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Explore the interpenetration of solids via lectures on constructing hyperbolas. Understand cone-cutting plane intersection methods. Lecturer: Anupam Saxena.
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TA 101Think and Analyze AnupamSaxena Associate Professor Mechanical Engineering Compliant and Robotic Systems Lab Indian Institute of Technology Kanpur
TA:GIVEN THREE POINTS, POSSIBLE TO CONSTRUCT A HYPERBOLA THAT PASSES THROUGH THEM ? TA:NEED MORE CONDITIONS, OR WHAT IS GIVEN IS SUFFICIENT? ANUPAM SAXENA TA101 LECTURE XXIII CONSTRUCTION OF HYPERBOLA
1 3 5 7 1 3 5 7 TA: ADDITIONAL INFORMATION, IN TERMS OF THE CONE AND THE CUTTING PLANE ANUPAM SAXENA TA101 LECTURE XXIII CONSTRUCTION OF HYPERBOLA
1 3 5 7 1 3 5 7 TA: IS THE INFORMATION, IN TERMS OF THE CONE AND THE CUTTING PLANE IMPLICIT WITHIN THE GIVEN THREE POINTS? ANUPAM SAXENA TA101 LECTURE XXIII CONSTRUCTION OF HYPERBOLA
TA: TO DETERMINE THE INTERSECTION (CURVE) BETWEEN CONE AND CYLINDER j j k k i i TA: WHERE DO YOU EXPECT THE INTERSECTION POINTS TO BE ? l l a a g g b b 1 c c e e 2 TA: FROM WHICH VIEW CAN THEY BE EASILY AVAILABLE? 12 11 3 d d 10 4 5 9 TA: SELECTED LINE OR GENERATOR METHOD 6 8 7 a b, l a b l c c, k k j d, j d e i e, i g g 1 10 7 4 6, 8 5, 9 4, 10 3, 11 2, 12 3, 5 2, 6 1, 7 8, 12 9, 11 ANUPAM SAXENA TA101 LECTURE XXIII INTERPENETRATION OF SOLIDS
TA: CUTTING PLANE METHOD e d c b a b 1 c 2 3 d e 4 5 6 7 8 9 e e d d c c b b a 1 2 3 4 5 6 7 8 9 ANUPAM SAXENA TA101 LECTURE XXIII INTERPENETRATION OF SOLIDS
j j k k i i l l a a g g b b 1 c c e e 2 12 11 3 d d 10 4 5 9 6 8 7 a b, l a b l c c, k k j d, j d e i e, i g g 1 10 7 4 6, 8 5, 9 4, 10 3, 11 2, 12 3, 5 2, 6 1, 7 8, 12 9, 11 ANUPAM SAXENA TA101 LECTURE XXIII INTERPENETRATION OF SOLIDS
TA: TO DETERMINE THE INTERSECTION (CURVE) BETWEEN CONE AND RECTANGULAR PRISM n i i g k k TA: WHAT DOES ONE EXPECT? e e c ELLIPSE c a a l l b b TA: WHAT DOES ONE EXPECT? d d 1 j j 2 12 f PARABOLA h h 3 11 m 10 4 5 9 6 8 7 a a b, c c b d, e e d f, g g f m, n m n h i h, i k j j, k l l 1 7 10 4 6, 8 5, 9 4, 10 3, 11 2, 12 3, 5 2, 6 1, 7 8, 12 9, 11 ANUPAM SAXENA TA101 LECTURE XXIII INTERPENETRATION OF SOLIDS
Think and Analyze Until next time...