dynamic mechanisms problems - t4 mechanisms name ... attached to the axle of the ch ... the original...
TRANSCRIPT
D
YN
AM
IC M
EC
HA
NIS
MS
NA
ME
: __
____
____
____
____
____
____
____
D
AT
E:
___
____
____
__
Lea
rnin
g O
utco
mes
- St
uden
ts sh
ould
be
able
to:
1
A c
yclo
id is
the
path
trac
ed o
ut b
y a
____
____
____
____
on
the
circ
umfe
renc
e of
a c
ircle
as i
t ro
lls a
long
a fi
xed
____
____
____
___
____
____
___
with
out s
lippi
ng.
Figu
re 1
sho
ws
an i
mag
e of
a r
acin
g bi
cycl
e. T
he t
yres
are
inf
late
d th
roug
h a
valv
e lo
cate
d on
the
rim
of
the
whe
el. A
circ
le a
nd a
lin
e re
pres
entin
g th
e w
heel
and
the
grou
nd a
re d
ispl
ayed
in F
igur
e 2.
Poi
nt
‘P’ r
epre
sent
s the
val
ve o
n th
e w
heel
. Pl
ot th
e lo
cus
of p
oint
P a
s th
e ci
rcle
rolls
alo
ng th
e lin
e fo
r one
com
-pl
ete
revo
lutio
n.
The
Rom
an a
rchi
tect
Vitr
uviu
s de
velo
ped
mac
hine
s fo
r m
easu
ring
dist
ance
, one
suc
h m
achi
ne w
as a
n O
dom
eter
. Th
e di
amet
er o
f a
char
iot w
heel
was
4 f
eet.
If a
m
ark
is
plac
ed o
n a
whe
el w
here
it
touc
hes
the
grou
nd,
and
the
char
iot
then
mov
es u
ntil
the
mar
k co
mes
to
the
grou
nd
agai
n, th
e ch
ario
t will
hav
e m
oved
12.
6 fe
et. A
dev
ice
was
at
tach
ed to
the
axle
of
the
char
iot s
uch
that
whe
n a
whe
el
mad
e on
e re
volu
tion,
a d
rum
with
400
tee
th o
n it
mov
ed
roun
d on
e no
tch.
A c
ompl
ete
rota
tion
of t
he d
rum
was
eq
uiva
lent
to
a m
otio
n of
400
(12.
6)=
5,04
0 fe
et b
y th
e ch
ario
t. A
t th
is p
oint
the
dev
ice
drop
ped
a st
one
into
a
bron
ze b
owl,
5040
feet
was
one
Rom
an m
ile.
Figu
re 3
repr
esen
ts th
e w
heel
of a
Rom
an c
hario
t. Th
e lin
es A
B a
nd B
C
repr
esen
t the
gro
und
on w
hich
the
char
iot i
s tra
velli
ng.
Plot
the
locu
s of p
oint
P a
s the
circ
le ro
lls a
long
AB
and
BC
, with
out
slip
ping
, unt
il po
int P
com
es in
con
tact
with
the
line
BC
.
Figu
re 3
C
onst
ruct
Sta
ndar
d C
yclo
ids f
rom
giv
en d
ata
C
onst
ruct
a ta
ngen
t at a
poi
nt o
n a
cycl
oid.
CY
CL
OID
S
Figu
re 1
- R
acin
g B
icyc
le
Figu
re 2
D
YN
AM
IC M
EC
HA
NIS
MS
NA
ME
: __
____
____
____
____
____
____
____
D
AT
E:
___
____
____
__
Lea
rnin
g O
utco
mes
- St
uden
ts sh
ould
be
able
to:
2
LO
CI 1
A la
dder
is sh
own
lean
ing
agai
nst a
bric
k w
all.
An
eyel
et fo
r atta
chin
g a
safe
ty ro
pe is
la
belle
d as
poi
nt P
on
the
ladd
er. I
f the
ladd
er w
ere
to sl
ide
dow
n th
e w
all a
nd c
ome
to a
rest
on
the
grou
nd a
s ind
icat
ed, p
lot t
he lo
cus o
f the
poi
nt P
for t
his m
ovem
ent.
P
A g
arde
ner w
ishe
s to
mar
k ou
t an
ellip
tical
sha
ped
flow
erbe
d si
mila
r to
the
one
in th
e ph
otog
raph
acr
oss.
The
gard
ener
will
use
a tr
amm
el
to m
ark
out t
he c
urve
. Th
e m
ajor
and
min
or a
xes
are
1.5m
and
1.2
m re
spec
tivel
y. T
o a
scal
e of
1:1
0 m
ark
out t
he e
llips
e us
ing
a tra
mm
el o
n th
e ce
ntre
lines
dra
wn
belo
w.
P
PA
45
PB
75
P 1A
1
P 1B
1
P 2A
2
P 2B
2
Show
n be
low
is a
n el
lipse
with
maj
or a
nd m
inor
axe
s of 1
50m
m a
nd 9
0mm
, res
pect
ivel
y. T
he li
ne
PB is
equ
al in
leng
th to
hal
f the
maj
or a
xis a
nd is
pos
ition
ed w
ith P
on
the
curv
e an
d B
on
the
m
inor
axi
s. A
is th
e po
int w
here
the
line
inte
rsec
ts th
e m
ajor
axi
s. Th
e m
easu
rem
ents
PA
and
PB
are
reco
rded
in th
e ta
ble
acro
ss. F
ill in
the
rem
aini
ng m
easu
rem
ents
in
the
tabl
e. D
o yo
u no
tice
any
patte
rn e
mer
ging
? W
hat c
an w
e co
nclu
de fr
om th
is in
form
atio
n?
C
onst
ruct
the
locu
s of a
poi
nt d
efin
ed b
y th
e m
ovem
ent o
f a li
ne re
lativ
e to
ano
ther
line
Con
stru
ct a
n el
lipse
usi
ng a
tram
mel
D
YN
AM
IC M
EC
HA
NIS
MS
NA
ME
: __
____
____
____
____
____
____
____
D
AT
E:
___
____
____
__
Lea
rnin
g O
utco
mes
- St
uden
ts sh
ould
be
able
to:
3
LO
CI 2
C
onst
ruct
the
locu
s of a
poi
nt in
a li
nk m
echa
nism
An
inte
ract
ive
toy
for
a ch
ild i
s pi
ctur
ed i
n Fi
gure
1. T
he t
oy i
ncor
pora
tes
a m
echa
nism
whi
ch c
ause
s th
e fr
ont
load
er t
o ra
ise
and
low
er w
hen
the
back
w
heel
s ro
tate
. Fig
ure
2 sh
ows
the
fron
t loa
der
in it
s lo
wes
t pos
ition
. The
line
di
agra
m fo
r the
mec
hani
sm is
show
n be
low
. (a
) D
raw
the
fron
t loa
der w
hen
it is
in a
fully
ext
ende
d po
sitio
n.
(b)
Dra
w th
e lo
cus o
f poi
nt P
for t
his m
ovem
ent
Figu
re 2
- Lo
ader
in lo
wes
t pos
ition
Figu
re 1
- In
tera
ctiv
e To
y
Figu
re 3
- El
liptic
al
Exer
cise
Mac
hine
Dai
ly e
xerc
ise
is a
n es
sent
ial c
ompo
nent
of
a he
alth
y lif
esty
le.
Figu
re 3
dis
play
s an
imag
e of
a s
ki e
xerc
ise
mac
hine
com
mon
ly
foun
d in
the
gym
. A li
ne d
iagr
am re
pres
entin
g th
e m
ovem
ent o
f th
e sk
i m
achi
ne i
s ca
ptur
ed i
n fig
ure
4. P
oint
P r
epre
sent
s th
e fr
ont o
f the
foot
pla
tform
and
is fi
xed
on B
C. P
oint
s A a
nd O
are
fix
ed, B
is a
pin
join
t and
C is
con
stra
ined
to tr
avel
abo
ut O
Pl
ot th
e lo
cus o
f poi
nt P
for t
he m
ovem
ent o
f the
mec
hani
sm.
Figu
re 4
D
YN
AM
IC M
EC
HA
NIS
MS
NA
ME
: __
____
____
____
____
____
____
____
D
AT
E:
___
____
____
__
Lea
rnin
g O
utco
mes
- St
uden
ts sh
ould
be
able
to:
4
CA
MS
2
Figu
re 1
, acr
oss,
show
s a
pinb
all
mac
hine
com
mon
ly fo
und
in a
mus
emen
t arc
ades
. A c
am a
nd
follo
wer
mec
hani
sm is
use
d to
rele
ase
the
ball
to th
e pl
ayer
. W
hen
a co
in is
inse
rted
a ca
m ro
tate
s an
ticlo
ckw
ise
and
the
follo
wer
mec
hani
sm ra
ises
the
ball
to th
e la
unch
pad
in fr
ont o
f the
plu
nger
. The
bal
l is
held
mom
enta
rily
for t
he p
lung
er to
mak
e co
ntac
t with
it; t
hen
the
mec
hani
sm d
rops
bac
k do
wn
to re
ceiv
e th
e ne
xt b
all.
(a)
Plot
the
disp
lace
men
t dia
gram
for
the
cam
giv
en th
at it
impa
rts th
e fo
llow
ing
mot
ion
on
the
follo
wer
;
0° to
180
° ris
e of
30m
m w
ith u
nifo
rm a
ccel
erat
ion
and
reta
rdat
ion
18
0° to
270
° dw
ell
27
0° to
360
° fal
l of 3
0mm
with
uni
form
vel
ocity
The
near
est a
ppro
ach
of th
e fo
llow
er to
the
cam
cen
tre is
18m
m.
(b)
Con
stru
ct th
e co
rres
pond
ing
cam
pro
file
to im
part
this
mot
ion
Show
n in
figu
re 2
is a
mod
el o
f a c
am o
pera
ted
sled
ge h
amm
er
base
d on
an
idea
by
Leon
ardo
Da
Vin
ci. T
he c
am, b
ased
on
an
Arc
him
edea
n sp
iral,
is d
esig
ned
to ra
ise
the
ham
mer
slow
ly a
nd
then
dro
p it
from
a h
eigh
t. C
onst
ruct
the
cam
pro
file
give
n a
min
imum
radi
us v
ecto
r of 1
2mm
an
d a
max
imum
radi
us v
ecto
r of 6
0mm
.
Figu
re 2
- C
am o
pera
ted
Sled
ge H
amm
er
The
orig
inal
Da
Vin
ci s
ketc
h of
the
cam
op
erat
ed h
amm
er. I
t is
belie
ved
that
he
deve
lope
d th
e id
ea
of
an
auto
mat
ic
ham
mer
to h
elp
blac
ksm
iths,
who
use
d re
peat
ed b
low
s of a
ham
mer
in th
e
proc
ess o
f for
ging
stee
l.
C
onst
ruct
cam
pro
files
and
dis
plac
emen
t dia
gram
s
Con
stru
ct ra
dial
pla
te c
ams o
f giv
en u
nifo
rm v
eloc
ity, s
impl
e ha
rmon
ic
m
otio
n, u
nifo
rm a
ccel
erat
ion
and
reta
rdat
ion
to in
-line
kni
fe e
dge
follo
wer
s.
Figu
re 1
- Pi
nbal
l Mac
hine