Right Profile Plane in Engineering Drawing

mai 10, 2022 Enregistrer un commentaire

Profile Project

Contour Projection of a Point

Let airplane Π₃ be determined by axes y and z.
In the left coordinate arrangement O(x,y,z) the plane Π_three is chosen the
3rd projection plane or the profile projection plane.
Orthogonal projection of a point T on the plane Π₃ is called the
tertiary projection or the profile projection of the signal T and is denoted with T'''_iii.

The plane Π₃ is rotated clockwise effectually z-axis for 90^o (left or negative rotation) into the cartoon plane.
In this rotation the bespeak T'''_iii is mapped into the point T''' on the aeroplane Π₂ .

The bespeak

T''' ∈ Π₂ is also called the 3rd project or the
left profile projection of a point T.

The right profile projection T''' ∈ Π₂ is gained in the case of the correct or positive rotation (counterclockwise) around the z-axis for ninety^o.

In the post-obit, we will only observe the left contour project and therefore information technology will be merely be referred to as the profile projection.

At this indicate we have three projections of a point T in the plane Π_two - its horizontal, vertical and contour projection (T',T'',T''').

The following animated illustration and picture represents the described process for gaining those 3 projections of a indicate in the airplane Π₂ and connections between sure projections.

Click on the motion picture for blitheness HORIZONTAL P.+VERTICAL P.+PROFILE P.

Project of a point in the drawing plane.

The plane Π₃ divides the space into two half-spaces — left and right.

View for the left profile projection is the view from the right side.

The planes Π_i, Π₂ and Π_three divide the space into viii octants.

Point T(x,y,z) belongs to a certain octant depending on the sign of the coordinates x, y and z (run across table).

octant	x	y	z
I	+	+	+
2	+	−	+
Three	+	−	−
IV	+	+	−
V	−	+	+
Half-dozen	−	−	+
VII	−	−	−
VIII	−	+	−

Profile projections of all points of the airplane Π_i lie on the y-axis, (T ∈ Π₁ <=> T''' ∈ y).

Profile projections of all points of the aeroplane Π₂ lie on the z-axis, (T ∈ Π₂ <=> T''' ∈ z).

Horizontal and vertical projections of all points of the aeroplane Π₃ lie on the y and z-axis respectively (T ∈ Π₃ <=> T' ∈ y & T'' ∈ z).

The distance of a indicate from the plane Π₃ is determined past its x-coordinate:
d(T,Π_iii) = |x|,
for 10 > 0 bespeak T lies on the right side of the aeroplane Π₃,
for x < 0 signal T lies on the left side of the plane Π₃.

Determining the True Length of a Line Segment with the Profile Projection

The line segment A^o B^o in the plane Π₃, for which is valid
d (A^o, B^o) = d (A,B), is synthetic by the rotation of the trapezoid AA'''B'''B around the line A'''B''' for 90^o.

This procedure is analogous to the procedure before explained for determining the truthful size using rotation into plane Π_i or Π₂, wherein the length of the parallel edges of the trapezoid are determined by the x-coordinates of the points A and B.

If the sign of the x-coordinates of points A and B are unlike
(one point belongs to the left and other ro the right one-half-space) then the rotated positions we have two triangles instead of a trapezoid.

Profile Projection of a Straight Line

An arbitrary straight line p, not parallel to the x-axis has for the profile projection a straight line p'''.

Bespeak P₃ which is the intersection point of the straight line p and contour airplane Π₃ is called profile trace of the line p, P_three = p ∩ Π₃ .
The horizontal project of this point lies on the y-axis and the vertical projection on the z-axis.

Contour projection of other traces of the line p, points P'''_i and P'''₂, lie on the y or z-axis.

The 3rd angle of inclination of a directly line p is the angle between the line and the profile plane, i.e. it is the bending between that line and its profile projection,
ω₃ = ∠ (p, Π_three) = ∠ (p, p''').