
.....
.....
.....
.....
....
.....
.
2
4
0
7
.
9
S
o
l
v
e
d
P
r
o
b
l
e
m
s
...
.....
.....
.....
.....
.....
.....
....
.....
.
2
4
2
7
.
1
0
A
d
d
i
t
i
o
n
a
l
P
r
o
b
l
e
m
s
.....
.....
.....
.....
.....
.....
....
.....
.
2
4
7
8
G
ear
T
rains
.
.....
.....
.....
.....
.....
.....
.....
.....
....
.....
.
2
4
9
8
.
1
C
l
a
s
s
i

c
a
t
i
o
n
o
f
G
e
a
r
T
r
a
i
n
s
...
.....
.....
.....
.....
....
.....
.
2
4
9
8
.
2
S
i
m
p
l
e
G
e
a
r
T
r
a
i
n
s
.
.....
.....
.....
.....
.....
.....
....
.....
.
2
5
0
8.3
C
ompound
G
ear
T
rai
ns
.
.
.
.....
.....
.....
.....
.....
....
.....
.
2
5
1
8
.
4
S
y
n
t
h
e
s
i
s
o
f
G
e
a
r
T
r
a
i
n
s
.
.
.....
.....
.....
.....
.....
....
.....
.
2
5
2
8
.
5
G
e
a
r
T
r
a
i
n
A
p
p
l
i
c
a
t
i
o
n
s
t
o
M
a
c
h
i
n
e
T
o
o
l
s
..
.....
.....
....
.....
.
2
5
3
8
.
6
E
p
i
c
y
c
l
i
c
T
r
a
i
n
s
.
...
.....
.....
.....
.....
.....
.....
....
.....
.
2
5
7
8
.
7
I
n
v
e
r
s
i
o
n
s
o
f
E
p
i
c
y
c
l
i
c
T
r
a
i
n
s
..
.....
.....
.....
.....
....
.....
.
2
5
8
8
.
8
D
i
f
f
e
r
e
n
t
i
a
l
T
r
a
i
n
s
.
.
.....
.....
.....
.....
.....
.....
....
.....
.
2
6
1
8
.
9
T
o
r
q
u
e
D
i
s
t
r
i
b
u
t
i
o
n
i
n
E
p
i
c
y
c
l
i
c
T
r
a
i
n
s
....
.....
.....
....
.....
.
2
6
2
8
.
1
0
E
x
a
m
p
l
e
o
f
a
n
E
p
i
c
y
c
l
i
c
T
r
a
i
n
.
.
.....
.....
.....
.....
....
.....
.
2
6
3
8.11
C
oupl
ed
Epi
c
ycl
i
c
T
rai
ns
.
.....
.....
.....
.....
.....
....
.....
.
2
6
4
8
.
1
2
W
i
l
s
o
n
F
o
u
r
-
S
p
e
e
d
A
u
t
o
m
o
b
i
l
e
G
e
a
r
B
o
x
.
.
.....
.....
....
.....
.
2
6
7
x
Cont
ent
s
8
.
1
3
S
o
l
v
e
d
P
r
o
b
l
e
m
s
...
.....
.....
.....
.....
.....
.....
....
.....
.
2
6
8
8
.
1
4
A
d
d
i
t
i
o
n
a
l
P
r
o
b
l
e
m
s
.....
.....
.....
.....
.....
.....
....
.....
.
2
7
7
Index
..
.....
....
.....
.....
.....
.....
.....
.....
.....
.....
....
.....
.
2
7
9
Pr
eface
The
T
heory
o
f
M
achi
n
es
w
a
s
borne
as
a
s
ubj
ect
w
i
t
h
t
h
e
Indus
t
ri
a
l
R
e
v
ol
ut
i
o
n
a
nd
t
h
e
b
i
rt
h
of
R
eci
procat
i
n
g
S
t
eam
Engi
ne
nearl
y
230
years
a
go.
The
reci
procat
i
n
g
s
t
eam
engi
ne
w
a
s
t
he
mai
n
w
o
rk
hors
e
for
j
us
t
o
v
e
r
hundred
years
duri
n
g
t
he
19t
h
cent
u
ry
and
g
radual
l
y
l
o
s
t
i
t
s
pl
ace
i
n
hi
s
t
ory
b
y
t
he
t
u
rn
of
20t
h
cent
u
ry
.
It
i
s
t
hen
t
h
e
t
urn
o
f
Int
ernal
C
omb
u
s
t
i
o
n
E
ngi
nes
a
nd
R
o
t
a
t
i
n
g
M
achi
n
ery
.
K
i
nemat
i
c
s
a
nd
D
ynami
cs
of
R
eci
procat
i
n
g
a
nd
R
o
t
a
t
i
n
g
m
achi
n
ery
i
s
t
he
fun-
damental
s
t
udy
to
mechanical
engineers
b
efore
p
roceeding
t
o
s
tres
s
d
es
ign.
Thes
e
anal
ys
es
w
e
re
done
mai
n
l
y
by
graphi
cal
met
hods
for
p
l
a
nar
m
echani
s
ms
as
t
h
e
y
ga
v
e
good
ins
i
ght
into
the
m
echanis
m
a
nd
repetiti
v
e
his
t
ory
o
f
v
elocities
,
accel-
erat
i
ons
,
s
t
a
t
i
c
and
dynami
c
forces
,
e
t
c
.
A
l
l
m
achi
n
es
are
p
eri
odi
c
i
n
operat
i
o
n
d
ependi
ng
on
t
h
ermodynami
c
c
ycl
e
s
for
e
x
ampl
e
one
re
v
o
l
u
t
i
o
n
i
n
a
t
w
o-s
t
rok
e
engi
ne
or
t
w
o
r
e
v
ol
ut
i
ons
i
n
a
f
our
-s
t
r
ok
e
engi
ne.
B
es
i
d
es
t
h
ermodynami
cs
as
a
f
undament
al
mechani
cal
engi
neeri
n
g
s
ubj
ect
,
Theory
of
Machines
is
the

rs
t
s
ubject
a
fre
s
h
entrant
t
o
m
echan
ical
engineering
s
t
udies
f
aces
.
The
concepts
of
mo
ving
machine
m
embers
o
v
e
r
a
period
of
thermo-
dynamic
c
ycle
and
t
he
v
a
riation
o
f
d
is
pl
acements
,
v
elocities
a
nd
accelerations
form
t
h
e
s
ubj
ect
of
K
i
nemat
i
c
s
.
H
e
re
w
e
do
not
ques
t
i
o
n
w
hat
m
ak
es
t
h
es
e
m
achi
n
e
m
em-
bers
mo
v
e
b
u
t
m
erel
y

nd
t
h
e
k
i
n
emat
i
c
s
w
hen
t
here
i
s
a
m
ot
i
on.
W
h
en
w
e
as
k
t
he
q
u
e
stio
n
o
f
f
o
r
ces
th
at
m
a
k
e
th
e
m
o
tio
n
,
we
ar
e
d
ealin
g
k
in
etics;
to
g
e
th
er
we
h
a
v
e
Dynamics
of
Machinery
.
W
h
en
we
include
the
m
achinery
a
s
p
ects
s
uch
a
s
links
,
kinematic
chains
,
m
echanis
ms
,
e
tc.,
to
fo
rm
a
g
i
v
en
machine
w
e
h
a
v
e
t
he
s
ubject
of
Theory
of
Machines
.
Usu
a
lly
th
is
su
b
j
ect
is
in
tr
o
d
u
ced
as
a
t
w
o
-
s
em
ester
c
o
u
r
se,
k
in
em
atics
a
n
d
k
i
-
net
i
c
s
s
i
mul
t
a
neous
l
y
w
i
t
h
Thermodynami
cs
or
H
eat
Engi
nes
b
efore
t
he
des
i
gn
of
machi
n
e
members
be
gi
ns
.
T
hi
s
book
forms
t
he
mat
e
ri
al
for

rs
t
s
emes
t
e
r
o
f
T
heory
of
Machines
.
A
s
t
h
i
s
s
ubj
ect
i
s
o
v
e
r
200
years
o
l
d
,
t
here
are
s
e
v
eral
t
e
xt
books
al
ready
a
v
a
i
l
a
bl
e.
The
n
e
w
books
that
appear
from
time
t
o
time
t
ak
e
i
nto
account
ne
w
t
echniques
a
v
ailable;
the
s
ubject
matter
its
elf
h
as
not
ch
anged
p
articularly
for
t
he
entry
l
e
v
el.
Wh
at
is
th
e
d
if
f
e
r
e
n
c
e
h
er
e
th
e
n
?
xi
xii Preface
This book attempts to bring in the machine live on to the screen and explain the
theory of machines concepts through animations and introduce how the problems
are solved in industry to get complete history in the shortest possible time rather
than using graphical (or analytical) methods that are in vogue even today.Thus the
student is introduced to the concepts through visual means and brings him close
to industrial applications by the end of the two semester program taking him well
equipped for design courses.
International Federation for the Promotion of Mechanismand Machine Science
(IFToMM) has developed a standard nomenclature and notation on Mechanismand
Machine Science and this book adopts these standards so that any communication
between scientists and teachers in classrooms across the world can be with the same
terminology causing no confusion.
This book adopts HyperWorks MotionSolve to performthe analysis and visual-
izations,though the book is independent of the requirement of any software.Having
this software helps in further studies and analysis.The avis in this book can be ac-
cessed fromextras.springer.comby using the ISBN;they are:Figs.2.1,2.3,2.4,2.5,
2.6,2.7,2.8,2.9,2.10,2.11b,2.12a,2.12b,2.13,2.20,2.21,2.22,2.23,2.24,2.25,
2.26,2.27,2.28,2.29,2.30,2.31,2.32,2.33,3.1,3.2a,3.2b,3.2c,3.5a,3.13f,3.20,
3.28,3.30,3.38,4.1,4.2,4.3,4.4,4.5,4.6,4.8,4.9,4.10,4.11,4.12a,4.12b,4.12c,
4.13,4.14,4.15,4.16,4.18,4.19a,4.19b,4.20,4.22a,4.22b,4.22c,5.1,5.2,5.3,5.4,
5.5a,5.5b,5.6a,5.6b,5.6c,5.7,5.17,5.18a,5.18b,5.26,5.29,5.30,5.31,5.32-33,
5.34-35,6.1,6.2a,6.5a,6.7b,6.10,6.18a,6.18b,6.23a,6.23b,6.23c,6.24a,6.24b,
7.4c,7.4d and 8.1.
The author acknowledges help given by various students and colleagues over
four decades.Of particular mention,I thank Professor J.Srinivas,Anil Sakhamuri,
Uday M.Udapi and Sundar Nadimpalli.I am also thankful to Mr.Pavankumar and
Mr.Nelson Dias of Altair Engineering India.
Finally,I amever so thankful to my beloved wife Indira for her understanding in
my work and cooperation.

Chapter
1
Beginnings
o
f
t
he
Theory
of
Machines
1
It
i
s
al
w
a
ys
f
a
s
c
i
n
at
i
n
g
t
o
kno
w
t
he
ori
g
i
n
s
o
f
a
n
y
s
ubj
ect
.
T
he
s
ubj
ect
of
Theory
of
Machi
n
es
be
gan
duri
n
g
t
he
era
o
f
J
ames
W
a
t
t
w
i
t
h
t
h
e
Indus
t
ri
a
l
R
e
v
ol
ut
i
on.
W
e
w
i
l
l
l
ook
at
w
h
at
happened
p
ri
or
t
o
t
h
i
s
.
1
.
1
B
eg
i
nni
ng
o
f
the
W
heel
During
the
Mes
olithic,
o
r
Middle
S
tone
Age,
s
o
me
man
y
thous
ands
of
years
a
go,
man
found
t
h
at
a
s
ect
i
o
n
o
f
a
t
ree
t
runk
coul
d
b
e
m
o
v
ed
more
eas
i
l
y
under
t
he
force
o
f
g
ra
vity
becaus
e
it
w
a
s
r
ound.
If
the
b
ranches
a
nd
twigs
o
f
t
he
trunk
were
r
e
m
o
v
e
d
,
th
e
s
p
eed
o
f
th
e
r
o
llin
g
l
o
g
im
p
r
o
v
e
d
.
Earl
y
m
en
be
gan
t
o
p
l
ace
runners
under
a
hea
v
y
l
oad,
w
h
i
c
h
t
he
y
d
i
s
co
v
e
red
w
oul
d
m
ak
e
i
t
eas
i
e
r
for
t
h
e
l
oad
t
o
d
rag.
Thi
s
w
a
s
t
he
i
n
v
e
nt
i
o
n
o
f
t
he
s
l
edge.
Men
t
hen
b
e
g
an
t
o
combi
n
e
t
he
rol
l
e
r
a
nd
t
h
e
s
l
e
dge.
A
s
t
he
s
l
edge
mo
v
e
d
forw
a
rd
o
v
e
r
t
he

r
s
t
roller
,
a
s
econd
roller
w
as
placed
under
t
he
front
end
t
o
carry
the
l
oad
wh
en
it
m
o
v
e
d
o
f
f
th
e

r
s
t
r
o
ller
.
I
t
w
a
s
d
isco
v
e
r
e
d
t
h
a
t
t
h
e
r
o
ller
s
wh
ich
car
r
i
ed
th
e
s
l
edge
became
g
roo
v
e
d
w
ith
us
e
a
nd
that
th
es
e
d
eep
groo
v
es
actually
allo
wed
t
he
s
l
edge
to
adv
a
nce
a
greater
dis
t
ance
befo
re
the
n
e
x
t
r
oller
w
as
needed
to
come
on.
Thus
,
t
he
rol
l
e
rs
w
e
re
changed
i
nt
o
w
heel
s
.
In
t
h
e
p
roces
s
o
f
doi
ng
s
o
,
s
ect
i
ons
of
w
ood
bet
w
een
t
h
e
g
roo
v
e
s
o
f
t
he
rol
l
e
r
w
ere
c
ut
a
w
ay
t
o
form
an
axl
e
and
w
ooden
pe
gs
were
f
a
s
t
ened
to
the
r
unners
on
each
s
i
de
of
the
a
xle.
A
s
light
impro
v
e
ment
w
a
s
m
ade
t
o
t
he
cart.
This
time,
ins
t
ead
of
us
i
n
g
p
e
g
s
t
o
j
oi
n
t
he
w
h
eel
s
t
o
t
he
axl
e
,
holes
for
t
he
axle
were
drilled
t
hrough
the
frame
of
the
cart.
Axle
and
w
heels
w
ere
no
w
m
ade
s
eparately
.
Th
e
wh
eel
is
p
r
o
b
a
b
l
y
t
h
e
m
o
st
im
p
o
r
tan
t
m
ech
an
ical
in
v
e
n
tio
n
o
f
a
ll
tim
e.
N
earl
y
e
v
ery
machi
n
e
b
ui
l
t
s
i
nce
t
he
be
gi
nni
ng
of
t
h
e
i
ndus
t
r
i
a
l
r
e
v
ol
ut
i
o
n
i
n
v
ol
v
e
s
a
s
i
ngl
e,
bas
i
c
p
ri
nci
p
l
e
embodi
ed
i
n
one
of
manki
nd’
s
t
rul
y
s
i
gni

cant
i
n
v
ent
i
ons
.
1
Thi
s
chapt
er
i
s
based
on
t
he
paper
“H
i
s
t
ory
of
Rot
at
i
ng
M
achi
nes”,
IFT
o
M
M
W
o
rkshop
on
t
h
e
Hi
st
ory
of
M
ac
hi
nes
and
M
e
c
hani
sms,
HM
M
2007
,
B
angal
ore,
D
ecem
ber
14,
2007.
1
Science 18, DOI 10.1007/978-94-007-1156-3_1, © Springer Science+Business Media B.V. 2011
J.S. Rao,

Kinematics of Machinery Through HyperWorks
, History of Mechanism and Machine
2
1
Be
gi
nni
ngs
of
t
he
T
heory
of
M
achi
nes
It
i
s
hard
t
o
i
m
agi
n
e
a
n
y
mechani
zed
s
y
s
t
em
t
h
at
w
oul
d
b
e
pos
s
i
bl
e
w
i
t
hout
t
h
e
w
h
eel
or
t
h
e
i
dea
o
f
a
s
y
mmet
ri
cal
component
mo
vi
ng
i
n
a
c
i
rcul
a
r
m
ot
i
o
n
o
n
a
n
axi
s
.
F
rom
t
i
n
y
w
at
ch
gears
t
o
a
ut
omobi
l
e
s
,
j
e
t
e
ngi
nes
a
nd
comput
er
di
s
k
dri
v
es
,
th
e
p
r
i
n
c
ip
le
is
th
e
s
am
e.
Agricultural
v
illages
h
ad
be
gun
to
de
v
e
lop
b
y
8000
B
C
.
This
is
kno
wn
as
the
N
e-
o
lith
ic
p
e
r
i
o
d
,
o
r
Ne
w
S
to
n
e
Ag
e.
Du
r
i
n
g
th
is
tim
e
t
h
e
slo
w
p
o
tter

s
w
h
eel
w
a
s
i
n
-
v
e
nt
ed.
I
n
a
bout
3000
B
C
Egypt
i
a
ns
de
v
e
l
oped
t
he
f
a
s
t
w
h
eel
,
a
compl
e
t
e
l
y
mobi
l
e
,
carefully
balanced
apparatus
o
f
s
tone.
B
as
ed
on
diagrams
on
ancient
c
lay
t
ablets
,
th
e
ear
liest
k
n
o
wn
u
s
e
o
f
t
h
i
s
e
ssen
tial
i
n
v
en
tio
n
w
as
a
p
o
tter

s
w
h
eel
th
at
w
a
s
u
sed
at
Ur
i
n
Mes
opot
ami
a
(part
o
f
m
odern
day
Iraq)
as
earl
y
as
3500
B
C
.
The

rs
t
u
s
e
of
t
h
e
w
heel
for
t
rans
port
a
t
i
o
n
w
as
probabl
y
o
n
M
es
opot
ami
a
n
c
hari
ot
s
i
n
3200
B
C
.
It
i
s
i
n
t
e
res
t
i
n
g
t
o
not
e
t
hat
w
heel
s
m
ay
ha
v
e
had
i
ndus
t
ri
a
l
o
r
m
anuf
act
uri
n
g
appl
i
cat
i
ons
before
t
h
e
y
w
e
re
us
ed
on
v
e
hi
cl
es
.
The
w
heel
w
a
s
furt
h
ered
i
m
pro
v
ed
on
l
a
t
e
r
b
y
t
he
Egypt
i
a
ns
,
w
ho
made
w
h
eel
s
w
i
t
h
s
pok
es
,
w
hi
ch
coul
d
b
e
f
ound
on
Egypt
i
a
n
c
hari
ot
s
o
f
a
round
2000
B
C
.
O
v
er
i
n
A
n
ci
ent
Indi
a,
chari
o
t
s
w
i
t
h
s
pok
ed
w
h
eel
s
d
at
i
n
g
b
ack
t
o
around
1500
B
C
w
e
re
al
s
o
di
s
c
o
v
e
red.
The
G
reeks
t
oo,
adopt
ed
t
h
e
i
dea
o
f
w
heel
-maki
n
g
from
t
he
Egyp-
tian
s
an
d
m
ad
e
f
u
r
th
er
im
p
r
o
v
em
en
ts
to
it.
Later
,
d
u
r
in
g
t
h
e
tim
e
o
f
t
h
e
Ro
m
a
n
Empi
re,
t
he
R
o
mans
t
o
o
e
ngaged
t
hems
el
v
e
s
i
n
w
heel
-maki
n
g
a
nd
produced
t
h
e
greates
t
v
ariety
of
wheeled
v
e
hicles
.
T
he
y
h
ad
chariots
for
w
ar
,
hunting,
and
r
acing,
t
w
o-w
h
eel
ed
f
a
rm
cart
s
,
c
o
v
e
red
carri
ages
,
h
ea
vy
four
-w
heel
ed
frei
ght
w
a
gons
and
pas
s
e
nger
c
oaches
.
W
ith
the
c
ollaps
e
o
f
t
he
R
o
man
E
mpir
e
i
n
A
D
476,
the
w
heel
became
w
idely
us
ed
for
w
ar
machines
acros
s
t
he
old
e
mp
i
re.
The
g
ri
ndi
ng
w
h
eel
w
a
s
i
nt
roduced
from
A
rabi
a
t
o
E
urope
i
n
t
h
e
m
i
ddl
e
a
ges
,
great
l
y
i
m
pro
v
i
n
g
t
he
ef
fect
of
bl
aded
combat
w
eapons
.
1.2
A
r
c
h
i
med
e
s
(
287–212
B
C
)
The

rs
t
t
o
s
ys
t
e
mat
i
z
e
t
he
s
i
mpl
e
machi
n
es
and
p
ropound
t
h
e
t
heory
o
f
t
hei
r
func-
t
i
ons
w
a
s
A
rchi
medes
o
f
S
yracus
e
i
n
S
i
ci
l
y
.
It
w
as
probabl
y
h
e
w
ho
i
n
v
e
nt
ed
t
h
e
compound
pul
l
e
y
,
a
d
e
v
i
c
e
for
i
n
creas
i
n
g
t
ract
i
o
n
o
r
l
i
ft
i
n
g
p
o
w
er
and
h
e
p
ro-
pounded
t
he
t
h
eory
of
t
h
e
l
e
v
er
,
bot
h
one-
a
nd
t
w
o-armed.
H
e
re
garded
t
h
e
w
heel
as
a
c
i
rcul
a
r

gure
d
es
cri
b
ed
by
a
rot
at
i
n
g
one-armed
l
e
v
e
r
,
and
t
he
s
c
re
w
a
s
t
he
ci
rcu-
l
a
r
a
nal
ogy
of
t
h
e
i
ncl
i
n
ed
pl
ane.
O
n
e
o
f
h
i
s
f
a
mous
s
a
yi
ngs
i
s
“G
i
v
e
m
e
a
pl
ace
t
o
stan
d
a
n
d
I
w
ill
m
o
v
e
th
e
ear
th
”.
Archimedes
recei
v
e
d
h
is
education
a
t
t
he
Uni
v
ers
ity
of
Ale
x
andria,
w
here
groups
o
f
m
a
th
em
atician
s
an
d
s
cien
tists
w
o
r
k
ed
,
d
e
v
o
tin
g
t
h
e
m
s
elv
e
s
t
o
t
h
e
co
n
s
tr
u
c
tio
n
o
f
numerous
f
a
s
c
i
n
at
i
n
g
m
achi
n
es
.
T
he
great
es
t
a
nd
mos
t
col
o
rful
o
f
w
hat
i
s
kno
w
n
as
t
h
e
A
l
e
xandri
a
n
s
chool
of
engi
neers
w
as
undoubt
edl
y
H
e
ro
w
h
o
l
i
v
ed
s
o
met
i
me
during
t
he
s
econd
century
B
C
.
His
b
es
t
i
n
v
ention
w
as
the
ael
opi
l
e
,
t
he
firs
t
reaction
t
u
rbi
n
e,
w
h
i
c
h
c
on
v
e
rt
ed
heat
i
n
t
o
mechani
cal
ener
gy
t
h
rough
t
h
e
m
edi
u
m
o
f
s
t
eam.
1.
3
W
at
er
W
heel
s
3
Hero

s
ael
opi
l
e
,
t
he

rs
t
react
i
o
n
t
urbi
ne,
c
oul
d
not
produce
u
s
e
ful
w
ork,
as
t
h
e
s
p
eed
w
a
s
not
s
u
f

ci
ent
t
o
c
reat
e
t
he
requi
red
h
i
g
h
h
ead
of
s
t
eam.
In
t
he
1780s
J
a
mes
W
at
t
w
ork
e
d
o
n
t
he
t
h
eoret
i
cal
operat
i
n
g
c
ondi
t
i
ons
of
a
react
i
o
n
t
urbi
ne
and
he
concl
uded
t
hat
s
uch
a
t
u
rbi
n
e
c
oul
d
not
be
b
u
i
l
t
gi
v
e
n
t
he
s
t
at
e
o
f
c
ont
emporary
t
echnol
ogy
.
1.3
W
ater
W
h
eel
s
In
al
l
l
i
k
el
i
hood,
t
h
e
earl
i
e
s
t
t
ool
s
e
mpl
o
yed
b
y
humanki
nd
for
c
rus
h
i
n
g
o
r
g
ri
nd-
ing
s
eeds
,
nuts
,
and
o
ther
food-s
t
uf
fs
c
ons
is
ted
o
f
little
more
than
a

at
rock,
upon
w
h
i
c
h
t
he
mat
e
ri
al
w
a
s
c
rus
h
ed
by
poundi
ng
w
i
t
h
a
s
t
one
or
t
ree
branch.
T
he
ar
-
chaeol
ogi
cal
records
s
ho
w
t
hat
a
s
earl
y
as
30,000
years
a
go,
C
ro-Magnon
art
i
s
t
s
empl
o
y
ed
t
h
e
m
ort
a
r
a
nd
pes
t
l
e
t
o
gri
n
d
a
nd
mi
x
t
he
pi
gment
s
t
h
e
y
us
ed
t
o
creat
e
their
m
agnificent
“ca
v
e-art”.
F
a
r
m
ore
e
f

ci
ent
t
han
t
he

a
t
rock
o
r
e
v
e
n
t
he
mort
ar
and
p
es
t
l
e
w
a
s
t
he
hand-
m
ill,
wh
ich
a
p
p
ear
s
t
o
h
a
v
e
l
o
n
g
p
r
e-
d
a
ted
t
h
e
ag
r
i
cu
ltu
r
a
l
r
e
v
o
l
u
tio
n
.
Th
e
h
an
d
m
ill
cons
i
s
t
s
of
a

at
rock,
o
ft
en
hol
l
o
w
e
d
o
r
c
onca
v
e,
on
w
h
i
c
h
t
he
grai
n,
s
eeds
,
or
ot
her
materials
i
s
p
laced,
a
nd
a
g
ri
nding
s
t
one,
w
hich
is
rolled
acros
s
t
he
grain,
thus
re-
ducing
t
he
grain
t
o

our
.
A
lthough
the
h
andmill
is
s
till,
today
,
in
us
e
i
n
m
an
y
p
arts
of
t
h
e
w
orl
d
,
a
pproxi
mat
e
l
y
2,000
years
a
go
humanki
nd
be
gan
t
o
h
arnes
s
w
a
t
e
r
-
po
w
e
r
t
o
t
urn
t
he
s
t
ones
t
hat
g
round
i
t
s
grai
n.
The
y
w
e
re
probabl
y
t
he

r
s
t
t
ool
s
f
or
creating
m
echanical
ener
gy
th
at
replaced
humans
a
nd
animals
.
Th
e

r
s
t
d
escr
ip
tio
n
o
f
a
w
a
ter
w
h
eel
is
f
r
o
m
V
itr
u
v
i
u
s
,
a
Ro
m
a
n
e
n
g
i
n
eer
(
3
1
B
C
–14
A
D
),
w
ho
compos
ed
a
1
0
v
ol
ume
t
reat
i
s
e
o
n
a
l
l
as
pect
s
o
f
R
oman
engi
neer
-
ing.
From
clas
s
i
cal
times
,
t
here
ha
v
e
e
x
is
ted
t
hree
general
v
arieties
o
f
w
ater
wheels
:
the
horizontal
wheel
and
t
w
o
v
a
riations
of
the
v
ertical
wheel.
W
a
t
e
rpo
w
er
w
a
s
a
n
i
mport
a
nt
s
ource
of
ener
gy
i
n
anci
ent
C
hi
nes
e
ci
vi
l
i
zat
i
on.
O
n
e
o
f
t
he
mos
t
i
n
t
r
i
gui
ng
appl
i
cat
i
ons
w
a
s
f
or
i
r
on
cas
t
i
ng.
A
ccordi
n
g
t
o
a
n
a
nci
e
nt
t
e
xt
,
i
n
3
1
A
D
t
he
engi
neer
T
u
S
h
i
h
i
n
v
e
nt
ed
a
w
ater
-po
w
ered
reciprocator
for
t
he
castin
g
o
f
(
ir
o
n
)
ag
r
i
cu
ltu
r
a
l
i
m
p
lem
e
n
t
s.
W
a
ter
p
o
w
er
w
a
s
a
lso
a
p
p
lied
a
t
a
n
ear
ly
dat
e
t
o
gri
ndi
ng
grai
n.
R
e
nai
s
s
a
nce
e
ngi
neers
s
t
udi
ed
t
h
e
w
at
erwheel
and
r
ealized
th
at
th
e
actio
n
o
f
w
a
ter
o
n
a
wheel
with
blades
w
ould
b
e
m
uch
m
ore
e
f
f
ecti
v
e
i
f
t
he
entire
w
heel
were
s
o
meho
w
e
ncl
o
s
e
d
i
n
a
ki
nd
of
chamber
.
The
y
kne
w
v
ery
w
el
l
t
hat
onl
y
a
s
mal
l
amount
of
the
w
ater
pus
hing
or
f
a
lling
o
n
a
wh
eel
blade
o
r
p
addle
actually
s
t
rik
es
i
t
,
and
t
hat
much
o
f
t
he
ener
gy
cont
ai
ned
i
n
t
he
onrus
hi
ng
w
a
t
e
r
i
s
l
os
t
o
r
n
e
v
er
actually
captured.
4
1
Be
gi
nni
ngs
of
t
he
T
heory
of
M
achi
nes
1.4
W
in
d
M
ills
O
v
er
5,000
years
a
go,
t
h
e
a
nci
e
nt
Egypt
i
a
ns
us
ed
w
i
nd
t
o
s
a
i
l
s
h
i
p
s
o
n
t
he
N
i
l
e
Ri
v
e
r
.
Wh
ile
th
e
p
r
o
lif
er
atio
n
o
f
th
e
w
a
ter
m
ill
w
a
s
in
f
u
ll
s
win
g
,
win
d
m
ills
ap
-
peared
t
o
harnes
s
m
ore
i
nani
mat
e
ener
gy
by
empl
o
y
i
n
g
w
i
n
d
s
ai
l
s
.
P
rot
o
t
ypes
o
f
win
d
m
ills
wer
e
p
r
o
b
a
b
l
y
k
n
o
wn
in
Per
s
ia
(
p
r
e
sen
t
d
a
y
I
r
a
n
)
as
ear
ly
as
7
t
h
cen
tu
r
y
A
D
w
i
t
h
t
h
e
s
ai
l
s
mount
ed
on
a
v
ert
i
cal
axi
s
.
T
o
w
ards
t
h
e
e
nd
of
t
h
e
12t
h
cent
u
ry
,
wind
mills
with
s
a
ils
mounted
on
a
horizont
al
axis
appeared
in
Europe;
t
he
firs
t
of
th
is
k
i
n
d
p
r
o
b
a
b
l
y
a
p
p
ear
ed
in
No
r
m
an
d
y
,
E
n
g
l
an
d
.
Th
ese
a
r
e
p
o
s
t
m
ills,
w
h
e
r
e
th
e
s
a
i
l
s
and
machi
n
ery
a
re
mount
ed
on
a
s
t
out
pos
t
a
nd
t
h
e
e
nt
i
re
a
pparat
u
s
h
as
t
o
be
r
o
tated
t
o
f
ace
th
e
win
d
.
T
w
o
cen
tu
r
i
es
later
t
h
e
to
wer
m
ill
w
a
s
i
n
t
r
o
d
u
ced
,
e
n
c
lo
sin
g
th
e
m
ach
in
er
y
i
n
a
statio
n
a
r
y
to
wer
s
o
t
h
a
t
o
n
l
y
t
h
e
cap
car
r
y
in
g
t
h
e
sails
n
eed
ed
to
b
e
tu
r
n
ed
to
th
e
w
i
nd.
In
1854
Daniel
Halliday
obtained
t
he
firs
t
American
windmill
patent.
H
is
wind-
mill
had
f
our
w
ooden
b
lades
t
hat
p
i
v
oted
and
w
ould
s
elf
a
djus
t
according
t
o
w
ind
s
p
eed.
I
t
h
ad
a
t
ail
w
hich
caus
e
d
i
t
t
o
t
urn
i
nto
t
he
wind.
1.5
R
enai
ssance
E
ngi
n
eers
The
c
redi
t
for
maki
ng
pres
s
u
re
e
x
ert
e
d
b
y
t
he
at
mos
phere
ent
i
rel
y
e
xpl
i
c
i
t
bel
ongs
t
o
O
t
t
o
v
o
n
G
ueri
ck
e,
w
h
o
i
n
1672
publ
i
s
hed
t
he
f
a
mous
book
i
n
w
h
i
c
h
h
e
d
es
cri
b
ed
hi
s
a
i
r
pump
a
nd
t
h
e
e
xperi
ment
s
t
hat
h
e
made
w
i
t
h
i
t
from
t
he
mi
d
1650s
onw
ards
.
O
n
ce
i
t
w
a
s
unders
t
ood
t
h
at
at
mos
phere
e
x
ert
s
pres
s
u
re,
i
t
w
as
a
m
at
t
e
r
o
f
c
reat
i
n
g
a
v
acu
u
m
an
d
u
tilizin
g
a
tm
o
s
p
h
e
r
ic
p
r
e
ssu
r
e
to
m
o
v
e
th
e
p
isto
n
in
a
c
y
lin
d
e
r
.
D
e
ni
s
P
api
n
(1647–1712)
a
F
rench
phys
i
c
i
s
t
,
mat
h
emat
i
c
i
a
n
a
nd
i
n
v
e
nt
or
i
s
bes
t
kno
w
n
for
h
i
s
pi
oneeri
n
g
i
n
v
ent
i
o
n
o
f
t
he
s
t
eam
di
ges
t
er
,
t
he
forerunner
o
f
t
he
s
t
eam
engi
ne.
H
e
v
i
s
i
t
e
d
L
ondon
i
n
1675,
and
w
ork
e
d
w
i
t
h
R
obert
B
o
yl
e
from
1676
to
1679,
publis
hing
an
account
of
his
w
ork
i
n
C
ont
i
nuat
i
o
n
o
f
N
e
w
Exper
i
m
e
nt
s
(1680).
D
uri
n
g
t
hi
s
p
eri
od,
P
a
pi
n
i
n
v
ent
e
d
t
he
s
t
eam
d
ig
es
ter
,
a
t
ype
of
pres
s
u
re
cook
er.
H
e

rs
t
a
ddres
s
e
d
t
he
R
o
yal
S
oci
e
t
y
i
n
1679
on
t
h
e
s
ubj
ect
of
hi
s
d
i
g
es
t
e
r
,
and
r
emained
m
os
tly
in
London
until
about
1687,
when
he
left
to
tak
e
up
an
acad-
emi
c
pos
t
i
n
G
erman
y
.
W
hi
l
e
i
n
Lei
p
zi
g
i
n
1690,
ha
vi
ng
obs
erv
e
d
t
he
mechani
cal
po
w
e
r
o
f
a
t
mos
pheri
c
p
res
s
u
re
on
hi
s

di
ges
t
er’,
he
b
u
i
l
t
a
model
o
f
a
pi
s
t
on
s
t
eam
engi
ne,
t
he

r
s
t
of
i
t
s
ki
nd.
Thomas
Sa
v
e
ry
(1650–1715)
w
a
s
a
n
E
nglis
h
m
ilitary
engineer
and
i
n
v
entor
w
ho
i
n
1698
pat
e
nt
ed
t
h
e

rs
t
c
rude
s
t
eam
engi
ne,
b
as
ed
on
D
e
ni
s
P
api
n

s
D
i
ges
t
er
or
pres
s
u
re
cook
er
of
1679.
H
i
s
m
achi
n
e
c
ons
i
s
t
e
d
o
f
a
cl
os
ed
v
e
s
s
e
l

l
l
e
d
w
i
t
h
w
a
t
e
r
i
n
t
o
w
h
i
c
h
s
t
eam
under
p
res
s
u
re
w
a
s
i
nt
roduced.
T
hi
s
forced
t
h
e
w
at
er
upw
ards
and
out
of
t
h
e
mi
n
e
s
haft
.
T
hen
a
col
d
w
a
t
e
r
s
pri
nkl
er
w
a
s
u
s
e
d
t
o
c
ondens
e
t
he
s
t
eam.
Thi
s
creat
ed
a
v
acuum
w
h
i
c
h
s
uck
e
d
m
ore
w
at
er
out
of
t
h
e
m
i
n
e
s
haft
t
h
rough
a
b
o
tto
m
v
alv
e
.
1.
6
I
ndust
r
i
al
R
e
v
ol
ut
i
on
5
In
1705
P
a
pi
n
d
e
v
el
oped
a
s
econd
s
t
eam
engi
ne,
w
i
t
h
t
h
e
h
el
p
o
f
G
ot
t
fri
ed
Lei
b
-
niz,
us
ing
s
team
pres
s
u
re
rather
than
at
mos
pheri
c
p
res
s
u
re.
P
api
n

s
s
t
eam
engi
ne
w
a
s
a
breakthrough
s
i
nce
H
ero’
s
reaction
t
urbine
of
the
s
econd
century
B
C
ne
v
e
r
f
u
n
c
tio
n
e
d
i
n
r
eality
.
The
N
e
w
comen
s
t
eam
engi
ne
w
a
s
t
he

rs
t
pract
i
cal
de
vi
ce
t
o
harnes
s
t
he
po
w
e
r
of
s
t
eam
t
o
produce
mechani
cal
w
o
rk.
N
e
w
comen’
s

rs
t
w
orki
ng
engi
ne
w
a
s
i
n-
s
t
al
l
e
d
a
t
a
coal
mi
ne
at
D
udl
e
y
C
a
s
t
l
e
i
n
S
t
af
fords
h
i
re
i
n
1712.
The
y
w
e
re
us
ed
t
h
roughout
Engl
and
a
nd
Europe
t
o
pump
w
at
er
out
of
mi
nes
s
t
a
rt
i
n
g
i
n
t
he
earl
y
18t
h
cent
u
ry
and
w
ere
t
he
bas
i
s
for
J
a
mes
W
at
t

s
l
at
er
i
m
pro
v
e
d
v
ers
i
ons
.
A
l
t
hough
W
a
t
t
i
s
f
a
r
m
ore
f
amous
t
oday
(due
l
a
r
g
el
y
t
o
M
at
t
h
e
w
B
oul
t
on’
s
t
i
rel
es
s
s
al
es
mans
hi
p),
N
e
w
c
omen
ri
ght
l
y
des
e
rv
es
t
h
e
m
aj
ori
t
y
of
t
h
e
c
redi
t
for
w
i
des
p
read
i
n
t
roduct
i
o
n
of
s
t
eam
po
w
e
r
.
1
.
6
I
ndus
tri
a
l
R
e
v
o
l
uti
o
n
B
e
tween
1780
and
1850,
in
a
s
pace
of
jus
t
s
e
v
e
n
d
ecades
,
t
he
f
ace
of
England
w
as
changed
b
y
a
f
a
r
-reaching
r
e
v
olution,
w
ithout
precedent
i
n
t
he
his
t
ory
o
f
m
ankind.
G
l
as
go
w
U
ni
v
e
rs
i
t
y
had
one
of
t
h
e
N
e
w
comen
e
ngi
nes
for
i
t
s
nat
u
ral
phi
l
o
s
o
-
phy
cl
as
s
.
In
1763,
one
hundred
years
a
ft
er
t
h
e
b
i
rt
h
of
N
e
w
c
omen,
t
hi
s
a
pparat
u
s
w
e
nt
out
of
order
a
nd
P
r
ofes
s
o
r
J
ohn
A
nders
on
ga
v
e
t
h
e
opport
uni
t
y
t
o
J
a
mes
W
at
t
(1736–1819)
t
o
repai
r
i
t
.
A
f
t
e
r
t
he
repai
r
and
w
hi
l
e
e
xperi
ment
i
n
g
w
i
t
h
i
t
,
he
w
a
s
s
t
ruck
by
t
h
e
e
normous
cons
umpt
i
o
n
o
f
s
t
eam;
a
t
e
v
e
ry
s
t
rok
e
,
t
he
c
y
l
i
nder
a
nd
p
i
sto
n
h
a
d
t
o
b
e
h
eated
to
th
e
t
em
p
e
r
a
tu
r
e
o
f
b
o
ilin
g
w
ater
an
d
c
o
o
l
ed
ag
ain
.
Th
is
p
r
e
v
en
ted
t
h
e
ap
p
a
r
a
tu
s
f
r
o
m
m
ak
in
g
,
with
th
e
a
v
a
ilab
l
e
b
o
iler
cap
acity
,
m
o
r
e
t
h
a
n
a
f
e
w
s
t
rok
e
s
e
v
e
ry
minute.
He
quickly
realized
that
the
w
as
tage
of
s
t
eam
is
inher
-
ent
i
n
t
he
des
i
gn
of
the
e
ngine
and
b
ecame
obs
es
s
e
d
w
ith
the
i
dea
o
f

nding
s
o
me
remedy
.
F
rom
t
he
di
s
c
o
v
e
ry
of
D
r
.
J
os
eph
B
l
ack
(1728–1799),
h
e
d
educed
t
h
at
t
h
e
l
o
s
s
of
l
a
t
e
nt
heat
w
a
s
t
he
mos
t
s
e
ri
ous
defect
i
n
t
h
e
N
e
w
comen
e
ngi
ne.
T
he
w
o
rk
o
f
Jam
e
s
W
att
i
s
t
h
u
s
th
e
a
p
p
licatio
n
o
f
s
cien
ce
to
en
g
i
n
eer
in
g
t
h
a
t
l
ed
to
th
e
b
ir
th
of
i
ndus
t
r
i
a
l
r
e
v
ol
ut
i
on.
In
1765
he
concei
v
e
d
t
he
i
d
ea
of
a
s
eparat
e
c
ondens
i
n
g
c
hamber
for
t
he
s
t
eam
engi
ne
t
o
s
e
parat
e
t
h
e
c
ondens
at
i
o
n
s
ys
t
e
m
from
t
he
c
y
l
i
nder
,
i
n
j
ect
i
n
g
t
he
cool
i
n
g
w
a
t
e
r
s
pray
i
n
a
s
econd
c
y
l
i
nder
,
connect
ed
t
o
t
h
e
m
ai
n
one.
W
hen
t
he
pi
s
t
on
had
reach
ed
th
e
t
o
p
o
f
th
e
c
y
lin
d
e
r
,
th
e
i
n
l
et
v
a
lv
e
w
as
clo
s
ed
an
d
t
h
e
v
a
lv
e
c
o
n
t
ro
llin
g
t
h
e
p
as
s
a
ge
t
o
t
h
e
c
ondens
er
w
a
s
opened.
Ext
e
rnal
at
mos
pheri
c
p
res
s
u
re
w
oul
d
t
hen
pus
h
t
he
pi
s
t
on
t
o
w
a
rds
t
he
condens
er
.
T
hus
t
h
e
c
ondens
er
coul
d
b
e
k
ept
c
ol
d
a
nd
under
l
es
s
t
han
a
t
m
os
pheri
c
p
res
s
u
re,
w
hi
l
e
t
h
e
c
yl
i
nder
remai
ned
hot
.
Import
a
nt
as
t
h
e
s
eparat
e
c
ondens
er
i
d
ea
w
a
s
,
i
n
t
h
e
ful
l
y
de
v
e
l
oped
v
ers
i
on
of
1775
t
h
at
w
e
nt
into
production,
changes
h
ad
to
be
more
f
a
r
-reaching.
There
w
as
no
s
p
ray
,
the
c
on-
dens
er
being
i
mmers
ed
in
a
w
ater
tank
and
a
t
each
s
t
rok
e
the
w
arm
c
ondens
ate
w
as
dra
w
n
o
f
f
and
s
ent
u
p
t
o
a
hot
w
e
l
l
by
a
v
acuum
pump
w
hi
ch
al
s
o
hel
p
ed
t
o
e
v
acuat
e
the
s
team
from
under
t
he
po
wer
c
ylinder
.
The
s
till-w
a
rm
condens
ate
w
as
rec
y
cled
as
f
eed
w
a
ter
f
o
r
th
e
b
o
iler
.
6
1
Be
gi
nni
ngs
of
t
he
T
heory
of
M
achi
nes
R
eciprocating
m
achinery
h
as
inherent
di
s
a
dv
ant
a
ges
a
t
h
i
g
h
s
peeds
;
t
h
e
y
ha
v
e
p
r
actically
d
i
sap
p
ear
ed
in
th
e
m
o
d
e
r
n
d
a
y
w
o
r
ld
.
T
h
e
r
e
ar
e
s
till
steam
lo
co
m
o
ti
v
e
s
operating
i
n
a
fe
w
p
laces
,
e
.g.,
F
a
iry
Q
ueen
,
t
he
oldes
t
running
vi
ntage
s
team
loco-
moti
v
e
in
the
w
orld
b
u
ilt
in
the
y
ear
1855
by
the
B
ritis
h

rm
Kins
ton,
Thomps
on
&
He
witso
n
fo
r
t
h
e
British

rm
East
In
d
i
a
R
ail
w
ay
s
a
n
d
o
ccasio
n
a
l
r
ecip
r
o
catin
g
engines
f
or
producing
s
mall
amounts
o
f
p
o
w
er
in
s
ugar
m
ills
,
b
ut
otherwis
e
t
he
y
a
re
gone.
I
nternal
c
omb
u
s
tion
e
ngines
s
till
thri
v
e
for
t
rans
portation,
po
wer
g
eneration,
a
n
d s
o o
n
.
1.7
T
h
e
Natu
r
e
of
T
h
is
B
ook
The
s
ubj
ect
Theory
of
Machi
n
es
i
s
about
200
years
o
l
d
and
h
as
under
gone
t
remen-
dous
changes
duri
n
g
t
hes
e
t
w
o
cent
u
ri
es
.
It
b
e
g
an
w
i
t
h
t
h
e
n
eed
t
o
de
v
e
l
o
p
un-
ders
t
a
ndi
ng
of
v
a
ri
ous
l
i
nks
of
di
s
p
arat
e