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Design and Communication Graphics
The Oblique Plane
Oblique Planes 1Pictorial views of three planes are shown. In the space provided below draw the line of intersection of these planes with the planes of reference (traces of the planes).
Oblique Planes 1
At the end of this sheet, the students should be able to
• Draw the line of intersection between the various planes and the planes
of reference
• Understand what is meant by the vertical and horizontal trace of simply inclined planes. (resource DVD, Plane and descriptive geometry slides No. 62-71 )
• Realise that the inclination of the inclined plane to the vertical plane is seen in plan
• The inclination of the inclined plane to the horizontal plane is seen in elevation
Oblique Planes 1
Oblique Planes 2
Oblique Planes 2
At the end of the sheet the students should be able to
• Determine the projections of solids cut by simply inclined planes
• Determine the true shape of sections cut by simply inclined planes
• Understand the concept of rebating planes ( see Resource DVD Plane and Descriptive geometry slide No.72-79 )
Oblique Planes 2
Oblique Planes 3A pyramid is cut by a simply inclined plane as shown.
Complete the elevation and show the true shape of the cut section
A cone cut by a simply inclined plane is used to design the seat shown.
Complete the plan and show the true shape
of the cut section
Oblique Planes 3
At the end of this sheet , the students should be able to
• Determine the projections of objects cut by simply inclined planes
• Determine the true shape of the cut sections
• Practice rebatting inclined planes
Oblique Planes 3
Oblique Planes 4
At the end of this sheet, the students should be able to
• Distinguish between simply inclined and obliquely inclined plane surfaces
• Understand the concept of a plane surface defined by its traces
• Draw the projections of lines on an oblique plane that are parallel to the HP
• Draw the projections of lines on an oblique plane that are parallel to the VP
Oblique Planes 4
Oblique Planes 4
Oblique Planes 5The building shown consists of a cylinder cut by an oblique plane.
The incomplete elevation and plan of the cylinder and the traces of an oblique plane are shown below.
(a) Complete the elevation and determine the true shape of the cut surface. (b) Identify the major and minor axes in the true shape of the cut surface.
Copenhagen Planetarium
Oblique Planes 5At the end of this sheet the students should be able to
• Draw an edge view of an oblique plane (convert an oblique plane into a simply inclined plane)
• Determine the projection of solids cut by an oblique plane
• Rebatt an oblique plane
• Establish the true shape of objects cut by an oblique plane
Oblique Planes 5
Oblique Planes 6
Oblique Planes 6
At the end of this sheet the students should be able to
• Locate points on the oblique plane in elevation from the plan.
See also Resource DVD, Plane and Descriptive geometry slides No. 84-115
• Show by two methods the inclination of the oblique plane to the horizontal plane
• Establish the true shape of the cut section
Oblique Planes 6
Oblique Planes 7
Oblique Planes 7
At the end of this sheet, the students should be able to
• Draw cut sections of a sphere knowing that a sphere cut by any plane will produce circular sections
• Locate points in elevation from the plan
Oblique Planes 7
Oblique Planes 8
The partial elevation and plan of a jewellery display stand is shown.
Draw the projections of the jewellery stand when cut by the oblique plane VTH.
Oblique Planes 8
At the end of this sheet the students should be able to
• Apply what they have learnt from the previous sheets to solve the problem
Oblique Planes 8
Oblique Planes 9
Oblique Planes 9
At the end of this sheet the students should be able to
• Understand that any point on the plane touching the XY line in elevation is on the Horizontal Trace in plan
• Understand that any horizontal line on the plane in elevation, will be parallel to the horizontal trace in plan
Oblique Planes 9
Oblique Planes 10
A
B
lid
base
Oblique Planes 10
At the end of this sheet, the students should be able to
• Draw the traces of an oblique plane given its inclination to the horizontal plane by two methods.
• Find the inclination of the oblique plane to the vertical plane.
Oblique Planes 10
A
B
lid
base
Oblique Planes 11
Oblique Planes 11At the end of this sheet, the students should be able to
• Use information gathered in the previous sheet to complete the elevation and plan of the cut solid
• Establish the true shape of the cut section
• Establish that the true length of the handle will be seen in the auxiliary elevation
• Understand that the right angle will be seen if one line is seen as a true length
• Understand that a line perpendicular to a plane is perpendicular to every line on that plane
Oblique Planes 11
Oblique Planes 12
Oblique Planes 12At the end of this sheet, the students should be able to
• Identify the dihedral angle between two intersecting vertical surfaces
• Determine the dihedral angle between two intersecting roof surfaces when given the line of intersection which is horizontal
• Determine the dihedral angle between two intersecting planes
• Determine the line of intersection between two intersecting planes
Oblique Planes 12
Oblique Planes 13
Oblique Planes 13
At the end of this sheet, the students should be able to
• Determine the traces of oblique planes that contain given surfaces
• Determine the line of intersection between two planes
• Determine the inclination of a plane to the planes of reference
Oblique Planes 13
Oblique Planes 14
Oblique Planes 14
At the end of this sheet, the students should be able to
• Determine the horizontal and vertical traces of two intersecting laminae
• Determine the line of intersection between oblique planes from their traces
• Determine the dihedral angle between two oblique planes from their traces
• Determine the angle of inclination of an oblique plane to the planes of reference
Oblique Planes 14
Oblique Planes 15
At the end of this sheet, the students should be able to
• Determine the height and draw the elevation of the roof surfaces A, B and C
• Determine the true length of an oblique line
• Establish the dihedral angle between two intersecting roof surfaces
• Establish the true shape of an obliquely inclined plane
• Determine the projections of a line drawn from point X which is 45mm long and rests on the roof surface C
• Determine the true inclination of a line to the H.P.
Oblique Planes 15
Oblique Planes 15
Oblique Planes 16
Oblique Planes 16
At the end of this sheet, the students should be able to
• Determine the true length of the line of intersection between two planes
• Determine the dihedral angle between two planes
• Determine the true shape of oblique planes
• Determine the projections of a line 45mm long resting on a plane having an apparent angle of 45 degrees
• Solve problems involving the reversal of the dihedral angle between two planes
Oblique Planes 16
