SECTIONING A SOLID. An object ( here a solid ) is cut by some imaginary cutting plane
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SECTIONING A SOLID. SECTIONING A SOLID. An object ( here a solid ) is An object ( here a solid ) is cut by cut by some imaginary cutting plane some imaginary cutting plane to understand internal details to understand internal details of that object. of that object. The action of cutting is calle The action of cutting is calle SECTIONING SECTIONING a solid a solid & The plane of cutting is calle The plane of cutting is calle SECTION PLANE. SECTION PLANE. actions means section planes are recommended actions means section planes are recommended . Plane perpendicular to Vp and inclined to Hp. Plane perpendicular to Vp and inclined to Hp. is a definition of an Aux. Inclined Plane i.e. A.I.P.) is a definition of an Aux. Inclined Plane i.e. A.I.P.) This section plane appears This section plane appears as a straight line in FV. as a straight line in FV. Plane perpendicular to Hp and inclined to Vp. Plane perpendicular to Hp and inclined to Vp. is a definition of an Aux. Vertical Plane i.e. A.V.P.) is a definition of an Aux. Vertical Plane i.e. A.V.P.) This section plane appears This section plane appears as a straight line in TV. as a straight line in TV. nching a section plane nching a section plane n FV or TV, the part towards observer n FV or TV, the part towards observer ed to be removed. ed to be removed. possible the smaller part is possible the smaller part is to be removed. to be removed. OBSERVER OBSERVER ASSUME ASSUME UPPER PART UPPER PART REMOVED REMOVED SECTON PLANE SECTON PLANE IN FV. IN FV. OBSERVER OBSERVER ASSUME ASSUME LOWER PART LOWER PART REMOVED REMOVED SECTON PLANE SECTON PLANE IN TV. IN TV. (A) (A) (B) (B)
description
OBSERVER. ASSUME UPPER PART REMOVED. SECTON PLANE IN FV. ASSUME LOWER PART REMOVED. SECTON PLANE IN TV. OBSERVER. SECTIONING A SOLID. An object ( here a solid ) is cut by some imaginary cutting plane to understand internal details of that object. - PowerPoint PPT Presentation
Transcript of SECTIONING A SOLID. An object ( here a solid ) is cut by some imaginary cutting plane
SECTIONING A SOLID.SECTIONING A SOLID.An object ( here a solid ) is cut by An object ( here a solid ) is cut by
some imaginary cutting planesome imaginary cutting plane to understand internal details of that to understand internal details of that
object.object.
The action of cutting is calledThe action of cutting is called SECTIONINGSECTIONING a solid a solid
&&The plane of cutting is calledThe plane of cutting is called
SECTION PLANE.SECTION PLANE.
Two cutting actions means section planes are recommendedTwo cutting actions means section planes are recommended..
A) Section Plane perpendicular to Vp and inclined to Hp.A) Section Plane perpendicular to Vp and inclined to Hp. ( This is a definition of an Aux. Inclined Plane i.e. A.I.P.)( This is a definition of an Aux. Inclined Plane i.e. A.I.P.) NOTE:- This section plane appears NOTE:- This section plane appears as a straight line in FV.as a straight line in FV. B) Section Plane perpendicular to Hp and inclined to Vp.B) Section Plane perpendicular to Hp and inclined to Vp. ( This is a definition of an Aux. Vertical Plane i.e. A.V.P.)( This is a definition of an Aux. Vertical Plane i.e. A.V.P.) NOTE:- This section plane appears NOTE:- This section plane appears as a straight line in TV.as a straight line in TV.Remember:-Remember:-1. After launching a section plane 1. After launching a section plane either in FV or TV, the part towards observereither in FV or TV, the part towards observer is assumed to be removed.is assumed to be removed.2. As far as possible the smaller part is 2. As far as possible the smaller part is assumed to be removed. assumed to be removed.
OBSERVEROBSERVER
ASSUME ASSUME UPPER PARTUPPER PARTREMOVED REMOVED SECTON PLANE
SECTON PLANE
IN FV.
IN FV.
OBSERVEROBSERVER
ASSUME ASSUME LOWER PARTLOWER PARTREMOVEDREMOVED
SECTON PLANE
SECTON PLANE IN TV.IN TV.
(A)(A)
(B)(B)
DEVELOPMENT OF SURFACES OF SOLIDS.DEVELOPMENT OF SURFACES OF SOLIDS.
MEANING:-MEANING:-ASSUME OBJECT HOLLOW AND MADE-UP OF THIN SHEET. CUT OPEN IT FROM ONE SIDE AND ASSUME OBJECT HOLLOW AND MADE-UP OF THIN SHEET. CUT OPEN IT FROM ONE SIDE AND UNFOLD THE SHEET COMPLETELY. THEN THE UNFOLD THE SHEET COMPLETELY. THEN THE SHAPE OF THAT UNFOLDED SHEET IS CALLEDSHAPE OF THAT UNFOLDED SHEET IS CALLED DEVELOPMENT OF LATERLAL SUEFACESDEVELOPMENT OF LATERLAL SUEFACES OF THAT OBJECT OR SOLID. OF THAT OBJECT OR SOLID.
LATERLAL SURFACELATERLAL SURFACE IS THE SURFACE EXCLUDING SOLID’S TOP & BASE. IS THE SURFACE EXCLUDING SOLID’S TOP & BASE.
ENGINEERING APLICATIONENGINEERING APLICATION::THERE ARE SO MANY PRODUCTS OR OBJECTS WHICH ARE DIFFICULT TO MANUFACTURE BY THERE ARE SO MANY PRODUCTS OR OBJECTS WHICH ARE DIFFICULT TO MANUFACTURE BY CONVENTIONAL MANUFACTURING PROCESSES, BECAUSE OF THEIR SHAPES AND SIZES. CONVENTIONAL MANUFACTURING PROCESSES, BECAUSE OF THEIR SHAPES AND SIZES. THOSE ARE FABRICATED IN SHEET METAL INDUSTRY BY USING THOSE ARE FABRICATED IN SHEET METAL INDUSTRY BY USING DEVELOPMENT TECHNIQUE. THERE IS A VAST RANGE OF SUCH OBJECTS. DEVELOPMENT TECHNIQUE. THERE IS A VAST RANGE OF SUCH OBJECTS.
EXAMPLES:-EXAMPLES:-Boiler Shells & chimneys, Pressure Vessels, Shovels, Trays, Boxes & Cartons, Feeding Hoppers,Boiler Shells & chimneys, Pressure Vessels, Shovels, Trays, Boxes & Cartons, Feeding Hoppers,Large Pipe sections, Body & Parts of automotives, Ships, Aeroplanes and many more.Large Pipe sections, Body & Parts of automotives, Ships, Aeroplanes and many more.
WHAT IS WHAT IS OUR OBJECTIVE OUR OBJECTIVE IN THIS TOPIC ?IN THIS TOPIC ?
To learn methods of development of surfaces ofTo learn methods of development of surfaces ofdifferent solids, their sections and frustumsdifferent solids, their sections and frustums..
1. Development is different drawing than PROJECTIONS.1. Development is different drawing than PROJECTIONS.2. It is a shape showing AREA, means it’s a 2-D plain drawing.2. It is a shape showing AREA, means it’s a 2-D plain drawing.3. Hence all dimensions of it must be TRUE dimensions.3. Hence all dimensions of it must be TRUE dimensions.4. As it is representing shape of an un-folded sheet, no edges can remain hidden4. As it is representing shape of an un-folded sheet, no edges can remain hidden And hence DOTTED LINES are never shown on development.And hence DOTTED LINES are never shown on development.
But before going ahead,But before going ahead,note following note following
ImportantImportant points points..
Study illustrations given on next page carefully.Study illustrations given on next page carefully.
D
H
D
SS
H
L
= RL
+ 3600
R=Base circle radius.L=Slant height.
L= Slant edge.S = Edge of base
L
S
S
H= Height S = Edge of base
H= Height D= base diameter
Development of lateral surfaces of different solids.(Lateral surface is the surface excluding top & base)
Prisms: No.of Rectangles
Cylinder: A RectangleCone: (Sector of circle) Pyramids: (No.of triangles)
Tetrahedron: Four Equilateral Triangles
All sides equal in length
Cube: Six Squares.
L L
= RL
+ 3600
R= Base circle radius of coneL= Slant height of coneL1 = Slant height of cut part.
Base side
Top side
L1 L
1
L= Slant edge of pyramidL1 = Slant edge of cut part.
DEVELOPMENT OF FRUSTUM OF CONE
DEVELOPMENT OF FRUSTUM OF SQUARE PYRAMID
STUDY NEXTSTUDY NEXT NINE NINE PROBLEMS OF PROBLEMS OF SECTIONS & DEVELOPMENTSECTIONS & DEVELOPMENT
FRUSTUMSFRUSTUMS
X Y
X1
Y1
a’
b’ e’
c’
d’
A
B
C
E
D
a
e
d
b
c
TRUE SHAPE
A B C D E A
DEVELOPMENT
a”
b”
c”d”
e”
Problem 1:Problem 1: A pentagonal prism , 30 mm base side & 50 mm axis A pentagonal prism , 30 mm base side & 50 mm axis is standing on Hp on it’s base whose one side is perpendicular to Vp.is standing on Hp on it’s base whose one side is perpendicular to Vp.It is cut by a section plane 45It is cut by a section plane 450 0 inclined to Hp, through mid point of axis.inclined to Hp, through mid point of axis.Draw Fv, sec.Tv & sec. Side view. Also draw true shape of section and Draw Fv, sec.Tv & sec. Side view. Also draw true shape of section and Development of surface of remaining solid.Development of surface of remaining solid.
Solution Steps:Solution Steps:for sectional views:for sectional views: Draw three views of standing prism.Draw three views of standing prism.Locate sec.plane in Fv as described.Locate sec.plane in Fv as described.Project points where edges are getting Project points where edges are getting Cut on Tv & Sv as shown in illustration.Cut on Tv & Sv as shown in illustration.Join those points in sequence and showJoin those points in sequence and showSection lines in it.Section lines in it.Make remaining part of solid dark.Make remaining part of solid dark.
For True Shape:For True Shape:Draw xDraw x11yy11 // to sec. plane // to sec. plane
Draw projectors on it from Draw projectors on it from cut points.cut points.Mark distances of points Mark distances of points of Sectioned part from Tv, of Sectioned part from Tv, on above projectors from on above projectors from xx11yy11 and join in sequence. and join in sequence.
Draw section lines in it.Draw section lines in it.It is required true shape.It is required true shape.
For Development:For Development: Draw development of entire solid. Name from Draw development of entire solid. Name from cut-open edge I.e. A. in sequence as shown.cut-open edge I.e. A. in sequence as shown.Mark the cut points on respective edges. Mark the cut points on respective edges. Join them in sequence in st. lines.Join them in sequence in st. lines.Make existing parts dev.dark.Make existing parts dev.dark.
Y
h
a
bc
d
e
g
f
X a’ b’ d’ e’c’ g’ f’h’
o’
X1
Y1
g” h”f” a”e” b”d” c”
A
B
C
D
E
F
A
G
H
SECTIONAL T.V
SECTIONAL S.V
TRUE SHAPE O
F SECTIO
N
DEVELOPMENT
SECTION
PLANE
Problem 2:Problem 2: A cone, 50 mm base diameter and 70 mm axis is A cone, 50 mm base diameter and 70 mm axis is standing on it’s base on Hp. It cut by a section plane 45standing on it’s base on Hp. It cut by a section plane 4500 inclined inclined to Hp through base end of end generator.Draw projections, to Hp through base end of end generator.Draw projections, sectional views, true shape of section and development of surfaces sectional views, true shape of section and development of surfaces of remaining solid. of remaining solid.
Solution Steps:Solution Steps:for sectional views:for sectional views: Draw three views of standing cone.Draw three views of standing cone.Locate sec.plane in Fv as described.Locate sec.plane in Fv as described.Project points where generators are Project points where generators are getting Cut on Tv & Sv as shown in getting Cut on Tv & Sv as shown in illustration.Join those points in illustration.Join those points in sequence and show Section lines in it.sequence and show Section lines in it.Make remaining part of solid dark.Make remaining part of solid dark.
For True Shape:For True Shape:Draw xDraw x11yy11 // to sec. plane // to sec. plane
Draw projectors on it from Draw projectors on it from cut points.cut points.Mark distances of points Mark distances of points of Sectioned part from Tv, of Sectioned part from Tv, on above projectors from on above projectors from xx11yy11 and join in sequence. and join in sequence.
Draw section lines in it.Draw section lines in it.It is required true shape.It is required true shape.
For Development:For Development: Draw development of entire solid. Draw development of entire solid. Name from cut-open edge i.e. A. Name from cut-open edge i.e. A. in sequence as shown.Mark the cut in sequence as shown.Mark the cut points on respective edges. points on respective edges. Join them in sequence in Join them in sequence in curvature. Make existing parts curvature. Make existing parts dev.dark.dev.dark.
X Ye’a’ b’ d’c’ g’ f’h’
a’h’b’
e’
c’g’d’f’
o’
o’
Problem 3: A cone 40mm diameter and 50 mm axis is resting on one generator on Hp( lying on Hp) which is // to Vp.. Draw it’s projections.It is cut by a horizontal section plane through it’s base center. Draw sectional TV, development of the surface of the remaining part of cone.
A
B
C
D
E
F
A
G
H
O
a1
h1
g1
f1
e1
d1
c1
b1
o1
SECTIONAL T.V
DEVELOPMENT
(SHOWING TRUE SHAPE OF SECTION)
HORIZONTALSECTION PLANE
h
a
b
c
d
e
g
f
O
Follow similar solution steps for Sec.views - True shape – Development as per previous problem!Follow similar solution steps for Sec.views - True shape – Development as per previous problem!
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A Feeding HopperIn industry.
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Two Cylindrical surfaces.
SOME ACTUAL OBJECTS ARE SHOWN, SHOWING CURVES OF INTERSECTIONS. BY WHITE ARROWS.
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