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Projection of a Line -- VektorCAD Tutorial

This exercise guides you through drawing the projections of a straight line inclined to both reference planes. You will construct the XY reference line, locate endpoint projections, build auxiliary views for each inclination, and rotate to satisfy both given angles.

What you'll learn

  • Drawing XY line and locating endpoint projections
  • Constructing auxiliary front view (inclination to HP)
  • Constructing auxiliary top view (inclination to VP)
  • Using arc rotation to obtain final views
  • Dimensioning true length and distances from XY

Problem Statement

Draw the projections of a line AB of true length 80 mm.

Endpoint A is 20 mm above HP and 25 mm in front of VP. The line is inclined at theta = 35 degrees to HP and phi = 45 degrees to VP.

Given Value
True length (AB) 80 mm
Point A above HP 20 mm (a' is 20 mm above XY)
Point A in front of VP 25 mm (a is 25 mm below XY)
Inclination to HP (theta) 35 degrees
Inclination to VP (phi) 45 degrees

Objective:

Requirement Details
Commands used XYLine, UCS, Point, Line, Arc, DimLin, DimAlign, Text
Construction lines Normal thickness
Final views (ab, a'b') Thick thickness
Entity Snap ON throughout

Step-by-Step

1) Prepare Drafting Settings

  1. Set Line Thickness: Select Normal from the thickness options (Thin / Normal / Thick) Normal Thickness

  2. Enable Snaps: Turn Snap ON and Entity Snap ON from the status bar Snap ON

  3. (Optional) Toggle Ortho ON to keep XY and projectors strictly horizontal/vertical

2) Draw the XY Reference Line

  1. From the Line dropdown, click XY Line
  2. Pick two points horizontally to draw XY (e.g., ~180 mm)
  3. Move UCS to one endpoint of XY:
    • Click UCS, hover over XY until the Endpoint snap glyph appears, then click
    • The UCS origin is now fixed at one end of XY

XY Line

3) Locate Endpoint A in Both Views

Place a (top view) and a' (front view) aligned vertically with the XY reference.

View Command Coordinates Position
a (Top View) POINT 0,-25 25 mm below XY
a' (Front View) POINT 0,20 20 mm above XY
  1. Draw projector: Run Line, snap to XY, draw a short vertical (Normal thickness)
  2. Mark a (Top View): Run Point, type 0,-25 and press Enter
  3. Mark a' (Front View): Run Point, type 0,20 and press Enter
  4. Label Points: Use Text to label the lower point as a and upper as a'

Point a and a'

Note

The projector ensures that a and a' are vertically aligned (same generator line).

4) Draw Locus Lines

  1. Turn Ortho ON from the status bar
  2. From point a', draw a horizontal line (locus of front view endpoints)
  3. From point a, draw another horizontal line (locus of top view endpoints)
  4. Turn Ortho OFF when done

Locus Lines

Tip

Locus lines define the horizontal paths along which the other endpoint (b/b') must lie at the same height from XY.

5) First Inclination -- Line Inclined to HP (theta = 35 degrees), Parallel to VP

Construct an auxiliary front view with true length at 35 degrees.

  1. Click Line on the toolbar
  2. Click point a' as the start point
  3. Type @80<35 in the command prompt and press Enter -- draws a line of 80 mm at 35 degrees
  4. Mark the endpoint as b1'
  5. Line a'b1' is the auxiliary front view (Normal thickness)
  6. Use Copy to transfer the locus line from a' to pass through b1'

Auxiliary a'b1'

Note

At this stage the line is assumed parallel to VP, so the front view shows the true length at the given angle theta.

6) Second Inclination -- Line Inclined to VP (phi = 45 degrees)

Construct an auxiliary top view at 45 degrees.

  1. Click Line on the toolbar
  2. Click point a as the start point
  3. Type @80<-45 in the command prompt and press Enter -- draws a line of 80 mm at 45 degrees below horizontal
  4. Mark the endpoint as b2
  5. Line ab2 is the auxiliary top view (Normal thickness)
  6. Use Copy to transfer the locus line from a to pass through b2

Auxiliary ab2

Note

At this stage the line is assumed parallel to HP, so the top view shows the true length at the given angle phi.

7) Obtain the Final Top View

  1. From b1', draw a vertical projector down to meet the locus line through a
  2. Mark this intersection as b1
  3. From the Arc dropdown, choose Start, Center, End

  4. At the prompts:

    Prompt Action
    Start point Select b1
    Center point Select a
    Direction Choose Clockwise
    End Drag until it meets the locus at b2, then click

  5. Mark the intersection as b

  6. Switch thickness to Thick
  7. Draw the final line from a to b

Top View

Tip

The arc radius equals |ab1| (the projected length). Rotating from b1 to the locus of b2 satisfies both inclinations simultaneously.

8) Obtain the Final Front View

Repeat the rotation process using the auxiliary top view to locate b' and draw line a'b' in Thick thickness.

  1. From b2, draw a vertical projector up to meet the locus line through a'
  2. Mark this intersection as b2'
  3. Use arc rotation (center = a', radius = |a'b1'|) to locate b'
  4. Switch to Thick and draw line a'b'

Front View

9) Dimensions and Labels

  1. Switch back to Normal thickness for dimensions

  2. Add dimensions:

    Dimension From To Value
    DimLin XY a' 20 mm
    DimLin XY a 25 mm
    DimAlign a' b1' 80 mm (true length)

  3. Label angles theta and phi using Text

Dimensions

Result Checklist

Item Status
XY drawn with Normal thickness
Entity Snap ON throughout
a placed 25 mm below XY; a' placed 20 mm above XY
Auxiliary front view a'b1' at 35 degrees (Normal)
Auxiliary top view ab2 at 45 degrees (Normal)
Arc rotation used to locate final b and b'
Final views ab and a'b' drawn in Thick
Dimensions: 20 mm, 25 mm from XY; true length 80 mm
Labels: a, a', b, b', theta, phi

Variations (Practice)

Variation What to try
Single inclination theta = 0 degrees, phi = 40 degrees (line parallel to HP, inclined to VP only)
Reverse order First assume phi, then rotate in front view to impose theta
Different UCS Move UCS to different working points for faster typed inputs
Different true length Use 60 mm or 100 mm and observe how views change
Both endpoints given Given distances for both A and B from HP/VP -- verify by construction

Commands Recap

Command Purpose
xyline Draw XY reference line (Normal)
ucs Reposition origin near work area
point Mark a, a', and intermediate b points
line Draw projectors, auxiliary views, and final segments
arc Rotate top/front view about A to match phi/theta while keeping radius = true length
dimlin Linear dimensions from XY to a/a'
dimalign Aligned dimension for true length
text Labels for points, angles, and notes
Format Normal for construction; Thick for final ab and a'b'

Complete

You've completed the projection of a line using auxiliary views and arc rotation to satisfy both theta and phi, with final views clearly emphasized using Thick line weight. Export to PDF to verify and share.