Draw the half development of a hemispherical bowl of radius 3 cm by any method
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1 o a c b d o’ e 1 3 5 4 2 6 7 8 9 1 0 Draw the half development of a hemispherical bowl of radius 3 cm by any method The approximate method is used Divide the top view into sectors as shown The lengths of one sector are required and 6 of them should be drawn adjacent to each other Linear distances o’a’, a’b’, b’c’,…1-2, 3-4 etc. are taken T F e’ d’ c’ b’ a’ 1 3 5 7 9 4 2 8 1 0 6 e’ d’ c’ b’ a’ o’ e’ d’ c’ b’ a’ o’ e’ d’ c’ b’ a’ o’ e’ d’ c’ b’ a’ o’ e’ d’ c’ b’ a’ o’ e’ d’ c’ b’ a’ o’ Divide into meridian sections – Gore development
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Draw the half development of a hemispherical bowl of radius 3 cm by any method. Divide into meridian sections – Gore development. 10. 8. 6. The approximate method is used Divide the top view into sectors as shown - PowerPoint PPT Presentation
Transcript of Draw the half development of a hemispherical bowl of radius 3 cm by any method
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Draw the half development of a hemispherical bowl of radius 3 cm by any method
The approximate method is used
Divide the top view into sectors as shown
The lengths of one sector are required and 6 of them should be drawn adjacent to each other
Linear distances o’a’, a’b’, b’c’,…1-2, 3-4 etc. are taken
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d’c’
b’a’
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c’b’a’
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c’b’a’
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c’b’a’
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Divide into meridian sections – Gore development
Sphere development – Cone method (Zone development)
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Applications of auxiliary views
Concept of Principal lines of a plane
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CPoint view
All the points lie on a straight line representing the edge of
the plane
Principal line
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A1T Draw a line on the plane in one view parallel to the other plane.
The corresponding projection in the other plane will give the true length.
Frontal line (parallel to frontal plane)
Principal lines: Lines on the boundary or within the surface, parallel to the principal planes of projection -They can be frontal lines (parallel to frontal plane)-Horizontal lines (parallel to top plane)
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b’
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True length
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F
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True length
Horizontal line (parallel to top plane)
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To obtain the edge view of a plane
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F
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True length
Horizontal line (parallel to top plane)
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-Draw a principle line in one principle view and project the true length line in the other principle view
-With the reference line perpendicular to the true length line, draw a primary auxiliary view of the plane, to obtain the edge view
Distances:
a1, b1, c1 from x1y1 = a’, b’, c’ from xy respectively
Edge view of the plane
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c1
a1
b1
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y1
Cutting plane is oblique
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y
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•Draw lines across the Top View (generator lines) starting from one corner of the plane upto the opposite side (AB).
•Project the intersection points between the generator lines and the side (AB) into the Front View
•Join these points with the corresponding corner C in the FV
•Project points of intersection of the section and the generator lines from the TV into the FV
•Two generator lines should be tangent to the section in the TV to get the width of the section in the FV
Generator lines
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A cylinder, diameter of base 30 mm is standing on its base on ground and positioned in third quadrant. The position of center of upper base is O1 (25, 30, 25) and the center of the lower base is O2 (25, 30, 75). Points A (0,60,45), B(15, 5, 70) and C(65, 35, 35) lie on a plane that cuts the cylinder in two parts. Draw the two orthographic views of the cut portion of the cylinder. The coordinates of any point (x, y, z) represent distances measured from left profile plane, frontal plane and top plane respectively.
A cylinder, diameter of base 30 mm is standing on its base on ground and positioned in third quadrant. The position of center of upper base is O1 (25, 30, 25) and the center of the lower base is O2 (25, 30, 75). Points A (0,60,45), B(15, 5, 70) and C(65, 35, 35) lie on a plane that cuts the cylinder in two parts. Draw the two orthographic views of the cut portion of the cylinder. The coordinates of any point (x, y, z) represent distances measured from left profile plane, frontal plane and top plane respectively.
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y
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AUXILIARY VIEW METHOD
•Draw the top and front views using the given coordinates
•Draw the auxiliary view in order to obtain the edge view of the plane passing through the cylinder
•From this view, project back in the Top and Front views, the points of intersection of plane and cylinder.
O1
O2
Principle line
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This color is used for projecting the top, front and auxiliary viewsThis color is used to project back the points of intersection
True length line
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BC
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Auxiliary view of TRUE SHAPE of a plane always gives an EDGE VIEW
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c’
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True length
Horizontal line (parallel to top plane)
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a1
b1Edge view of the plane
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x1
y1
c2 a2
b2
True shape and dimensions of the plane
True shape is the auxiliary view obtained from the edge view
Edge view of plane
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b3
c4
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b4
To obtain the angle of inclination and true shape of a plane
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F
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b’
c’
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b
c
True length
Horizontal line (parallel to top plane)
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lc1
a1
b1 Edge view of the plane
x y
x1
y1
c2
a2
b2
True shape and dimensions of the plane
Obtain edge views of the lines as discussed earlier
is the inclination with top plane
is the inclination with frontal plane
parallel
True shape is the auxiliary view obtained from the edge view
SECONDARY AUXILIARY VIEW
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Shortest distance between the point and line in True Length
Point
Point view of line
TO OBTAIN THE SHORTEST DISTANCE BETWEEN A POINT AND A LINE
Obtain the true length (shown in red) of a line by drawing the primary auxiliary view of the line with the reference line parallel to the original view and project the point also into the view
Draw the point view of the line by obtaining the secondary auxiliary view of the line with the reference line perpendicular to the line
The distance from the point view of the line to the point is the shortest distance between the line and point
a2, b2
p2
TF
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y1
x2
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a1
p1
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Point on line at shortest distance
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•Find the true length of one of the lines and project its point view using auxiliary plane method
•Project the other line also in each view
•The perpendicular distance between the point view of one line and the other line is the required shortest distance between the two lines
Required distance
* Point can be projected back into the other planes
TF
Primary auxiliary view
Secondary auxiliary view
DISTANCE BETWEEN 2 LINES
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b1
c1
d1TL
PAV
Parallel
True length
x1
y1
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b1
c1 d1
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TRUE LENGTH OF BOTH LINES
True Angle between the two lines
Draw primary auxiliary view such that one line (blue) shows in True Length
Draw secondary auxiliary view with reference line perpendicular to the True Length of the line to get the point view of the line
Draw a tertiary auxiliary view with reference line parallel to the other line (light green) in order to get its True Length
Since the secondary auxiliary view had the point view of the first line, the tertiary auxiliary view will have the True Length of the first line also (blue)
ANGLE BETWEEN TWO INTERSECTING LINES
x y
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c’ b’
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cd
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y2
a2 ,b2
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Point view of one line SECONDARY AUXILIARY VIEW
d2
TERTIARY AUXILIARY VIEW
Parallel
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Angle between 2 planesLine of intersection of the 2 planes (here it is True Length)
Basically you have to view the two planes in such a way that the line of intersection of the planes is perpendicular to the plane of view (point view)
•Obtain an auxiliary view such that the reference line is perpendicular to the True Length of the line of intersection of the planes
•In this case, the intersection line is parallel to both principle planes and hence is in True Length in both front and top views
•Both planes will be seen as edge views in the auxiliary view.
•The angle between the edge views is the angle between the planes
TF
PAV-Edge view of both planes
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x1y1
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Angle between the 2 planes
A decoration piece is being hung from the ceiling by three chains at points A, B and C as shown. Find the true lengths of the chains and true angle between AO and BO and between AO and CO. (Dimensions are given in m.)
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True angle between AO and BO
True lengths of chains AO and BO
Primary auxiliary view to obtain edge view of triangle AOB
Secondary auxiliary view showing true shape and dimensions of triangle AOB
True length (Principal line) of AB
a1, b1
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Figure shows the Top and Front views of an oblique square pyramid with base abcd and apex o. Find the true lengths of the edges by any method and draw the true shape of the face oab. What is the angle that the plane makes with the horizontal plane?-Identify the faces in the Front and Top views having true shape and/or edge views.
In the Front and Top views, identify the planes having an edge view and/or true shape. Draw the true shape of the plane ADC. What is the angle between planes ADC and ABC?
