Intern
ati
o
n
a
l Jo
urn
a
l
o
f
R
o
botics
a
nd Au
tom
a
tion
(I
JR
A)
Vol
.
3
,
No
. 2,
J
une
2
0
1
4
,
pp
. 11
8~
13
0
I
S
SN
: 208
9-4
8
5
6
1
18
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJRA
Desi
gn of Pian
o-
playing Robotic Hand
Jen
-
Ch
an
g L
i
n, Hsi
n
-
C
hen
g
L
i
,
Ku
o-
Che
n
g
Hu
an
g,
Sh
u-Wei
L
i
n
Department o
f
Mechanical Eng
i
neering
,
Minghs
in
University
of
Science and
Technolog
y
,
Taiw
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 30, 2013
Rev
i
sed
Feb
27
, 20
14
Accepted
Mar 15, 2014
Unlike the mar
k
et slowdown of industr
ial robo
ts, service & en
tertainment
robots have
be
en highl
y
reg
a
r
d
ed b
y
m
o
st r
obotics r
e
seach
and m
a
rke
t
research ag
encies. In this study
we
developed a
music play
ing r
obot (which
can also work as a service robo
t) for public per
f
ormance.
The r
e
search
is
m
a
inl
y
fo
cus
e
d on the m
echani
cal and
electrical contro
l of piano-play
ing
robot, th
e exp
l
or
ation of
correlations among mu
sic theor
y
, rh
y
t
hm
and piano
ke
y
s
, and
ev
ent
u
all
y
the
rese
ar
ch on p
l
a
y
ing
skill of
ke
ybo
a
rd
instrum
e
nt.
The p
i
ano-play
ing robot
is capable of
control
linear motor
,
serv
o-motor and
pneum
atic
devi
c
e
s
in
acco
rdanc
e
with th
e no
tes
a
nd rh
ythm
in or
der to
driv
e
the m
echani
c
a
l
s
t
ructure to p
r
oper
positions
for pressing the key
s
and
generating music. Th
e devices
used
for this robot are mainly
crucial
components produced b
y
HIWIN Technolog
y
Corp. The desig
n
of robotic
hand is based
on
the d
i
rection
of
anth
ropomorphic hand such
th
at
five fing
ers
will be used for
pla
y
ing pi
ano.
T
h
e finger
actu
a
ti
ons include a
c
t
i
o
n
s of finger
rotation
,
f
i
nger
pressing, and
finger liftin
g
;
t
i
m
e
requ
ired
for th
es
e 3 s
t
ages
must
meet the r
e
quirement of r
h
y
t
hm
. Th
e pur
pose of en
tertainment robot
can b
e
achi
e
ved
b
y
pl
a
y
ing
el
ec
tric
piano
with
robotic hand
, an
d we hop
e
this
resea
r
ch ca
n
contribu
te to the
dev
e
lopment of domestic
en
tertainment
music play
ing
ro
bots.
Keyword:
En
tertain
m
en
t robo
t
Fast finge
r
s
Pi
ano
-
pl
ay
i
ng ro
b
o
t
Ro
bo
tic h
a
nd
Ro
bo
tic p
a
lm
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Jen
-
C
h
an
g Lin,
Depa
rt
m
e
nt
of
M
echani
cal
E
n
gi
nee
r
i
n
g, M
i
n
ghsi
n
Uni
v
er
si
t
y
of
Sci
e
nce
an
d Tec
h
nol
ogy
,
Tai
w
an
Em
a
il: tsan
g
083
0@g
m
ai
l.co
m
1.
INTRODUCTION
Th
e
t
r
end
s
of ro
bo
tics research
h
a
s b
e
en
g
e
ttin
g
m
o
re
pop
ular in recen
t
years,
wh
ile th
ere h
a
v
e
b
e
en
cont
i
n
u
o
u
s
a
p
peara
n
ce
o
f
v
a
ri
o
u
s t
y
pes
o
f
r
o
bot
s
i
n
d
o
m
est
i
c
and i
n
t
e
rnat
i
o
nal
m
e
di
a wi
t
h
a
ppl
i
cat
i
ons
ran
g
i
n
g f
r
o
m
educat
i
o
n, e
n
t
e
rt
ai
nm
ent
,
medical care, to hom
e care service.
Th
is is
an
ind
i
catio
n
t
h
at th
e
scop
e of
r
obo
t app
licatio
n
has alr
ead
y
b
e
en
ex
tend
ed b
e
yo
nd
th
e f
actor
y and
en
ter
i
ng
o
u
r
d
a
ily liv
es and
vari
ous
ot
her
fi
el
ds.
Th
e
g
r
adu
a
lly ag
ing
p
opu
latio
n d
i
stri
b
u
tion in
th
is cen
t
u
ry
and
d
ecreasing
an
nu
al
b
i
rth
rates am
o
n
g
devel
opi
ng
co
unt
ri
es ha
ve l
e
d t
o
t
h
e a
g
i
n
g
soci
et
y
an
d
dram
at
i
c
change
t
o
t
h
e
p
r
o
d
u
ct
i
v
i
t
y
-ge
n
erat
i
n
g
y
o
u
ng/
m
i
ddl
e-
aged/
e
l
d
erl
y
p
o
p
u
l
a
t
i
on st
ru
ct
ures. T
h
us i
t
can
b
e
pred
icted
th
e i
m
ag
in
ary era of
robots in
fut
u
re world will soon be
develope
d an
d real
ized in hum
an technology wo
rld followi
ng t
h
is trend. Unlike the
m
a
rket
sl
ow
d
o
w
n
of i
n
d
u
st
ri
al
rob
o
t
s
, se
rv
i
ce & ent
e
rt
ai
nm
ent
rob
o
t
s
have
bee
n
hi
g
h
l
y
rega
rde
d
b
y
m
o
st
r
obo
tic
s
r
e
s
e
arc
h
an
d ma
r
k
e
t
r
e
s
e
a
r
ch
ag
en
cie
s
.
In
r
e
spo
n
s
e
to the t
r
end a
n
d pulse
of t
h
is
era a
n
d base
d
on the
con
s
i
d
erat
i
o
ns
of
m
a
nufact
u
r
i
n
g co
st
an
d
m
a
rket
dem
a
nd, e
d
ucat
i
o
n
,
l
e
i
s
ure,
an
d e
n
t
e
rt
ai
nm
ent
t
ypes
of
r
obo
ts ar
e go
ing
to b
e
th
e t
o
p cho
i
ces for
futu
r
e
i
n
v
e
stm
e
n
t
s. In
th
is study w
e
p
l
an
t
o
fo
cus
o
u
r
r
e
sear
ch on
ent
e
rt
ai
nm
ent
t
y
pe key
boa
r
d
i
n
st
r
u
m
e
nt
pl
ay
i
ng
r
o
b
o
t
s
.
Key
b
o
ar
d i
n
st
r
u
m
e
nt
i
n
cl
udes
har
p
si
ch
or
d,
o
r
ga
n,
pi
an
o an
d el
ect
ro
ni
c ke
y
boa
rd
, w
h
i
l
e
m
u
si
c
t
ones
o
f
sp
eci
f
i
c fr
eq
u
e
n
c
ies ar
e
gen
e
r
a
ted
b
y
tap
p
i
n
g
k
e
ys b
y
f
i
ng
er
s.
K
e
yboar
d
in
stru
m
e
n
t
is su
itab
l
e fo
r
so
lo or
accom
p
anim
en
t with wide
popula
r
ity a
m
ong gene
ral public
. Along with t
h
e enha
nce
d
living sta
n
dards in our
co
un
tr
y,
p
i
ano
an
d
electron
i
c Th
e
4
3
r
d
In
tl. Sy
m
p
. on
Robo
tics (
I
SR20
12)
,Taip
e
i,
Taiw
an
,
A
u
g
.
29
-3
1, 2
012
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3,
No
. 2,
J
u
ne 2
0
14:
1
1
8
– 13
0
11
9
key
b
o
ar
d ha
ve
becom
e
t
h
e im
port
a
nt
i
n
st
r
u
m
e
nt
s for m
a
ny
fam
i
l
i
e
s t
o
enco
u
r
age t
h
ei
r chi
l
d
ren t
o
l
e
arn
ho
w
to
p
l
ay. In
light o
f
th
is
po
pu
larity o
f
k
e
ybo
ard
in
stru
m
e
nt
and t
h
e a
dva
nce
m
ent
of
ro
b
o
t
i
c
t
echn
o
l
o
gy
, i
n
t
h
i
s
pr
o
j
ect
we pl
an
t
o
devel
op
a ro
b
o
t
whi
c
h
i
s
capabl
e
of pl
a
y
i
ng
key
boa
r
d
i
n
st
rum
e
nt
.
Th
ere
ha
ve been m
a
ny
m
u
si
c pl
ayi
n
g
ro
bot
s de
vel
o
pm
ent
i
n
vari
ous c
o
unt
ri
es
.
Toy
o
t
a
M
o
t
o
r C
o
r
p
orat
i
o
n (TM
C
) [
1
]
i
n
Japa
n
devel
ope
d Pa
rt
ner R
o
b
o
t
i
n
2
0
0
4
f
o
r t
h
e
20
05
Wo
rl
d E
x
p
o
si
t
i
on i
n
Ai
chi
,
Japa
n w
h
i
c
h was s
p
eci
al
i
zed i
n
han
d
m
o
t
i
ons suc
h
as m
u
si
c
pl
ay
i
ng. T
h
e fi
rst
gene
rat
i
o
n of t
h
i
s
r
o
bot
i
s
capabl
e
o
f
pl
a
y
i
ng t
r
um
pet
for t
h
e
p
u
rp
o
s
e
o
f
edu
t
ain
m
en
t. The n
e
w m
o
d
e
l
o
f
Partn
e
r R
o
bo
t [2
] ann
o
u
n
c
ed
in
Dece
m
b
er 200
7
utilized
tech
no
log
i
es
of precise co
n
t
ro
l and
coo
r
d
i
natio
n
for
en
h
a
n
c
ing
th
e flex
ib
ilities o
f
p
a
lm
an
d
arm
lea
d
ing
t
o
ad
d
ition
a
l v
i
o
lin
-p
layin
g
featu
r
e. Th
e
W
a
sed
a
Un
iv
er
sity in
Jap
a
n
an
nou
n
c
ed
WA
B
O
T-2
[3
] in
1984
as
a
ro
b
o
t
capa
b
l
e
of
pl
ay
i
ng
o
r
g
a
n i
n
acc
or
da
nce wi
t
h
m
u
sic st
anda
rd
. T
h
e next
y
ear
WA
SUB
O
T
[
4
]
wa
s
an
nou
n
c
ed wit
h
add
itio
n
a
l m
u
sic sco
r
e readin
g feature and cap
ab
ility o
f
p
l
ayin
g k
e
y
b
oard in
stru
m
e
n
t
s with
16
ki
n
d
s o
f
t
u
nes.
Al
t
h
o
u
gh
al
l
aforem
ent
i
one
d m
u
si
c ro
bot
s a
r
e capa
b
l
e
of creat
i
n
g
di
ffe
re
nt
m
u
si
c, t
h
ey
h
a
v
e
b
e
en
li
mited
to
m
ech
an
ical fin
g
er mo
tio
ns or m
u
sic p
l
ayin
g
wit
h
in
sm
all aco
u
s
tic rang
e, an
d
t
h
e
in
stru
m
e
n
t
s in u
s
e are li
m
i
t
e
d
to certain
mech
an
is
m
wh
ile th
e en
tire acou
s
tic range h
a
s no
t
b
e
en
fu
lly
u
tilized
.
W
e
ho
p
e
th
e
d
e
velop
m
en
t o
f
th
is
keyb
o
a
rd
i
n
st
rumen
t
p
l
ayin
g
ro
bo
t can
b
e
d
i
fferen
t fro
m
o
t
hers as
a
m
u
sic robot whic
h plays
music faster wit
h
out being li
mited
b
y
certain
mech
an
ism
.
We wou
l
d
lik
e to fu
lly
u
tilize th
e ex
istin
g
rob
o
tic
d
e
sig
n
cap
a
b
ility
o
f
ou
r schoo
l in
ord
e
r t
o
d
e
v
e
lop
a
p
r
od
u
c
t filled
with
m
a
rk
et
p
o
t
en
tial.
We
wo
ul
d
l
i
k
e
t
o
ha
ve t
h
e
el
ect
ro
ni
c key
b
o
a
rd
pl
ay
i
n
g
ro
bot
de
vel
o
pe
d
by
t
h
i
s
p
r
o
j
ect
t
o
pl
ay
t
h
e
electro
n
i
c
k
e
y
b
o
a
rd
with an
t
h
rop
o
m
o
r
ph
ic
ap
pro
ach wh
ile u
tilizin
g
lin
ear m
o
to
r, step
m
o
to
r and
pn
eu
m
a
t
i
c
cylin
d
e
r to
con
t
ro
l th
e
m
ech
an
ism
o
f
m
u
sic playing robot. The m
echanical
-electrical
syste
m
we utilize is
com
posed o
f
c
o
m
put
er base
d
cont
r
o
l
l
e
rs, w
h
ere t
w
o set
s
o
f
lin
ear m
o
to
rs sh
aring
the s
a
m
e
driver boa
r
d are
use
d
for drive
two palm
s. There are
five
fingers
with each palm
, and th
ere are one
joi
n
t mechanism
an
d one
finger m
echanism in each fi
nger c
ont
rolled
by step m
o
tor and
pneum
a
tic
device. T
h
e st
ep m
o
tor, pne
u
matic
devi
ce a
n
d l
i
n
e
a
r m
o
t
o
r are c
o
nt
r
o
l
l
e
d by
t
h
e
sy
st
em
t
h
ro
ugh
FPGA
con
t
ro
ller
s
. Ev
er
y
no
te is g
e
n
e
rated
with
t
h
e ro
b
o
t
t
o
u
c
hi
n
g
t
h
e
key
i
n
fo
ur st
a
g
es:
p
a
lm
m
ovem
e
nt
(i
ncl
u
di
n
g
fi
n
g
er
rot
a
t
i
o
n)
, f
i
nge
r p
r
essi
n
g
,
fi
nge
r
hol
ding,
a
n
d finge
r
releasi
n
g. Upon recei
ving
inform
ation of m
u
sic note a
n
d
rhyt
hm
, the system
wil
l
det
e
rm
i
n
e next
t
a
rget
ed
p
o
si
t
i
on
f
o
r m
u
si
c p
l
ay
i
ng base
d
o
n
m
u
si
c not
e i
n
f
o
rm
at
i
on. Fi
gu
re
1 i
s
com
pos
ed
w
ith
an
thr
opom
o
r
p
h
i
c ap
pr
oach
.
Fi
gu
re
1.
O
v
er
al
l
di
agra
m
of
mechanical ha
nds
2.
DESIG
N
OF HORIZ
ONTAL
H
A
ND MOVE
MENT
In a
u
t
o
m
a
t
i
c
prod
uct
i
o
n p
r
oce
ss t
h
e l
i
n
ear m
ovem
e
nt
m
echani
s
m
i
s
t
h
e ki
nd
of m
o
st
fre
que
nt
l
y
seen
appl
i
cat
i
o
n car
ri
er wi
t
h
de
g
r
e
e
of fr
eed
om
of o
n
e t
o
m
u
l
t
i
p
l
e
dim
e
nsi
o
n
s
. The
r
e i
s
m
o
re t
h
an
one
ki
nd
of
mech
an
ism
d
e
sig
n
for selectio
n. Th
e classificatio
n
b
a
se
d
o
n
m
o
v
e
m
e
n
t
style will lead
to
th
e categ
ories o
f
i
ndi
rect
t
r
a
n
sm
i
ssi
on a
nd
di
re
ct
t
r
ansm
i
ssi
on. The i
ndi
rect
t
r
ansm
i
ssi
on i
s
t
h
e m
o
st
wi
del
y
used
fo
rm
wher
e
rot
a
t
i
n
g m
ovem
e
nt
i
s
conv
ert
e
d i
n
t
o
l
i
n
ear m
ovem
e
nt
t
h
ro
u
gh m
e
chani
cal
m
echani
s
m
.
The com
m
on
exam
ples of indirect transm
is
sion a
r
e ball sc
rew m
echan
i
s
m
,
rack and
pi
ni
o
n
m
echani
s
m
s
, and con
v
e
y
or bel
t
.
The exam
ples of direct tra
n
smi
ssion include pneum
a
tic
device,
hydr
aulic device and linear
m
o
tor. For
p
n
e
u
m
atic an
d
h
y
d
r
au
lic d
e
v
i
ces to
ach
iev
e
en
erg
y
tran
sm
issio
n
, flu
i
d
m
u
st b
e
u
s
ed
as th
e m
e
d
i
a. Th
is will
n
o
t
on
ly in
crease th
e
syste
m
co
m
p
lex
ity, bu
t also lead to v
a
riou
s issu
es su
ch
as m
a
in
t
e
n
a
n
c
e an
d reg
u
l
ar
service, m
e
dia replacem
ent, and i
n
crease
d
c
o
st. T
h
e linear
m
o
tor with el
ectrom
a
gnetic field as the media is
cap
ab
le of
g
r
eatly red
u
c
i
n
g
syste
m
co
m
p
l
e
x
ity and
is
s
u
es of m
a
intenance a
n
d se
rvi
ce. T
h
e i
n
dust
ry ha
s
al
way
s
bee
n
p
u
rs
ui
n
g
hi
g
h
e
r
pr
eci
si
on
, m
o
r
e
ra
pi
d
pr
o
duc
t
i
on, a
n
d l
e
ss
bu
r
d
en
o
f
m
a
int
e
na
nce,
w
h
i
l
e
l
i
n
ear
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
D
e
sign
o
f
Piano
-p
la
yi
n
g
Robo
tic Ha
nd
(Jen-
C
ha
ng
Lin
)
12
0
m
o
tor can m
e
et all these criteria. The c
o
ntact dri
v
in
g
syste
m
o
f
lin
ear m
o
to
r has
in
trodu
ced
stru
ctural
revo
lu
tion
for
trad
itio
n
a
l t
o
o
l
m
ach
in
e, au
tomatio
n
equ
i
p
m
en
t and
insp
ectio
n
in
st
ru
m
e
n
t
s with
n
o
n
e
ed
for
beari
ngs
an
d c
o
u
p
l
i
n
gs.
2.
1.
An
al
ysi
s
o
f
H
a
nd
Mo
vi
n
g
T
i
me
There a
r
e numerous
factors affecting the
m
oving
s
p
ee
d of the m
e
c
h
anical ha
nd.
First we can
ex
clud
e th
e
weig
h
t
fact
o
r
and
calcu
late th
e resu
lt of in
itial stag
e o
f
h
a
n
d
sp
eed
.
So
far th
e hand
pro
m
o
t
er
m
ovem
e
nt
s can f
o
l
l
o
w se
ver
a
l
fact
ors s
u
ch
as t
h
e i
n
t
e
rval
cont
ai
ni
ng se
ven
key
s
(C
,
D
,E,F
,G,
A
,B
) o
b
t
a
i
n
e
d
fr
om
research
on
f
u
ndam
e
nt
al
acou
s
t
i
c
ra
ng
e, t
h
e
t
i
m
e
req
u
i
r
e
d
f
o
r t
h
e
h
a
nd
t
o
m
ove f
r
o
m
one i
n
t
e
rva
l
t
o
t
h
e
next
, t
h
e st
udy
on basi
c di
m
e
nsi
o
n o
f
pi
an
o,
t
h
e l
e
ngt
h o
f
pi
an
o key
s
, an
d t
h
e ha
nd m
ovi
n
g
spee
d fr
o
m
t
h
e
l
e
ft
-m
ost
si
de to t
h
e ri
g
h
t
-
m
o
st
si
de. The st
ud
y
shows t
h
e
r
e are t
w
o st
ages
of t
h
e seq
u
e
n
c
e
of ha
nd m
ovem
e
nt
as sh
o
w
n
i
n
Fi
gu
re
2:
t
h
e
s
p
e
e
d
of
m
ovem
e
nt
f
r
om
C
5
t
o
F5,
an
d
t
h
e
sp
eed
of
m
ovem
e
nt
f
r
o
m
F5 t
o
C
6
o
f
th
e n
e
x
t
in
terval.
Fig
u
re
2
.
Fing
er m
o
v
e
m
e
n
t
p
o
sitio
n
2.
2.
An
al
ysi
s
o
n
the
Sel
ecti
o
n o
f
L
i
ne
ar
M
o
t
o
r
The m
ovem
e
nt of m
echani
cal
han
d
i
s
d
r
i
v
e
n
by
th
e lin
ear
m
o
to
r. A certain
distance of mechanica
l
hand m
ovem
e
nt will be set for calc
u
lation
of t
h
e speed
, a
cceleration a
n
d ti
m
e
requi
re
d for
suc
h
m
ovem
e
nt.
As one
of the
necessa
ry factors
for
procure
m
ent of linear
m
o
to
r, this setting
will lead to
m
o
re accurate spee
d
of
l
i
n
ear m
o
t
o
r
d
u
ri
ng
t
h
e m
ovem
e
nt
.
This calculation is base
d on the relations
hip be
twee
n s
p
eed and accel
eration. The
m
ove
m
e
nt of
lin
ear m
o
to
r is d
i
fferen
t from
th
e op
erating a
p
proac
h
of circular rotary
m
o
tor s
u
c
h
that the calcul
a
tion
of
rotation spee
d and accelerat
ion/decele
r
ation is base
d
on the pri
n
ciple
of linea
r m
ove
m
e
nt. During linear
m
ove
m
e
nt, the tim
e
needed for a
stationary object
to
be accelerate
d
to the
m
a
xim
u
m
speed is calle
d
acceleration ti
me.
W
h
ile the
object is m
o
ving at m
a
xi
m
u
m
speed, it is
called the s
p
ee
d
of c
o
nstant
spee
d
m
ove
m
e
nt. The tim
e
neede
d
for an obj
ect
to decelerate
from
this const
a
nt
s
p
eed to the stationary
s
t
ate is
called decelera
tion ti
m
e
. The
linear stru
ct
ure
of linear m
o
tor will lead to fi
xed m
o
tion stroke suc
h
that there
will be spee
d
planning c
u
rve
s
of accelerati
o
n, c
o
nstant
spe
e
d,
a
n
d deceleration fo
r t
h
e movem
e
nt spee
d, a
nd
the acceleration,
deceleration
and tim
e
can
be calculated
by
usi
n
g the
formula.
2
.
3
.
Ca
lculation of Specificatio
n
Selectio
n
The following study
is
to de
rive
re
quire
d
form
ula of acceleration a
(2
.1),
form
ula of s
p
e
e
d
v (2.2),
tim
e
t and spee
d curve
form
ula (2.3)
base
d on continuous thrust
of linear
m
o
tor, while
the acceleration can be
d
i
rectly calcu
lated
fro
m
m
o
to
r
ou
tpu
t
and lo
ad. Th
e m
o
to
r
o
u
t
pu
t in
t
h
is stud
y is
based
o
n
statistics o
f
pr
o
duct
i
o
n s
p
e
c
i
f
i
cat
i
ons,
wh
i
l
e
t
h
e l
o
ad i
n
c
l
udes t
h
e c
u
st
o
m
-desi
gned c
o
nt
ai
ned m
a
ss o
f
m
echani
cal
hand
,
com
b
i
n
at
i
on
m
a
ss of m
o
t
o
r prom
ot
er, an
d fri
ct
i
o
n (
w
hi
ch can be
neg
l
ect
ed i
n
t
h
i
s
st
udy
)
.
The f
o
l
l
o
wi
n
g
analysis is foc
u
se
d on t
h
e time requi
red
for the LMC
and LMS lin
ear m
o
tors
o
f
HIWINMIKRO t
o
m
o
v
e
th
e
mechanical by
16.5cm
.
The LM
C
serie
s
o
f
c
o
reless
m
o
to
rs a
r
e the
fi
rst to
be a
n
al
y
z
ed,
w
h
ere
t
h
e c
a
l
c
ul
at
i
on i
s
ba
sed
o
n
t
h
e
heavi
e
st
m
a
ss of co
nt
ai
ne
d m
a
ss of m
ech
ani
cal
han
d
l
i
m
i
t
e
d t
o
2kg
. Thi
s
n
u
m
e
ri
c
val
u
e i
s
use
d
as t
h
e
calcu
latio
n
p
a
ra
m
e
ter.
2.
4. Resul
t
of
Speci
fi
ca
ti
on
Sel
ecti
o
n
From
the Tabl
e 1 below we
find that the
num
e
ric
values
of eac
h se
ries
of linea
r m
o
tor calculated
base
d o
n
t
h
e
d
i
st
ance o
f
1
6
.
5
cm
(60
pe
r m
i
nut
e a
n
d q
u
a
r
t
e
r n
o
t
e
s
p
eed
0.
13
3
3
s) ca
n a
l
l
m
eet
t
h
e st
anda
r
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3,
No
. 2,
J
u
ne 2
0
14:
1
1
8
– 13
0
12
1
But the diffe
re
nce between si
zes of pr
o
m
o
t
er vo
lu
m
e
is r
a
th
er larg
e. Th
e sa
m
e
P60 quarter notes all meet
st
anda
rd t
i
m
e, but
t
h
e v
o
l
u
m
e
or pr
om
ot
er of LM
C
ser
i
es i
s
sm
al
l
e
r than t
h
at
of L
M
S seri
es. Th
us LM
C
series is the
more s
u
itable linear m
o
tor for t
h
e piano pl
ay
i
ng r
o
bot
o
f
t
h
i
s
st
udy
d
u
e to the visual, aest
h
etic
and pe
rform
a
nce factors.
Tabl
e
1. Ti
m
e
of
n
o
t
e
In
th
is p
l
an
we u
s
e LMX1
E-C lin
ear
m
o
to
r p
l
atfo
rm
with
co
reless m
o
to
r wh
ich
is su
itab
l
e for h
i
gh
spee
d an
d m
u
l
t
i
-
axi
s
si
m
u
l
t
a
n
e
ou
s m
ovem
e
nt
appl
i
cat
i
ons.
The com
p
act volum
e is
the
main feature
,
and the
increm
ent-type of anal
og or
digita
l optical scale is use
d
for t
h
e
pos
i
t
i
o
n
feed
bac
k
. LM
X1
E-C
pl
at
fo
r
m
has
superior dynamic
features with
length up to 4000 mm
,
maxi
m
u
m
acceleration as high as 100m/s
2
, and
maxim
u
m
speed as high as
5m
/s. Ther
efore it is
th
e lin
ear m
o
to
r
m
eetin
g
th
e req
u
i
remen
t
o
f
th
is
p
r
o
j
ect as
sho
w
n i
n
Fi
gu
r
e
3.
Fig
u
re
3
.
LMX1
E-C
lin
ear m
o
tor
3.
SY
STEM
STR
U
C
T
UR
E
OF M
E
C
H
A
N
IC
A
L
HAND
The a
p
pl
i
cat
i
on
of
c
o
m
m
on m
echani
cal
ha
nd
i
s
l
i
m
it
ed t
o
gra
b
bi
n
g
o
b
j
ect
wi
t
h
a
n
t
h
r
o
p
o
m
o
rp
hi
c
approach.
W
ith the space limit
of hand de
sign,
m
a
ny se
nsors a
nd
wirings ha
ve be inst
alled in the hand s
u
c
h
th
at th
e flex
ibilit
y o
f
fing
ers are li
m
i
ted
lead
ing
to
th
e l
ack
of d
e
x
t
erit
y wh
en
flex
i
b
le fin
g
e
r actions are
neede
d
.
In t
h
i
s
st
udy
t
h
e de
xt
eri
t
y
of fi
n
g
er
has bee
n
dem
onst
r
at
ed i
n
t
h
e
fo
rm
of pi
an
o-
pl
ay
i
ng. T
h
e
p
i
ano
-
pl
ay
i
ng m
echani
cal
ha
nd
i
s
b
a
sed
on
ant
h
r
o
pom
or
phi
c
des
i
gn.
Th
e ha
n
d
i
s
sl
i
ght
l
y
wi
de
r t
h
a
n
hum
an h
a
nd
at
12
0 m
m
, whi
l
e
t
h
e ap
peara
n
ce of
fi
n
g
er i
s
im
it
at
i
ng t
h
e b
e
ndi
ng
o
f
h
u
m
a
n fi
nge
r d
u
r
i
n
g pi
a
no
pl
ay
i
n
g.
O
n
one
ha
nd i
t
i
s
an i
m
i
t
a
ti
on o
f
hum
an pl
ay
i
ng pi
a
n
o
,
o
n
t
h
e
ot
her
ha
nd i
t
al
l
o
ws o
n
l
y
t
h
e fi
nge
r p
u
l
p
t
o
t
o
uch
the surface of piano key. T
h
e
ope
ning
and closing actions
of ha
nd duri
ng
piano
playing
can dem
onstrat
e the
technical as
pe
ct and a
n
thropom
o
rphic
effe
ct. As
for the
chrom
a
tic keys, th
ey ca
n be
reache
d
by all fingers
expect
f
o
r t
h
e
t
hum
b, and t
h
i
s
i
s
t
h
e desi
gn
whi
c
h has
not
bee
n
seen
from
previ
o
u
s
l
y
anno
un
ced
pi
ano
-
pl
ay
i
ng m
echa
n
i
cal
ha
nd
s.
3.
1.
Mec
h
a
n
i
c
al
H
a
nd
S
y
st
em
The second generation m
e
c
h
anical ha
nd
syste
m
in
clud
es finge
r r
o
tar
y
actuator, fin
g
er
-p
ressi
n
g
pne
um
at
i
c
cy
linde
r,
fi
nge
r
fl
exi
b
l
e
c
o
nnect
i
on,
l
i
n
ear
gui
deway
,
s
w
i
n
gi
ng
arm
pr
ot
ec
t
i
on
de
vi
ce,
b
o
t
t
o
m
pl
at
e st
r
u
ct
u
r
e,
an
d sl
i
d
i
n
g
p
a
nel
devi
ce. T
h
e st
ruct
ure
of this m
echanic
al
ha
nd
i
s
as
s
h
o
w
n i
n
Fi
gu
r
e
3
.
2
“The p
h
y
s
i
cal
appea
r
a
n
ce o
f
t
h
e seco
nd
ge
n
e
rat
i
on
han
d
”
,
an
d
d
e
tailed
statistics refer to Tab
l
e 3
.
1
“Tab
le of
perform
a
nce param
e
ters of mechanical ha
nd”
. T
h
e botto
m plate of the
mechanical
ha
nd i
s
m
a
i
n
l
y
606
1
-
T6
al
um
i
num
pl
ate wi
t
h
4 set
s
of
pne
um
at
i
c
fi
n
g
er
-p
ressi
n
g
m
odul
es a
nd
an i
n
depe
n
d
en
t
pne
um
ati
c
t
hum
b-
pressi
n
g
m
odu
l
e
i
n
st
al
l
e
d o
n
t
op
of
i
t
.
The
r
e
are
4 SB
R
0
6
pne
um
at
i
c
cyl
i
nde
rs
be
neat
h t
h
e a
nd
b
o
t
t
o
m
pl
at
e
m
a
i
n
l
y
for t
h
e
ext
e
n
d
ed act
i
o
ns o
f
4 set
s
of
m
odul
es. Th
us
t
h
ere are l
i
n
ea
r g
u
i
d
e
w
ay
s i
n
st
al
l
e
d at
t
h
e bot
t
o
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
D
e
sign
o
f
Piano
-p
la
yi
n
g
Robo
tic Ha
nd
(Jen-
C
ha
ng
Lin
)
12
2
of t
h
e 4 set
s
o
f
p
n
eum
a
t
i
c
finge
r-
p
r
essi
n
g
m
odul
es m
a
i
n
l
y
for al
l
o
wi
n
g
t
h
e 4 set
s
of
pne
um
at
i
c
fi
ngers t
o
reach the c
h
romatic keys.
The
decom
pos
i
t
i
on o
f
fi
n
g
er
p
n
eum
a
t
i
c
m
o
d
u
l
e
of m
echani
cal
ha
nd
i
s
base
d
on
si
n
g
l
e
m
odul
e
,
wh
ere th
e servo
is u
s
ed
as an
actu
a
to
r at th
e ro
tary jo
in
t. The actu
a
to
r is in
stalled
in
th
e rectan
gu
lar groo
v
e
o
n
th
e slid
in
g
bo
t
t
o
m
p
l
ate with
th
read
ed
ho
les o
n
bo
th
sid
e
s fo
r fi
x
i
ng
.
Wh
en
th
e signal o
f
ro
tating
an
g
l
e is
receive
d by the servo, it will
dri
v
e th
e prote
c
tion swi
ngi
ng arm on top
of
th
e servo. This pr
otection swi
ngi
ng
arm is in
stal
le
d
at th
e b
o
ttom o
f
sp
ecial ro
tary j
o
i
n
t, and
th
ere are thread
s on
th
e ro
t
a
ry j
o
in
t fo
r integ
r
ation
with
au
x
iliary cla
m
p
p
l
ate.
Th
ere are b
e
aring
h
o
u
s
ing
s
in
t
h
e au
x
iliary cl
a
m
p
p
l
ate. Th
i
s
pressing
p
l
ate will
be
placed on t
o
p of
rota
ry joi
n
t durin
g installation. The
auxiliary cla
m
p plate is installed on t
h
e slidi
n
g
plate
wh
ere th
ere are h
o
l
es fo
r fi
x
i
n
g
an
d
lo
ck
ing. Screws are
u
t
ilized
to
p
e
n
e
trate th
rou
g
h
b
e
aring
s
un
til th
e ro
tary
j
o
in
t
i
s
s
c
r
e
w
e
d
i
n
to
th
e
th
r
e
a
d
.
T
h
i
s
is m
a
in
ly for
reinforcem
en
t o
f
t
h
e stren
g
t
h
o
f
rotary jo
in
t
wh
ere th
e
o
r
i
g
in
al stru
ctu
r
e
o
f
can
tilever b
eam
is co
nv
erted
to
sh
ear free
b
eam
fo
r d
i
stribu
tin
g
t
h
e force on
b
o
t
h
end
s
su
ch
th
at t
h
e
p
r
o
l
on
g
e
d
stress
will n
o
t
lead
t
o
th
e lo
ad
of th
e serv
o m
o
to
r.
Th
ere is t
h
e seco
nd
d
e
gree
o
f
freedo
m
o
n
th
e ro
tary jo
i
n
t fo
r the in
st
allatio
n
o
f
fing
er
ro
tation
cent
e
r. T
h
e
r
e
are bea
r
i
n
g h
o
u
si
n
g
s i
n
t
h
e f
i
nge
rs f
o
r i
n
st
al
l
a
t
i
on of
bea
r
i
n
gs. I
n
t
h
e e
nd t
h
e pe
net
r
a
t
i
on o
f
st
eel
shaft
i
s
ut
i
l
i
zed and t
h
e
E-t
y
pe ri
ng i
s
use
d
f
o
r
buc
kl
i
ng m
a
i
n
l
y
for
avoi
di
n
g
axi
a
l
m
ovem
e
nt
. Ins
i
de t
h
e
fing
er th
ere are g
r
oo
v
e
s
fo
r i
n
tegratio
n
with
flex
ib
le
de
vi
ce, where
flexi
b
le de
vices are
connected
by
using
1m
m
st
eel
wi
re. The
b
o
u
n
ci
ng
bac
k
act
i
o
n
of
fi
n
g
er i
s
a
c
hi
eve
d
by
pl
a
c
i
ng c
o
m
p
ress
spri
ng
s ar
ou
n
d
st
eel
wi
re.
Du
ri
n
g
c
o
m
p
ressi
o
n
of
spri
n
g
s t
h
e
r
e
m
u
st
be gui
de
way
s
fo
r g
u
i
d
i
ng
di
rect
i
o
n o
f
spri
n
g
c
o
m
p
ressi
on
su
ch
th
at th
e
steel wire p
l
ays an
im
p
o
r
tan
t
ro
le in
th
e cen
t
e
r of sp
ri
n
g
. As for the selectio
n
o
f
spring
, i
f
th
e
wi
re di
am
et
er
i
s
t
oo l
a
rge, t
h
e ri
gi
di
t
y
can be t
oo st
r
o
ng
and ca
usi
n
g f
r
act
ures.
If t
h
e
spri
ng i
s
t
oo s
o
ft
, t
h
e
fing
er
b
oun
cing
-b
ack
w
ill n
o
t
b
e
fast eno
ugh to
k
eep
u
p
w
ith
th
e b
eat. Th
e flex
ib
le d
e
v
i
ce is co
n
n
ected
to
th
e
co
m
b
in
atio
n
of pn
eu
m
a
t
i
c cylin
d
e
r an
d linear gu
id
eway.
Th
e
p
n
e
u
m
atic
cylin
d
e
r is m
a
in
ly for g
e
n
e
ratin
g
t
e
nsi
o
n wi
t
h
r
e
spect
t
o
fl
e
x
i
b
l
e
devi
ce
w
i
t
h
st
ro
ke ar
o
u
n
d
10m
m
.
The t
e
nsi
on i
s
cont
rol
l
e
d
by
fl
ow
ad
ju
stm
e
n
t
b
y
th
ro
ttle v
a
lv
e on
p
n
e
u
m
ati
c
cylin
d
e
r.
The d
i
rection
o
f
lin
ear
gu
id
eway shou
ld
be k
e
p
t
co
nsisten
t
with th
e au
x
iliary fo
rce, su
ch
th
at
atten
tio
n
m
u
st
b
e
p
a
id
to
t
h
e in
terferen
ce issu
e du
ri
n
g
assem
b
l
y
of l
i
n
ear
gui
de
way
and p
n
e
u
m
a
t
i
c
cy
li
nder
,
ot
her
w
i
s
e t
h
e resp
o
n
se spee
d
of fi
n
g
ers
du
ri
ng
pi
an
o pl
ay
i
ng ca
n
be a
ffecte
d
.
As f
o
r t
h
e i
d
e
n
t
i
f
i
cat
i
on of c
o
rres
p
on
di
n
g
sa
m
e
m
u
si
c al
phabet
,
t
h
e
num
ber can
be use
d
t
o
cl
assi
fy
th
e in
terv
al lev
e
l. Th
e
n
u
m
b
e
r “5
”
will b
e
attach
ed
to the m
u
sic alp
h
a
b
e
t of th
e
k
e
y
in
th
e sam
e
set with
central C. Num
b
ers such as
“6”, “
7
”
are attached t
o
the notes
h
i
gh
er th
an
th
e set of cen
t
ral C, wh
ile n
u
m
b
e
rs
suc
h
as “
4
”, ”3” are attache
d
t
o
the
notes l
o
wer
tha
n
t
h
e set
of central C
as
shown in Fi
gure 4.
Fig
u
re
4
.
Illu
st
ratio
n of th
e seco
nd
g
e
n
e
ration
m
ech
an
ical han
d
3.
2.
De
vi
ce De
si
gn
of
Mec
h
a
n
i
c
al
H
a
nd
-
R
ot
ar
y
Actu
a
t
o
r
For t
h
e fi
n
g
e
r
rot
a
t
i
on
of
pi
ano
-
pl
aying mechanical ha
nd, feat
ures
s
u
c
h
as fast
r
o
t
a
t
i
on,
preci
se
p
o
s
ition
,
and
co
m
p
act
m
o
to
r
size are req
u
i
red
,
so
is a
certain
lev
e
l or torq
u
e
. A
lthoug
h th
e req
u
i
red
t
o
rqu
e
f
o
r
ce is
n
o
t
too
larg
e, cer
t
ain lev
e
l of
su
ppor
t f
r
o
m
r
a
ted
to
rqu
e
is r
e
qu
ired
.
No
n
e
t
h
eless, th
e m
o
st i
m
p
o
r
t
ant
factor is the si
ze of m
o
tor. If the si
ze of m
o
t
o
r pl
us
red
u
c
e
r b
ox i
s
t
oo l
a
rge
,
t
h
e desi
g
n
ed m
echani
c
a
l
han
d
will b
e
to
o
larg
e. On
th
e contrary, a sm
a
ller
m
o
to
r will lea
d
to
a s
m
aller
mech
an
ical h
a
n
d
wh
ich
is
mo
re lik
e
a hum
a
n hand.
As
for the re
ducer
bo
x
,
th
e
fing
er m
o
to
r do
es no
t n
e
ed
a v
e
ry larg
e
redu
cti
o
n ratio.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3,
No
. 2,
J
u
ne 2
0
14:
1
1
8
– 13
0
12
3
The desi
gn
of
seco
nd ge
ne
rat
i
on m
echani
cal
hand i
s
di
f
f
e
r
ent
fr
om
t
h
e fi
rst
gener
a
t
i
o
n
where t
h
e
t
o
r
que t
r
a
n
sm
issi
on
by
act
uat
o
r i
s
con
d
u
ct
ed by
di
r
ection transm
ission approach
inste
a
d of the connecting
ro
d ap
pr
oac
h
.
Thi
s
i
s
m
a
i
n
l
y
due t
o
t
h
e ad
di
t
i
onal
t
h
i
r
d d
e
gree
of f
r
eed
om
i
n
st
al
l
e
d on t
h
e m
ovem
e
nt
joi
n
t
with
in
th
e m
e
c
h
an
ical h
a
nd
lead
ing
to
th
e
m
o
d
i
fied
d
e
sign
of
th
e second
g
e
n
e
ration
mechanical ha
nd. The
p
r
o
t
ectio
n
swi
n
g
i
n
g
arm
is i
n
stalled
on
th
e servo
ax
is
su
ch
th
at th
ere
will n
o
t
b
e
an
y po
sitio
n
sli
d
ing
d
u
ring
fi
n
g
er
r
o
t
a
t
i
o
n
wi
t
h
gea
r
s
of
swi
n
gi
n
g
a
r
m
an
d se
rv
o a
x
i
s
m
e
shi
ng
wi
t
h
eac
h
ot
he
r.
The sc
re
w fi
x
a
t
i
o
n
approach
bet
w
een protection swinging
a
r
m
and rotary
j
o
i
n
t is m
a
inly
for
facilitating the
re
placem
ent duri
ng
m
a
i
n
t
e
nance. The
p
r
i
n
ci
pl
e
of pr
ot
ect
i
on swi
n
gi
n
g
arm
is when t
h
e finger is h
it by external force, the
man
d
a
tory ro
tatio
n
un
der th
e
ex
citatio
n
state o
f
pro
t
ecti
o
n
servo
m
o
to
r will lead
to
sk
ipp
i
n
g
o
f
in
tern
al
g
ear.
The a
p
peara
n
c
e
di
m
e
nsi
ons
o
f
t
h
e
act
uat
o
r i
n
st
al
l
a
t
i
on a
r
e
as sh
o
w
n
i
n
Fi
gu
re
5.
Fig
u
re
5
.
Act
u
atio
n
installati
o
n
lo
cation
Th
e fi
n
g
e
r ro
tatio
n
is tran
sm
it
ted
to
th
e ro
tary j
o
in
t throug
h p
r
o
t
ectio
n
d
e
vice. Sin
ce th
e
p
r
o
t
ection
device is a flexible connecti
on
part, reacti
on
will be
generated duri
ng finge
r pressi
ng process affecting the
ro
tary jo
i
n
t. Th
e pro
t
ection
dev
i
ce cann
o
t
with
stan
d
su
ch
fo
rce, th
u
s
t
h
e au
x
iliary clamp
p
l
ate is d
e
sign
ed
i
n
response to this issue. The a
u
xiliary
cla
m
p plate is
installed on top of th
e rotary joint. Th
e reaction will cause
th
e ro
tary
j
o
i
n
t
to
b
e
lifted, and
th
is is wh
en
t
h
e au
x
iliary cl
a
m
p
p
l
ate can
b
a
lan
ce t
h
e
force.
3.
3.
De
vi
ce De
si
gn
of
Mec
h
a
n
i
c
al
H
a
nd
-Pr
e
ssi
ng
Act
u
a
t
or
Fo
r t
h
e fi
n
g
e
r
p
r
essi
ng
actio
ns o
f
p
i
ano-p
l
ayin
g
m
ech
an
ical h
a
nd
,
features su
ch
as sp
eed
,
stab
ility,
and com
p
act device size a
r
e
require
d
. By
studying t
h
e acti
o
n of
f
i
ng
er pressin
g
th
e p
i
ano
k
e
y,
w
e
f
i
nd th
at
currently the
r
e
is no contro
l
o
v
er
f
o
rce
fo
r
fi
nge
r act
i
o
n s
u
c
h
t
h
at
t
h
e co
nt
r
o
l
de
vi
ce i
s
onl
y
han
d
l
i
n
g c
o
n
s
t
a
nt
spee
d m
ovem
e
nt
wi
t
h
fi
xed s
t
ro
ke. I
n
t
e
rm
s of t
h
e
vol
um
e req
u
i
r
em
ent
,
t
h
ere m
u
st
be 5
act
uat
o
rs
pl
ac
ed o
n
th
e h
a
nd
for
pu
llin
g
steel wi
res, t
h
us lie-fl
at in
stallatio
n
is requ
ired
for th
e
d
e
v
i
ces to b
e
u
s
ed
i
n
o
r
d
e
r to
pre
v
e
n
t
t
h
e ha
nd
fr
om
bei
ng
t
oo t
h
i
c
k.
In t
e
rm
s of t
h
e p
r
e
ssi
ng s
p
ee
d, t
h
ere m
u
st
be ve
ry
fast
reci
p
r
o
cat
i
ng
m
o
t
i
o
n
in
a rath
er sh
ort stroke su
ch
th
at th
ere will n
o
t
b
e
v
e
ry h
i
g
h
d
e
man
d
o
n
p
r
ecisi
o
n
. In
term
s o
f
o
u
t
pu
t
force, th
is fi
ng
er m
ech
an
ism will req
u
i
re at least fo
rce o
f
1kg
f and
ab
ov
e.
Su
mm
a
r
izin
g
features o
f
all
aforem
entione
d de
vice requi
r
em
ents, we concl
ude that pn
eum
a
tic cylinder is the best
choice.
It is equipped
wi
t
h
af
orem
ent
i
one
d feat
ures
of c
o
m
p
act
si
ze, sh
ort
st
r
o
ke,
l
a
rge f
o
rce
,
an
d hi
gh s
p
ee
d. P
n
eum
a
t
i
c
cyl
i
nder i
s
a ki
n
d
o
f
pne
um
ati
c
dri
v
e
r
gene
rat
i
n
g l
i
n
ear m
ovem
e
nt w
h
i
c
h
has
be
en
wi
del
y
a
d
o
p
t
e
d i
n
t
h
e i
n
dust
r
y
.
Because
pne
umatic cylinder is capa
b
le
of
gene
ration si
mple m
echanical actions
, the
r
e
are
various
ki
nds
of
pne
um
at
i
c
cy
linde
rs wi
t
h
n
u
m
erous
m
e
t
hods of
use
.
In t
h
e desi
g
n
of fi
nge
r pr
ess
i
ng m
echani
s
m
of
m
ech
anical hand, the pneum
a
tic cylinder is used a
s
th
e actu
a
tor in co
ord
i
n
a
tion
with
o
t
h
e
r auxiliary d
e
v
i
ces. Th
e
recipro
c
atin
g
action
s
are g
e
nerated by th
e
pne
um
at
i
c
cyl
i
nde
r t
o
p
u
l
l
fi
nge
r
by
p
u
l
l
i
ng co
n
n
ect
i
on
s
t
eel
wi
res.
W
i
t
h
o
n
e e
nd
o
f
t
h
e fi
nge
r fi
xed
on
a
ro
tation
ax
is, t
h
e
fing
er m
o
tio
n of
u
p
and
d
o
wn
swing
i
ng
is cen
t
ering
o
n
th
e
ro
tatio
n ax
is.
Wh
en
the steel
wi
re i
s
pul
l
i
n
g
t
h
e fi
nge
r
bas
e
d
on t
h
e
pri
n
c
i
pl
e of
l
e
ver
a
g
e
, i
t
i
s
a fi
xe
d
rat
i
o
bet
w
ee
n t
h
e
di
st
ance f
r
o
m
t
h
e
j
o
i
n
t of steel
wire and
fing
er to
th
e ro
tatio
n cen
t
er, and
t
h
e
d
i
stan
ce
fro
m
fin
g
e
r tip
t
o
th
e
ro
tation
cen
t
er. Th
is
is m
a
in
ly th
e in
crease of
pressin
g
s
p
eed
w
h
i
c
h
re
duce
s
t
h
e m
ovem
e
nt
of
p
n
e
u
m
a
ti
c cy
l
i
nder.
D
u
e
t
o
t
h
i
s
ratio
, th
e i
n
creased
sp
eed
will lead
to
redu
ced
actio
n
forc
e.
Wh
en
t
h
ere i
s
larg
er
resistan
ce at th
e finger tip
,
larger
f
o
rce is
req
u
ire
d
at the
stressin
g
e
nd
fo
r achie
vi
ng
balance
due to the princi
ple of force
a
r
m
.
For
the
ove
ral
l
beaut
y
of fi
nge
rs, t
h
i
s
desi
g
n
al
so p
r
e
v
ent
s
t
h
e e
x
p
o
s
ed echa
n
i
s
m
f
r
om
bei
ng see
n
d
u
ri
ng act
uat
i
on o
f
mechanism
such t
h
at the
overall app
eara
n
ce is a
better
fit for
ant
h
ropom
o
rphic de
sign. T
h
is is
going
t
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
D
e
sign
o
f
Piano
-p
la
yi
n
g
Robo
tic Ha
nd
(Jen-
C
ha
ng
Lin
)
12
4
cont
ri
b
u
t
e
grea
t
l
y
t
o
m
u
si
c
pl
ay
i
ng
where
m
o
re lively
music can be
pl
ay
ed as t
h
e de
m
onst
r
at
i
on o
f
fi
nge
r
dext
e
r
i
t
y
whi
l
e
m
e
et
i
ng t
h
e
fe
at
ure
of
ant
h
r
o
pom
or
phi
c
fi
n
g
ers
.
The
differe
n
c
e
between the
desi
gn of t
h
e sec
ond
g
e
ner
a
tio
n m
ech
an
ical f
i
ng
er
an
d th
e f
i
r
s
t
gene
rat
i
o
n desi
gn i
s
at
t
h
e po
si
t
i
on of
ben
d
i
ng
joi
n
t
.
B
a
sed
on t
h
e j
o
i
n
t
o
f
hum
an han
d
, t
h
e be
ndi
ng
po
s
i
t
i
on
of m
echani
cal
ha
nd i
s
at
t
h
e j
unct
i
o
n
bet
w
een
car
pal
b
one
an
d m
i
d bo
ne.
The
di
st
ance f
r
o
m
t
h
e fi
n
g
er
ben
d
i
n
g j
o
i
n
t
t
o
t
h
e fi
n
g
e
r
t
i
p
i
s
100m
m
,
whi
l
e
t
h
e di
st
ance from
t
h
e ju
nct
i
on o
f
st
eel
wi
re an
d fi
n
g
er t
o
t
h
e
b
e
nd
ing
jo
in
t is 1
7
m
m
.
Th
is
will lead
to
a l
a
rg
er ratio
su
ch
th
at th
e p
n
e
umatic
cyl
i
n
d
e
r
o
n
l
y n
e
ed
s to
m
o
v
e
by
5
m
m
for t
h
e
pres
si
n
g
di
st
ance t
o
reac
h
25
m
m
. Thi
s
way
t
h
e
spee
d
of
fi
n
g
e
r
press
i
ng
o
n
t
h
e
pi
ano
k
e
y
will b
e
greatly enh
a
n
c
ed
t
o
twice th
e sp
eed o
f
th
e
first
gen
e
ration
.
Ho
wev
e
r, in
term
s
o
f
t
h
e
p
r
essi
n
g
force,
the adopti
on
of ol
d pne
u
m
a
t
i
c
cylinder
will lead to slig
htly insufficient
force
output. The reaction
force is
increase
d
due to the en
l
a
r
g
e
d
fo
rce arm
of t
h
e pri
n
ci
pl
e of l
e
vera
ge
suc
h
that greate
r
force is require
d
at the
stressing end i
n
order to achi
e
ve the
balanc
e. The
r
ef
ore,
i
n
the
sec
o
nd generation desi
gn we replace the
old
p
n
e
u
m
atic
cyl
i
n
d
e
r with
th
e on
e with
ou
ter cylin
d
e
r d
i
am
et
er o
f
10
mm in
o
r
d
e
r to
ach
ieve id
eal o
u
t
pu
t fo
rce.
Fi
gu
re 6 i
s
ab
out
t
h
e
descri
p
t
i
on o
f
al
l
part
s of t
h
e sec
o
n
d
ge
nerat
i
o
n fi
nge
r, a
nd t
h
e s
i
m
u
l
a
t
i
on of p
r
essi
n
g
act
i
on.
Fi
gu
re
6.
Det
a
i
l
ed f
u
nct
i
ons
o
f
t
h
e
seco
n
d
ge
nerat
i
o
n
ha
nd
3.
4.
De
vi
ce De
si
gn
of
Mec
h
a
n
i
c
al
H
a
nd
-pr
e
ssi
ng
Si
mul
a
t
i
on
N
e
w
d
e
si
g
n
app
r
o
a
ch
h
a
s
b
e
en
u
s
ed
w
ith
r
e
sp
ect to
th
e speed
of
p
i
ano
key p
r
essi
n
g
b
y
th
e second
g
e
n
e
ration
fingers. Th
e d
i
stance fro
m
th
e fing
er
b
e
nd
ing
j
o
in
t to
th
e fing
er tip
is 1
0
0
mm, wh
ile th
e
d
i
stan
ce
fr
om
t
h
e junct
i
on
of st
eel
wi
re an
d fi
n
g
e
r
t
o
t
h
e be
n
d
i
n
g
joi
n
t
i
s
17m
m
.
The spee
d
of
fi
nge
r p
r
essi
n
g
t
h
e
pi
an
o
key
ca
n
be m
o
re
ob
vi
o
u
s t
h
r
o
u
g
h
t
h
e
p
r
i
n
ci
pl
e
o
f
l
e
vera
ge,
w
h
i
l
e
t
h
e
desi
g
n
o
f
fi
nge
r a
p
peara
n
c
e
has
been al
s
o
i
m
itat
i
ng t
h
e
ben
d
i
n
g o
f
h
u
m
a
n fi
nge
rs w
h
i
l
e pl
ay
i
ng
pi
ano
.
T
h
r
o
u
g
h
t
h
e com
put
er
-a
ssi
st
ed
m
echani
cal
d
r
a
w
i
n
g, 3
D
dra
w
i
ng has
be
en
ut
i
l
i
zed
fo
r
t
h
e si
m
u
la
tio
n
o
f
f
i
ng
er pr
essi
n
g
as show
n in Figur
e
7
an
d Figur
e
8
.
Fi
gu
re
7.
Si
m
u
l
a
t
i
on o
f
fi
n
g
er
p
r
essi
n
g
(f
ro
nt
)
Fig
u
r
e
8
.
Sim
u
latio
n
of
f
i
ng
er pr
essing
(
r
e
ar
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3,
No
. 2,
J
u
ne 2
0
14:
1
1
8
– 13
0
12
5
3.
5.
De
vi
ce De
si
gn
of
Mec
h
a
n
i
c
al
H
a
nd
–
Pressi
ng
Assi
s
t
an
ce G
u
i
d
ew
ay
Lin
ear
gu
id
eway h
a
s
b
een
u
tilized
, wh
ile the coo
r
d
i
n
a
tion
o
f
m
ech
an
ism
is b
a
sed
on
t
h
e con
n
ection
bet
w
ee
n p
n
e
u
m
a
t
i
c
cy
l
i
nder
and l
i
n
ea
r g
u
i
deway
t
h
r
o
ug
h st
eel
wi
re cl
am
p pl
at
e. Th
e st
eel
wi
re i
s
fi
xed
betwee
n t
h
e
pneum
a
tic cylin
der and t
h
e linear
gui
deway
su
ch
th
at
wh
en
th
e force is
tran
sm
it
ted
from
th
e
pne
um
at
i
c
cy
l
i
nde
r t
o
t
h
e st
eel
wi
re, i
t
i
s
not
easy
for t
h
e t
o
r
que
gene
rat
e
d
du
ri
n
g
p
u
l
l
i
ng
of st
eel
wi
re t
o
l
ead
to
in
creased
fri
ctio
n
of th
e linear gu
id
eway.
Based
on
t
h
is
d
e
sign
, t
h
ere is o
n
e
m
o
du
le per fing
er in
stal
led
in
t
h
e ha
nd
. D
u
e
t
o
t
h
e si
ze fact
or
, t
h
e l
i
n
ear
g
u
i
d
e
w
ay
m
u
st
be fi
xe
d
on t
h
e
han
g
er i
n
si
de
-l
y
i
ng fas
h
i
o
n.
There
are
2 M2 thre
ads
on the
slider for fi
xing t
h
e steel wi
re
c
l
a
m
p plate on
the slider
an
d
fo
r fi
xin
g
t
h
e
axis o
f
pne
um
atic cylinde
r
be
neath t
h
e slide
r
. The
r
e are two al
u
m
i
num
pl
at
es on
t
h
e
st
eel wire clam
p plate for
cla
m
ping t
h
e s
t
eel wire. The
double clam
ping approac
h
can
en
su
re th
e
steel wire
no
t
to
be loo
s
en
ed wh
ile
bei
n
g pul
l
e
d. The Fi
g
u
re
9
b
e
l
o
w
i
s
t
h
e des
c
ri
pt
i
o
n of
p
r
e
ssi
ng
de
si
g
n
o
f
t
h
e
sec
o
n
d
g
e
nerat
i
o
n
m
echani
cal
han
d
.
Fi
gu
re
9.
The
s
econ
d
ge
nerat
i
on
p
r
essi
ng
de
si
gn
3.
6.
De
vi
ce De
si
gn
of
Mec
h
a
n
i
c
al
H
a
nd
–
Pressi
ng
Assi
s
t
an
ce G
u
i
d
ew
ay
In the system design of the se
cond ge
nerati
on m
ech
ani
cal
hand
, t
h
e o
p
eni
ng a
ngl
e i
s
req
u
i
r
e
d
by
t
h
e
fi
n
g
ers
.
B
a
sed
on t
h
e desi
gn
pri
n
ci
pl
e of t
h
e fi
rst
ge
nera
t
i
on m
echani
cal
hand
, t
h
e fi
nge
r i
t
s
el
f
m
u
st
be
equi
ppe
d
wi
t
h
t
w
o
de
grees
o
f
free
d
om
. Ho
weve
r,
i
n
t
h
e f
i
nge
r
desi
g
n
o
f
t
h
e
seco
n
d
g
e
nerat
i
o
n m
echani
cal
han
d
,
a t
h
i
r
d
deg
r
ee
of
f
r
ee
dom
m
u
st
be
adde
d,
w
h
i
c
h
i
s
t
h
e p
o
si
t
i
o
n
req
u
i
r
e
d
fo
r t
h
e fi
ng
ers t
o
hi
t
t
h
e
chr
o
m
a
t
i
c
keys d
u
ri
ng
pi
a
n
o
pl
ay
i
n
g
,
whi
l
e
t
h
e a
ppe
ara
n
c
e
m
u
st
be eve
n
m
o
re a
n
t
h
r
o
pom
or
phi
c.
B
a
sed
o
n
t
h
ese t
w
o c
r
i
t
e
ri
a, t
h
e fi
n
g
e
r
desi
g
n
of t
h
e secon
d
g
e
ne
rat
i
on m
echan
i
cal
hand m
u
st
have 3
de
gr
ees o
f
free
dom
, w
h
er
e t
h
e t
h
i
r
d
deg
r
ee o
f
free
dom
i
s
fo
r t
h
e
fi
n
g
e
r t
o
be e
x
t
e
n
d
e
d t
o
t
h
e
posi
t
i
on
o
f
c
h
r
o
m
a
tic key
.
The basi
c act
uat
i
on
pri
n
ci
pl
e i
s
sim
ilar t
o
th
e first g
e
n
e
ration
m
ech
an
i
cal hand.
The differe
n
ce
is the
pne
um
at
i
c
cy
l
i
nde
r i
s
i
n
st
al
l
e
d i
n
t
h
e ha
n
d
o
n
a sl
i
d
i
ng m
odul
e s
u
ch t
h
at
t
h
e fi
n
g
er m
o
d
u
l
e
can be m
oved as
an e
n
tity. The
r
efore t
h
e
pres
sing m
odule itse
l
f m
u
st have
t
w
o de
grees
of
free
dom
. In term
s of the
m
odule, t
h
e
actio
n
force
g
e
n
e
rated
b
y
th
e pn
eu
m
a
tic cyl
i
n
d
e
r is tr
an
smitted
th
ro
ugh
t
h
e
flex
ib
le
d
e
vice. Th
e pn
eumati
c
cylin
d
e
r is i
n
st
alled
in
th
e rear of t
h
e fi
n
g
er
main
ly
for a
v
o
i
ding
the
friction
loss
d
u
ri
ng
fo
rce tra
n
sm
ission
.
The fle
x
ible device we use
is 1mm stee
l
wire. T
h
e pa
t
h
o
f
s
t
e
e
l
w
i
r
e
i
s
a
l
m
o
s
t
a
s
t
r
a
i
g
h
t
l
i
n
e
d
u
r
i
n
g
t
r
ansm
i
ssi
on f
o
r
ge
ne
rat
i
n
g
eno
u
g
h
f
o
rce
f
o
r
fi
nge
r
pre
s
s
i
ng.
Whe
n
t
h
e
fi
n
g
er
i
s
ope
ne
d
by
a
cert
a
i
n
angl
e,
th
e steel wire will b
e
b
e
n
t
wi
th
an
ang
l
e. This an
g
l
e is
n
o
t
v
e
ry larg
e, and th
e steel wire is in
tro
d
u
c
ed
in
to
th
e
ro
tary
jo
in
t
with
th
e tang
en
t ap
pro
ach, su
ch th
at th
e tran
sm
ission of steel
wire is
base
d
on a
n
a
r
c a
ngle
rathe
r
th
an
a
righ
t-ang
l
e b
e
nd
ing
.
Th
is b
e
nd
ing
is
with
in
t
h
e b
e
nd
ing
r
a
ng
e of
1
mm st
eel wire. The a
p
peara
n
ce of
th
e seco
nd
g
e
ner
a
tio
n m
ech
an
ical h
a
nd
is as
sh
own
in Fi
g
u
re 10
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
RA I
S
SN
:
208
9-4
8
5
6
D
e
sign
o
f
Piano
-p
la
yi
n
g
Robo
tic Ha
nd
(Jen-
C
ha
ng
Lin
)
12
6
Figure 10.
Mec
h
anical finger
flexible tra
n
sm
ission desi
gn
3.
7.
De
vi
ce De
si
gn
of
Mec
h
a
n
i
c
al
H
a
nd
–
Gl
i
d
i
n
g
Joi
n
t
First o
f
all th
e
relatio
n
s
h
i
p
b
e
tween
th
e ch
romatic
keys and the m
echanical hand is analyzed.
During
no
rm
al
pi
ano
-
pl
ay
i
n
g
p
r
oce
s
s t
h
e
fi
nge
r
s
of m
echanical hand are
place
d
on
t
h
e w
h
ite k
e
ys. W
h
en
ever
th
e
ch
ro
m
a
tic k
e
y
s
n
e
ed
t
o
b
e
pressed
d
u
ring
p
i
ano
-
p
l
ayin
g, th
e m
ech
an
ical h
a
nd
will be m
o
v
e
d
to the prop
er
p
o
s
ition
,
wh
ile th
e fin
g
e
r fo
r
p
r
essi
ng
th
e chro
m
a
tic k
e
y wi
ll b
e
stretch
e
d
to
th
e po
sitio
n an
d
th
e
fing
er will
b
e
p
r
essing
d
o
wn. After
th
e p
r
essi
ng
action
is
co
m
p
leted
,
th
e h
a
nd
will retu
rn
to th
e
norm
a
l state. Th
e fing
er
pressi
n
g
pr
oce
ss i
s
si
m
u
l
a
t
e
d by
com
put
er
s
o
ft
ware a
s
s
h
o
w
n
i
n
t
h
e
fol
l
o
wi
n
g
Fi
gu
re
1
1
an
d Fi
gu
re
1
2
.
Fig
u
re
11
. Mech
an
ical
fing
ers (n
orm
a
l p
o
s
itio
n)
Figure 12.
Mec
h
anical fingers
(stretc
h
ed)
Th
e d
i
stan
ce
fro
m
th
e fin
g
e
r p
o
s
ition
on
th
e wh
ite k
e
y to
t
h
e fing
er
p
o
s
iti
o
n
o
n
th
e ch
romatic
k
e
y is
3
0
mm
, th
e wid
t
h
o
f
ch
ro
m
a
t
i
c k
e
y is aro
und
8
mm
, an
d
th
e wi
d
t
h
o
f
b
u
ffer silico
n
e
at
fin
g
e
r tip
is 6
mm
.
There
f
ore,
t
h
e
r
e i
s
o
n
l
y
1 m
m
t
o
l
e
rance
of
l
e
ft
/
r
i
ght
de
vi
at
i
on
du
ri
n
g
fi
nge
r
pres
si
n
g
pr
ocess
,
w
h
i
c
h
i
s
ve
ry
i
m
p
o
r
tan
t
to
t
h
e stab
ility afte
r stretch
e
d
m
e
ch
an
ism
.
Th
ere is a d
r
op
h
e
ig
h
t
b
e
tween
the wh
ite k
e
y and
th
e
bl
ack key
,
whi
c
h m
eans t
h
e bl
ack key
i
s
15
m
m
above t
h
e whi
t
e
key
.
T
h
e
r
ef
ore
,
fo
r fi
n
g
e
rs t
o
reac
h fo
r t
h
e
chr
o
m
a
t
i
c
key
s
w
h
i
l
e
pl
ay
i
n
g
on
w
h
i
t
e
key
s
,
t
h
ey
m
u
st
be l
i
ft
ed.
H
o
we
ver
,
t
h
e act
uat
i
o
n
of
m
echani
s
m
m
u
st
b
e
in
a stab
le state su
ch
that th
e h
e
i
g
h
t
s of fi
n
g
e
rs
an
d k
e
ys will b
e
raised
b
y
a certain
d
i
stan
ce during
p
i
ano
-
pl
ay
i
ng
o
n
t
h
e
whi
t
e
key
s
. T
h
e di
m
e
nsi
ons
o
f
t
h
e
desi
gn
ap
peara
n
ce a
r
e as
sh
ow
n i
n
Fi
g
u
r
e
13
an
d
Fi
g
u
r
e
1
4
.
Fig
u
r
e
13
. H
e
i
g
h
t
s
of
f
i
ng
er
s an
d
wh
ite
k
e
ys
Fi
gu
re 1
4
. Hei
ght
s
o
f
fi
n
g
ers
and
bl
ac
k key
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
089
-48
56
IJR
A
V
o
l
.
3,
No
. 2,
J
u
ne 2
0
14:
1
1
8
– 13
0
12
7
3.
7. De
vi
ce
De
si
gn of
Mec
h
a
n
i
c
al
H
a
nd
–
Gl
i
d
i
n
g Joi
n
t
Mo
dul
e
In t
h
e m
echani
cal
hand
desi
gn
, fi
nge
rs ar
e desi
g
n
e
d
wi
t
h
m
odul
ari
zat
i
on a
p
p
r
oach
.
A fi
n
g
e
r
i
s
desi
g
n
e
d
t
o
be
a
m
odul
e ca
p
a
bl
e o
f
p
r
essi
ng t
h
e pi
a
n
o
key
an
d r
o
t
a
t
i
ng
by
a cert
a
i
n
an
gl
e, s
u
c
h
t
h
at
a
m
echani
cal
ha
nd i
s
c
o
m
pose
d
o
f
fo
ur i
d
e
n
t
i
f
i
cat
i
on
fi
n
g
er
m
odul
es an
d o
n
e t
h
um
b
m
o
d
u
l
e
. A
s
m
e
nt
i
oned i
n
pre
v
i
o
us c
h
a
p
t
e
rs, t
h
e
fi
n
g
e
r
m
odul
e i
n
cl
u
d
e
s ser
vo m
o
t
o
r
,
p
n
eum
a
t
i
c
cyl
i
nder
,
l
i
n
ear
g
u
i
d
e
w
ay
an
d fl
exi
b
l
e
tran
sm
issio
n
dev
i
ce. All d
e
v
i
ces will b
e
in
teg
r
ated
on
on
e
m
o
b
ile j
o
i
n
t mech
an
ism
to
form
a
m
o
b
ile
j
o
i
n
t
m
odul
e wi
t
h
t
h
e feat
u
r
e o
f
t
h
e
seco
nd
ge
nera
t
i
on m
echani
cal
han
d
as t
h
e t
h
i
r
d de
g
r
ee o
f
free
dom
fo
r pl
ay
i
n
g
t
h
e ch
r
o
m
a
ti
c key
.
T
h
e a
p
pea
r
ance
di
m
e
nsi
o
n
of
t
h
i
s
m
odul
e i
s
as s
h
ow
n i
n
Fi
gu
re
1
5
.
Fig
u
re
15
. M
o
b
ile jo
in
t m
o
dule
Th
e bo
tto
m
p
l
ate o
f
m
ech
an
ical h
a
nd
is in
tegrated
with
t
h
e m
o
b
ile j
o
in
t mo
du
le in
ord
e
r
to
facilitate
t
h
e act
i
o
n
of
f
o
r
w
ar
d st
ret
c
hi
ng
o
f
m
obi
l
e
j
o
i
n
t
.
The
r
ef
or
e
t
h
ere
m
u
st
be
gui
deway
at
t
h
e b
o
t
t
o
m
pl
at
e as t
h
e
j
u
n
c
tion
b
e
t
w
een
th
e bo
ttom p
l
ate an
d
th
e
m
o
b
ile j
o
i
n
t. Here we u
s
e th
e MGN5
C gu
id
eway of
HI
WI
NM
I
K
R
O
wi
t
h
7
0
m
m
l
e
ngt
h.
Th
e
act
i
on
fo
rce i
s
ge
nerat
e
d
by
t
h
e
pne
um
at
ic cy
l
i
nder
d
u
r
i
ng t
h
e
m
ovem
e
nt
. Th
e pne
um
at
i
c
cy
l
i
nder i
s
desi
gne
d t
o
be i
n
st
al
l
e
d at
t
h
e b
o
t
t
o
m
of m
echani
cal
ha
nd
w
h
ere t
h
e
m
o
b
ile j
o
in
t an
d
th
e ax
is o
f
p
n
e
u
m
atic
cy
lin
d
e
r are in
teg
r
ated
. The mo
v
i
n
g
sp
eed
of th
is
m
o
b
ile jo
in
t is
co
n
t
ro
lled
b
y
th
e exh
a
u
s
t th
ro
ttle v
a
lv
e. The h
i
gh
er sp
ee
d
will lead
to
larg
er im
p
act o
n
t
h
e m
ech
an
ical h
a
nd
,
th
u
s
th
is statistic
m
u
st b
e
ad
ju
sted
in
accord
an
ce
with
t
h
e
req
u
i
r
em
ent
of pi
an
o
-
pl
ay
i
n
g. T
h
e di
m
e
nsi
ons
o
f
the de
sign a
p
pearance
are
as
sho
w
n i
n
Fi
gu
r
e
1
6
.
Fi
gu
re 1
6
. Pres
si
ng
m
odul
e
4.
AN
ALY
S
IS
O
N
THE
FIN
G
ERS O
F
ME
CH
ANI
C
A
L
HA
ND
The R
&
D
of
t
h
e fi
n
g
ers
o
f
m
echani
cal
han
d
has
go
ne t
h
r
o
u
g
h
t
h
re
e ge
ne
r
a
t
i
ons
of
desi
g
n
s s
u
c
h
t
h
at
t
h
e anal
y
s
i
s
o
n
t
h
e
fi
n
g
er
s a
r
e f
o
c
u
sed
o
n
t
h
e com
p
ari
s
o
n
s am
ong t
h
e
st
ruct
u
r
al
st
re
n
g
t
h
s a
n
d st
ress
es o
f
t
h
ese t
h
ree
ge
nerat
i
o
ns, a
n
d t
h
e fo
rm
ul
a ca
lculated from
these stress
related statistics.
The analysis on the
f
i
ng
er
s th
rou
gh sof
t
w
a
r
e
ap
pro
ach an
d t
h
e
re
sults are
as s
hown bel
o
w.
4.
1. St
ati
c
An
al
ysi
s
o
f
t
h
e
Fi
ngers
Acco
r
d
i
n
g t
o
t
h
e dat
a
o
f
out
put
fi
l
e
of
AB
AQ
US/
C
A
E
, t
h
e m
a
xim
u
m
st
ress of m
echani
cal
fi
ng
e
r
takes
place at t
h
e elem
ent nea
r
the
fi
xed end. Since i
n
t
h
is st
udy
we
focus
a
ll the lo
a
d
s of mechanical
ha
nd
on
Evaluation Warning : The document was created with Spire.PDF for Python.