TRANSFORMATIONS AND PROJECTIONS 65
You can calculate the coordinates of the rectangular section FGHIthus created. This frustum is now
translated to S** as before with C coinciding with P. If J is the center of the rectangle FGHI, find the
direction cosines of vector O**J,O** is the center of the square BCDE**. Rotate the frustum by an
angle a about a line L through O**, where L is parallel to x-axis in the plane of BCDE**. Show
calculations and graphical results for α = 30° and 45°.
- A machine block is shown in Figure P2.2. Using transformations, show the following graphical results:
(a) Orthographic projections.
(b) The object is rotated about the y-axis by an angle φ and then about the x-axis through ψ. This is
followed by a parallel projection on z = 0 plane to get a trimetric projection. For φ = 30° and 45°, draw
figures for trimetric projections when ψ takes on the values 30°, 45°, 60° and 90°. Calculate the
foreshortening factors for each of the positions.
y-axis
x-axis
0
z-axis 10
45
30
120
60
40
15
15
Figure P2.2
- For the component shown in Figure P2.2, show the cavalier and cabinet projections for α = 30°, 0° and
–45°.
- Develop a procedure to handle transformations and projections in general of polyhederal solids.
