Birla Institute of Technology & Science, Pilani  Hyderabad
CAD
MF 312

Fall 2015
CAD
ME C382 /MF C382
A. M. Marathe
Dept. of Mech. Engg.
Chapter 1
Geometric transformations
Geometric transformations
A geometric transformation is a function whose
domain and range are one and the same with
some geometric structure, typically Euclidean
s
Birla Institute of Technology & Science, Pilani  Hyderabad
CAD
MF 312

Fall 2015
CAD
ME C382 /MF C382
A. M. Marathe
Dept. of Mech. Engg.
Chapter 3
Dierential geometry of curves and surfaces
Planar curves
A plane curve expressed in parametric form is
x = x(t), y = y (t),
t1 t t2 .
Coordinates of the curve are represented as
functions o
Birla Institute of Technology & Science, Pilani  Hyderabad
CAD
MF 312

Fall 2015
CAD
A. M. Marathe
Dept. of Mech. Engg.
February 4, 2013
ROTATIONS
Rotation about origin
Eulers theorem The most general displacement of a rigid
body with one point xed is rotation about some axis
passing through the xed point.
Prove the theorem for 3D cas
Birla Institute of Technology & Science, Pilani  Hyderabad
CAD
MF 312

Fall 2015
CAD
ME C382 /MF C382
A. M. Marathe
Dept. of Mech. Engg.
Chapter
Topological transformations
Topological transformations
Usually thought of compact surfaces, e.g.,
sphere instead of plane.
Bending, stretching, distortion, compression are
allowed.
Tearing a
Birla Institute of Technology & Science, Pilani  Hyderabad
CAD
MF 312

Fall 2015
Topology
BMC Notes by Maia Averett
April 26, 2011
A mathematician named Klein
Thought the M bius band was divine.
o
Said he, If you glue
The edges of two,
Youll get a weird bottle like mine.
Anonymous
1
Surfaces
What shape is the earth? Round? Round like
Birla Institute of Technology & Science, Pilani  Hyderabad
CAD
MF 312

Fall 2015
Parameterizing the Sphere
In spherical coordinates we know that the equation of a sphere of radius a is given by,
So the equation of this sphere (in spherical coordinates) is
(STEP 01) Now, convert Cartesian coordinates into spherical coordinates.
Replace
Birla Institute of Technology & Science, Pilani  Hyderabad
CAD
MF 312

Spring 2016
3. Completely dimension the objects shown (by hand) using proper dimensioning techniques.
Wherever a numeric dimension value is required, place an x. Use dimensioning symbols
where necessary.
Solution:
0.50
2.00
Birla Institute of Technology & Science, Pilani  Hyderabad
CAD
MF 312

Spring 2016
MEC203 Midterm Exam I
MEC203: Engineering Graphics and CAD
Midterm Exam I
Time & Date: 16:0017:20, October 8, 2013
Note: This is a closed book exam!
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1. Please answer the followin