Materials Science and Manufacturing Engineering Miscellaneous
- For the situation shown in the figure below the expression for H in terms of r, R and D is
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AB = √(R + r)² - (D - R - r)²
H = R + AB + r
H = R + r + √(R + r + D - R - r) - (R + r - D + R + r)
H = R + r + √D[2(R + r) - D]
H = R + r + √[2D(R + r) - D²]Correct Option: D
AB = √(R + r)² - (D - R - r)²
H = R + AB + r
H = R + r + √(R + r + D - R - r) - (R + r - D + R + r)
H = R + r + √D[2(R + r) - D]
H = R + r + √[2D(R + r) - D²]
- The figure below represents a triangle PQR with initial coordinates of the vertices as P(1, 3), Q(4, 5) and ft(5.3.5). The triangle is rotated in X-Y plane about the vertex P by angle θ in clockwise direction. If sinθ = 0.6 and cosθ = 0.8, the new coordinates of the vertex Q are
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If the ∆PQR rotator by θ Clockwise then abscissa value of Q must increase whereas ordinate value of Q must decreases and only satisfying option is (4.6, 2.8) i.e. A.
Correct Option: A
If the ∆PQR rotator by θ Clockwise then abscissa value of Q must increase whereas ordinate value of Q must decreases and only satisfying option is (4.6, 2.8) i.e. A.
- A triangular face in a CAD model has vertices: P1(0, 0, 0); P2(1, 1, 0) and P3(1,1, 1).The area of the facet is
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Area = 1 × √2 × 1 = √2 = 0.707 2 2 Correct Option: B
Area = 1 × √2 × 1 = √2 = 0.707 2 2
- A robot arm PQ with end coordinates P(0,0) and Q(2,5) rotates counter clockwise about P in the XY plane by 90°. The new coordinate pair of the end point Q is
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For the new coordinate pair
x' = cosθ -sinθ x y' sinθ cosθ y
where (x',y') is coordinate at point θ.
by putting θ = 90°x' = 0 -1 x = 0 -1 2 y' 1 0 y 1 0 5 x' = -5 y' 2
Correct Option: B
For the new coordinate pair
x' = cosθ -sinθ x y' sinθ cosθ y
where (x',y') is coordinate at point θ.
by putting θ = 90°x' = 0 -1 x = 0 -1 2 y' 1 0 y 1 0 5 x' = -5 y' 2
- For generating a Coon's surface we require
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NA
Correct Option: C
NA