True Length line lies on the planenrskumar/Index_files... · 2013-09-03 · True Length line lies on the plane . mF bF aF nF mH aH nH bH cF cH Line MN is a horizontal line. mHnH is

bF

aF

aH

bH

cF

cHmH

mF

nH

nF

iH

iF

jH

jFLine IJ is a front line.

iFjF is the true length of the

line IJ.

Line MN is a horizontal

line. mHnH is the true

length of the line MN.

True Length line lies on the plane

mF

bF

aF

nF

mH

aH

nH

bH

cF

cH




The bearing of this line

represents the strike of

the plane.

N

N59°E

Strike of a plane

mF

bF

aF

nF

mH

aH

nH

bH

cF

cH




The bearing of this line

represents the strike of

the plane.

N

N59°E

Strike of a plane

bF

aF

aH

bH

cF

cH

Edge View of a plane

Edge View of a plane

bF

aF

aH

bH

cF

cH

bF

aF

aH

bH

cF

cH Elevation

View

E.V

.

Horizontal plane

The Edge View (EV) of the plane is built in

an auxiliary view adjacent with the

Horizontal (Top) view. The angle of the EV

of the plane with the horizontal direction

represents the slope (dip ) of the planenFmF

mH

nH

Slope (dip) of a plane

Shortest line from a point to plane

bF

aF

aH

bH

cF

cH

To find the shortest line from point

to plane


TL cA

bA

aA

mF

bF

aF

nF

mH

aH

nH

bH

cF

cH

Find the EV of

plane


TL

eF

eH

eA

cA

bA

aA

mF

bF

aF

nF

mH

aH

nH

bH

cF

cH

Find the EV of

plane

Project point in

that view


TL

eF

eH

eA

cA

bA

aA

eA

eH

eF

mF

bF

aF

nF

mH

aH

nH

bH

cF

cH

Find the EV of plane

Project point in that

view

Draw perp from

point to EV

Traceback with perp

from TL in the HV

For FV use distance

mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL

eF

eH

eA

cA

bA

aA

eA

eH

eF

Horizontal directionrA

rH

rF

Shortest grade line - point to plane

mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL

eF

eH

eA

cA

bA

aA

eA

eH

eF

Horizontal directionrA

rH

rF



cH

cF

bH

aH

aF

bF


aA

bA

cATL

cH

cF

bH

nH

aH

mH

nF

aF

bF

mF


bA

aA

cA

eA

eH

eF

TL

cH

cF

bH

nH

aH

mH

nF

aF

bF

mF


eF

eH

eA

aA

bA

cA

eA

eH

eF

TL

cH

cF

bH

nH

aH

mH

nF

aF

bF

mF


rF

rH

rAHorizontal direction

eF

eH

eA

aA

bA

cA

eA

eH

eF

TL

cH

cF

bH

nH

aH

mH

nF

aF

bF

mF

qF

qH

Line at 20° slopeqA

rF

rH

rA

The slope could be

shown ONLY IN AN ELEVATION VIEW

Horizontal direction

eF

eH

eA

aA

bA

cA

eA

eH

eF

TL

cH

cF

bH

nH

aH

mH

nF

aF

bF

mF


Mechanical Engineering Drawing

MECH 211

LECTURE 6

• Continue to acquire knowledge in the

Descriptive Geometry – point and line and

plane concepts • True size (shape) of a plane

• Angle between two intersecting lines – plane method

• Location of a line through a given point intersecting a

given line to a given angle – plane method

• Location of a plane through a point parallel to two lines

• Shortest grade line between two skew lines – plane

method

The objectives of the lecture – cont’d

• Continue to acquire knowledge in the Descriptive

Geometry – point and line and plane concepts • Relative position of a line to a plane

• Line parallel to a plane

• Line intersecting a plane

• Line perpendicular to a plane

• Intersection of two planes – EV method

• The cutting plane method – intersection of a line with a plane

• Intersection of two planes – CP method

The objectives of the lecture – cont’d

True Shape of Plane

bF

aF

aH

bH

cF

cH

H

F

True Shape of a Plane (TSP) is seen in the second auxilairy view,

adjacent to the EV of the plane.

True Shape of Plane

mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

bA

aA

E.V

.

H

F

H A



mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

bA

aA

E.V

.

H

F

H A

A A1

cA1aA1

bA1



TSP

True Shape of Plane

True Shape of Plane Application, to find centre of circle in an oblique plane



Angle of Line with Oblique Plane

bF

aF

aH

bH

cF

cH

H

F

Angle of line with an oblique plane is seen when the line is seen in

true length and the plane in edge view

pH

qH

pF

qF


mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

bA

aA

E.V

.

H

F

H A



pH

qH

pF

qF

qA

pA


mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

bA

aA

E.V

.

H

F

H A

A A1

cA1aA1

bA1



TSPpH

qH

pF

qF

qA

pA

qA1

pA1

mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

bA

aA

E.V

.

H

F

H A

A A1

cA1aA1

bA1



TSPpH

qH

pF

qF

qA

pA

bA2

aA2

cA2

pA2

qA2

qA1

pA1EV

TL


Angle Between Intersecting Lines

mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

bA

aA

E.V

.

H

F

H A

The two lines AB and BC define a plane that is represented as a true

shape. In that TS plane, the angles are seen as real size and thus the

angle between the two lines could be measured there.

mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

bA

aA

E.V

.

H

F

H A

A A1

cA1aA1

bA1

The two lines AB and BC define a plane that is represented as a true

shape. In that TS plane, the angles are seen as real size and thus the

angle between the two lines could be measured there.

TSP

Angel Between Intersecting Lines

Dihedral angle between planes

For dihedral angles we go the view where the lines are seen as

points for which we go to aux view where the TL line is seen as

points.

Dihedral angle between planes

Since line 1-2 is common to both planes A and B, and if the line

is seen as point, then both planes will be seen as edge views and

the angle between the planes can be found

mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

bA

aA

E.V

.

H

F

H A

Draw a line CS that passes through the point C and intersects line AB

under an angle of 75°.

Location of Line - plane method through a given point intersecting a given line to a given angle

mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

bA

aA

E.V

.

H

F

H A

A A1

cA1aA1

bA1

Line AB and point C describe a plane that could be represented as a

TS plane (second auxiliary view).

TSP




mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

bA

aA

E.V

.

H

F

H A

A A1

cA1aA1

bA1

Line AB and point C describe a plane that could be represented as a

TS plane (second auxiliary view).

TSP

sA1

s'A1

s'A

sA

sH

s'H

sF

s'F



In this plane, draw a line passing throug a point which cuts another

line under the given angle.

One will encounter 2 solutions to the problem.


Location of Plane through a point parallel to two lines



Shortest line – point method between two given skew lines







Shortest Line – Plane Method between two given skew lines






Shortest Horizontal Line between two given skew lines - Plane Method




Aux view 2 is drawn

parallel to folding line for

aux view 1


Aux view 2 is drawn


aux view 1


Aux view 2 is drawn


aux view 1




Shortest Grade Line between two given skew lines




Aux view 2 is drawn at given

grade to folding line for aux

view 1



mF

bF

aF

eF

rF

nF

fF

eH

mH

aH

rH

nH

fH

bH

sF

cF

sH

cH

A line could be positioned

relative to a plane as:

1) Contained (MN)

2) Parallel (EF)

3) Intersecting (RS)

Relative position of line to plane

mF

bF

aF

nF

mH

aH

nH

bH

cF

cH

A line contained (MN) in a

plane has all the points

belonging to that plane (ABC)

Line contained in a plane

mF

bF

aF

eF

nF

fF

eH

mH

aH

nH

fH

bH

cF

cH

A line parallel to a plane (EF)

must be parallel to a line

belonging to that plane (MN)

Line parallel to plane

bF

aF

aH

bH

cF

A line (RS) intersecting a

plane (ABC) has a common

point to that plane (J)

cH

rF

rH

sF

sH

jH

jF

Line intersecting a plane If the line is not parallel to the plane, it should intersect the plane

and the common point is called the piercing point

Intersection of line with plane – CP Cutting Plane Method to see piercing points

bF

aF

rF

aH

rH

bH

sF

cF


plane (ABC) must have a

common point to that plane

sH

cH

H

F


• If a CP with line RS

is introduced to cut

abc, the line RS will

intersect at piercing

point with abc

bF

aF

rF

aH

rH

bH

sF

cF




sH

cH

H

F

Intersection of line with plane – CP Cutting Plane Method to see piercing points •Line RS is in

the since the EV

of CP coincides

RS

• If the two lines

are in a plane

and if they are

not parallel,

they must

intersect in the

plane

bF

aF

rF

aH

rH

bH

sF

cF




sH

cH

pH

qH

qF

pF

H

F

add a cutting plane whose

edge view conincides with

line RS in the top view


bF

aF

aH

bH

cF

cH

pH

qH

qF

pF

H

FrF

rH

sF

sHadd a cutting plane whose



the point of intersection between the

line RS and the projection of the CP in

the front view will give the common

point between the line RS and the

plane abc. The point J is the piercing

point




jH

jF


Rule of Visibility

• Information about visibility is collected in adjacent view

• Point 5 on edge 1-3 is nearer to the observer. So edge 1-3 is visible in view B

• Point 7 on edge 1-3 is nearer to the observer. So edge 1-3 is visible in view A


bF

aF

rF

aH

rH

bH

sF

cF




sH

cHjH

jF

pH

qH

qF

pF

H

F

add a cutting plane whose



The corner or edge of the object nearest to

the observer will be visible.

The corner or edge fartherest from the

observer will usually be hidden if it lies

within the outline of the view.

Information about the visibility in a view

will be collected in any adjacent view.

Intersection of line with plane – EV Edge View Method to see piercing points

bF

aF

aH

bH

cF

cH

H

F


bF

aF

aH

bH

cF

cH

H

F

pH qH

pF

qF


mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

aA

E.V

.

H

F

H A

pH qH

pF

qF

qA

pA

mF

bF

aF

nF

mH

aH

nH

bH

cF

cHTL cA

aA

E.V

.

H

F

H A

pH qH

pF

qF

qA

pA

jH

jF

jA


Intersection of two planes - EV Edge View Method







•The line must

intersect or be

parallel to the lines

in the plane

Intersection of two planes – CP Cutting Plane Method







Documents

True Length line lies on the planenrskumar/Index_files... · 2013-09-03 · True Length line lies on the plane . mF bF aF nF mH aH nH bH cF cH Line MN is a horizontal line. mHnH is