Biomedical Engineering Reference
In-Depth Information
Plane of silicon
b
r
b
0
θ
Ψ
d
d
1
Ψ
c
1
c
r
= Radius of cylinder (fiber)
c
= 1/2 Width of the groove
d
= Depth of the groove
Ψ
= 1/2 Angle of the “V”
θ = 1/2 Angle of the points of
contact cylinder and groove
b
= Height of cylinder center above plane
c
= Half width of the groove
FIGURE 7.4
V-groove geometry.
Assuming Ψ constant, we look for variations in
b
<
caused by variations in
c
.
d
d
b
c
1
(7.3)
<
=
1
2
2
⎣
(
r c
)
−
1
⎦
For values of
c/r
, such that
c/r
> cos ψ, we term the value of
b
as
b
>
:
b
=
0
b
−
(
d d
− ʹ
)
>
The values of
d
and
d
′ are
2
2
c
c
b
r
b
0
d
=
and
d
ʹ
=
=
−
b
(7.4)
0
tan
ψ
0
0
Substitution yields
r
c
r
c
r
⎛
⎜
⎞
⎟
b
>
=
−
or
b
=
1
−
cos
ψ
(7.5)
>
sin
ψ
tan
ψ
sin
ψ
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