Projection of Solids - Auxiliary Plane Method
THEORY:
Projections on Auxiliary Planes
Sometimes none of the three principal orthographic views of an object
show the different edges and faces of an object in their true sizes,
since these edges and faces, are not parallel to any one of the three
principal planes of projection. To show such edges and faces in their
true sizes, it becomes necessary to set up additional planes of
projection other than the three principal planes of projection in the
positions which will show them in true sizes. If an edge or a face is
to be shown in true size, it should be parallel to the plane of
projection. Hence the additional planes are set up to be parallel to
the edges and faces which should be shown in true sizes. These
additional planes of projection which are set up to obtain the true
sizes are called Auxiliary Planes The views projected on these
auxiliary planes are called Auxiliary Views.
The auxiliary view method may be applied
To find the true length of a line.
To project a line that is inclined to both HP and VP as a point.
To project a plane surface or a lamina as a line.
Types of auxiliary planes
Usually, the auxiliary planes are set up such that they are parallel to
the edge or face which is to be shown in true size and perpendicular to
any one of the three principal planes of projection. Therefore, the
selection of the auxiliary plane as to which of the principal planes of
projection it should be perpendicular depends on the shape of the object
whose edge or face is to be shown in true size.
Auxiliary Vertical Plane (AVP)
An AVP is placed in the first quadrant with its surface perpendicular to HP and inclined at Φ to VP. The object is assumed to be placed in the space in between HP, VP, and AVP. The AVP intersects HP along the X1Y1 line. The direction of the sight to project the auxiliary front view will be normal to AVP.
Auxiliary Inclined Plane (AIP)
AIP is placed in the first quadrant with its surface perpendicular to VP and inclined at q to HP. The object is to be placed in the space between HP, VP, and AIP. The AIP intersects the VP along the X1Y1 line. The direction of the sight to project the auxiliary top view will be normal to the AIP
Auxiliary Plane method for solids Start with a standard position of the solid. Here instead of reproducing the view, make a new XY line that satisfies the required condition , again step by step. So first draw a new XY line to say satisfy inclination with HP. Next , new XY to satisfy the condition of orientation wrt VP