Angle Between Lines And Planes 6i2i1j

ANGLE BETWEEN LINES AND PLANES

Angle Between Lines and Planes Concept: To determine the angle between the line and any plane, it is necessary to obtain a view that shows a normal (TL) view of the line and at the same time the edge view of the plane.

Angle Between Lines and Planes Method: 1. EV – TS – EV (Plane) 2. TL – PV – TL (Line)

Angle Between Lines and Planes EV-TS-EV Steps: 1. Draw the EDGE VIEW of plane ABC. 2. Draw a reference plane (ARP2) parallel to the EV. Plane ABC is TS in ARP2. 3. Draw a reference plane (ARP3) parallel to line 12. Line 12 is in TL and Plane ABC is in EV in ARP3. 4. Measure the angle between Line 12 and plane ABC (EV). 5. Complete all views and check visibility.

Angle Between Lines and Planes EV-TS-EV HRP B

1

B

ARP1 Cx

x

C

1 B x

1

A A

2

2

C

TS

HRP

1

FRP

2 A

2

C A

x B A

x

C 1

Ɵ

B 2

Angle Between Lines and Planes TL-PV-TL Steps: 1. Draw the True lengthof line 12. 2. Draw a reference plane (ARP2) perpendicular to the TL at the same time draw a line Bx contained in a plane parallel to ARP2. 3. Project the points, Line 12 is PV in ARP2 while line Bx is in TL. 4. Draw a reference plane (ARP3) perpendicular to line Bx. Line 12 is TL in ARP3 while plane ABC is in EV. 5. Measure the angle between Line 12 and plane ABC (EV). 6. Complete all views and check visibility.

Angle Between Lines and Planes TL-PV-TL 1 1

B

C

B

TL

B

C x

2 A

C

PV 2 HRP FRP

TL

A A

Piercing point coincides with the the PV of line 12

1

x A

2

C

TL B 2

A

Point of intersection is the piercing point.

EV C

Ɵ 1

ANGLE BETWEEN PLANES

Angle Between Planes Concept: The true angle between two surfaces can be found by constructing an auxiliary view wherein the LOI appears as a point or both surfaces appear in edge view.

Angle Between Planes • Method 1 : LOI • Method 2 : EV – TS – EV

Angle Between Planes LOI Method Steps: 1. Locate the line of intersection of the two planes. Label the two piercing points as x and y. 2. Draw a reference plane (ARP1) parallel to LOI. 3. Project all points, the LOI is TL in ARP1. 4. Draw a reference plane (ARP2) perpendicular to line line xy (LOI). Project all points, line xy is PV in ARP2 while the planes are in EV. 5. Measure the angle between plane ABC and plane DEF (EV). 6. Complete all views and check visibility.

Angle Between Planes LOI Method E E x

B

E C B

C

B

x

C

x

D y D

D F

F ARP

A

y HRP

y

F

A

A

D C A

E

PV B F

Angle Between Planes EV-TS-EV Steps: 1. Draw the Edge View of plane ABC. 2. Draw a reference plane (ARP2) parallel to the EV of plane ABC at the same time draw a line Fx contained in a plane parallel to ARP2. 3. Project the points, Plane ABC is TS in ARP2 while line Fx is in TL. 4. Draw a reference plane (ARP3) perpendicular to line Fx. Planes ABC and DEF are EV in ARP3. 5. Measure the angle between plane ABC and plane DEF (EV). 6. Complete all views and check visibility.

Angle Between Planes EV-TS-EV A

A

E

E

C

D

x

B

F HRP

Dx C F

B B

A

D

FRP

A

F x

D

E

TS x

C E

F

C B

E

B

Ɵ FD

x

A C