Transcript Department Of Technical Education Graphic Communication Tangency – 90o angle (1) Start the tangency with the two lines that are to be joined by.

Department Of Technical Education
Graphic Communication
Tangency – 90o angle (1)
Start the tangency with
the two lines that are
to be joined by the
curve.
In this case the two
lines are drawn at right
angles to each other.
The two lines are to be
joined by a 30mm
radius curve.
Tangency – 90o angle (2)
Draw two construction
lines which are parallel
with the outlines to be
joined.
30
Because the curve to
be drawn is 30mm
radius the two
construction lines
should be drawn 30mm
away from the outlines.
30
Where these two lines
cross will be the centre
for the tangency curve.
Tangency – 90o angle (3)
Mark where the two
construction lines cross
with a small dot as this will
act as the centre of the
curve to be drawn.
Project two construction
lines through this centre
until they cross the
outlines. These lines
should be projected at 90o
to the outlines.
Mark each of the points
where the construction
lines cross the outlines
with a small dot. These
are the two tangent points
where the straight lines
and the curve meet.
Tangency – 90o angle (4)
Draw a 30mm radius
arc using the centre
found, and starting and
ending at the tangent
points.
Note that it is usual to
draw the curves first
and then draw the
straight lines after.
Finish the drawing by
adding the straight
lines.
Tangency – <90o angle (1)
The second style of
tangency will join
together two lines that
meet at less than a 90o
angle.
Again the two lines will
be joined with an arc
which has a radius of
30mm.
Tangency – <90o angle (2)
Two construction lines
should be drawn 30mm
away from the outlines
and they should also be
parallel to the outlines.
30
Where these two lines
cross gives the centre
for the 30mm radius
tangency arc.
Tangency – <90o angle (3)
Mark the centre of the
arc with a small dot.
Project two
construction lines from
the centre at right
angles to the outlines.
Where these lines cross
the outlines gives the
tangent points for the
30mm radius curve.
Tangency – <90o angle (4)
Using the centre found
draw a 30mm radius
curve from the first
tangent point to the
second tangent point.
Complete the drawing
by adding the straight
lines.
R30
Tangency – >90o angle (1)
The final method of
drawing tangency arcs
to two straight lines
involves an angle of
more than 90o.
Again, start with the
two straight lines that
are to be joined.
Tangency – >90o angle (2)
Draw two construction
lines 30mm away from
the outlines.
Mark the point where
the two construction
lines cross with a small
dot. This is the centre
of the 30mm tangency
arc.
30
As with the previous
two methods these
construction lines
should be parallel to
the outlines.
Tangency – >90o angle (3)
Draw two construction
lines through the
centre point found.
These lines should be
at 90o to the outlines.
Mark each of the points
where these two lines
cross the outlines with
a small dot to indicate
where the tangent
points are.
Tangency – >90o angle (4)
Draw a 30mm radius
arc using the centre
found and starting and
ending at the tangent
points.
Complete the drawing
by adding the straight
outlines.
R30
Tangency – Below two circles (1)
The starting point for
this type of tangency is
finding the centres for
the two circles that the
tangency arc should
touch.
Two circles will be used
which are 70mm apart
and positioned on a
common horizontal
centre line.
70
Tangency – Below two circles (2)
The two circles are
added to the drawing.
The left circle has a
radius of 30mm, while
the right circle has a
radius of 20mm.
Tangency – Below two circles (3)
The circles are to be joined
with an arc of 60mm radius
which touches underneath
the circles.
The centres for the two
circles will be used to find
the position of the tangent
arcs centre.
Draw a small arc 90mm
radius (60mm radius for
tangent arc plus 30mm
radius for circle) from the
centre of the left circle.
Draw a small arc 80mm
radius (60mm radius for
tangent arc plus 20mm
radius for circle) from the
centre of the right circle.
Indicate where the two arcs
cross with a small dot.
Tangency – Below two circles (4)
Draw a construction line
from the centre of the
two arcs that you have
just found to the centres
of each circle.
Where this line crosses
the circle is the tangent
point and this position
should be marked with a
small dot.
Tangency – Below two circles (5)
Using the centre just
found, draw an arc from
the first tangent point to
the second tangent
point.
Tangency – Above two circles (1)
This time the tangent arc will
touch above the circles.
A tangency arc of 110mm
will be used.
As the centres of the circles
will be closer to the
tangencies centre than the
tangent points it is now
necessary to subtract the
radius of the circle from the
tangency dimension.
Draw arcs of 80mm radius
from the left circle and
90mm radius from the right
circle, marking the crossing
point with a small dot.
Tangency – Above two circles (2)
The tangent points can
now be marked.
As with the previous
version the centre of the
tangent arc and the
centres of the circles are
joined with a straight
line, but the line needs
to be extended this time
until it touches the top
part of the circle.
Mark the found tangent
points with a small dot.
Tangency – Above two circles (3)
Using the tangency
centre just found and
working from the first
tangency point to the
second, draw a 110mm
radius arc.
Tangency – Above two circles (4)
Complete this drawing by
adding the outlines to
the remaining parts of
the original circles.
Tangency – Inside and Outside circle (1)
The next tangency
problem will join two D60
circles with a tangency
arc which touches the
inside of one circle and
the outside of the second
circle.
In this case the
dimensions of the
tangency arc will be
100mm radius.
D40
70
Tangency – Inside and Outside circle (2)
This tangency requires a
combination of processes
done in the previous
examples.
The first arc should be
drawn at 70mm radius
(100mm arc minus 30mm to
centre of circle) from the
centre of the left circle.
The second arc should be
drawn at 120mm radius
(100mm arc plus an extra
20mm to reach the centre of
the circle) from the centre of
the right circle.
Mark the centre of the
tangency arc with a small
dot and draw construction
lines to find the position of
the two tangent points.
Tangency – Inside and Outside circle (3)
Draw the arc for the
tangency first and when
this is correctly in place
finish the rest of the
drawing.
R100