derive
that
force
graph
from
the
pin-column
mo
del.
Figure
5.2
shows
a
single
pin
p
osition
after
torque
has
b
een
applied
to
the
plug.
The
forces
acting
of
the
driv
er
pin
are
the
friction
from
the
sides,
the
spring
contact
force
from
ab ov
e,
and
the
con
tact
force
from
the
key
pin
b
elo
w.
The
amount
of
pressure
y
ou
apply
to
the
pick
determines
the
con
tact
force
from
b elow.
The
spring
force
increases
as
the
pins
are
pushed
into
the
h
ull,
but
the
increase
is
slight,
so
we
will
assume
that
the
spring
force
is
constan
t
ov
er
the
range
of
displacements
w
e
are
interested
in.
The
pins
will
not
mo
v
e
unless
you
apply
enough
pressure
to
o
v
ercome
the
spring
force.
The
binding
friction
is
prop ortional
to
how
hard
the
driver
pin
is
b eing
scissored
b
et
w
een
the
plug
and
the
h
ull,
which
in
this
case
is
prop
ortional
to
the
torque.
The
more
torque
you
apply
to
the
plug,
the
harder
it
will
b e
to
mov
e
the
pins.
T
o
make
a
pin
mov
e,
you
need
to
apply
a
pressure
that
is
greater
than
the
sum
of
the
spring
and
friction
forces.
When
the
b ottom
of
the
driver
pin
reac
hes
the
sheer
line,
the
situation
suddenly
changes.
See
Figure
5.3.
The
friction
binding
force
drops
to
zero
and
the
plug
rotates
slightly
(un
til
some
other
pin
binds).
Now
the
only
resistance
to
motion
is
the
spring
force.
After
the
top
of
the
key
pin
crosses
the
gap
b etw
een
the
plug
and
the
hull,
a
new
contact
force
arises
from
the
key
pin
striking
the
hull.
This
force
can
b e
quite
large,
and
it
causes
a
p eak
in
the
amount
of
pressure
needed
to
mov
e
a
pin.
If
the
pins
are
pushed
further
into
the
hull,
the
key
pin
acquires
a
binding
ction
lik
e
the
driver
pin
had
in
the
initial
situation.
See
Figure
5.4.
Thus,
the
amount
of
pressure
needed
11
Figure
5.1:
The
pin-column
mo del
to
mov
e
the
pins
b
efore
and
after
the
sheer
line
is
ab out
the
same.
Increasing
the
torque
increases
the
required
pressure.
At
the
sheer
line,
the
pressure
increases
dramatically
due
to
the
key
pin
hitting
the
hull.
This
analysis
is
summarized
graphically
in
gure
5.5.
12
Figure
5.2:
Binding
in
the
pin-column
mo
del
13
Figure
5.3:
Pins
at
the
sheer
line
14
Figure
5.4:
Key
pin
en
ters
h
ull
15
Figure
5.5:
Pressure
required
to
mov
e
pins
16