# Engineering Drawing Questions and Answers – Basics of Cycloidal Curves

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This set of Engineering Drawing Multiple Choice Questions & Answers (MCQs) focuses on “Basics of Cycloidal Curves”.

1. In the formation of the cycloidal curves, the circle which rolls with a fixed point without slipping is called _____________
a) Generating circle
b) Rolling circle
c) Slipping circle
d) Direct circle

Explanation: Cycloidal curves are formed by a point fixed on a circle called generating circling, rolling without slipping on the other circle or a straight line which is called a direct line or direct circle. As the circle which rolls generates the curve, hence called as generating circle.

2. The generating circle rolls on a circle called ________ to form the cycloidal curves.
a) Second circle
b) Rolling circle
c) Slipping circle
d) Direct circle

Explanation: Cycloidal curves are formed by a point fixed on a circle called generating circling, rolling over the circle called direct circle without slipping, even it can be a line, in that case, it is called a direct line.

3. In the design of gears tooth profile, we use cycloidal curves.
a) True
b) False

Explanation: Cycloidal curves are one type of engineering curves generated by the fixed point on a generating circle rolling on a direct circle without slipping. The tooth profile of gear in dial gauge is designed using cycloidal curves.
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4. A curve rolling on another curve is called _____ in general.
a) Trochoid
b) Epicycloid
c) Roulette
d) Hypocycloid

Explanation: Roulette is a path traced by the point fixed on a curve which is rolling on another curve which is fixed. It generalizes all epicycloids, hypocycloids, trochoids, and cycloids. The differential geometry of curves best describes the roulette.

5. Which of the following equation represents the cycloid curve?
a) Y = a(1-sinθ)
b) X = (θ-cosθ)
c) Y = a(1-cosθ)
d) Y = (1-cosθ)

Explanation: Cycloid is one such curve, where the point that formed the curve lies on the generating circle and rolls on the straight line called direct line. The equation which describes the curve best is Y = a(1-cosθ) or X = a(θ-sinθ).

6. For the cycloidal curves, the normal passes through which of the following?
a) Through the center of generating circle
b) Through the center of direct circle
c) Through the point of contact of the generating and direct circle
d) Through the midpoint of the direct line

Explanation: The normal drawn at any point on the cycloidal curves formed by generating circle and the direct circle or line, passes through the corresponding point of contact of generating circle and direct circle or line.

7. Two circles of radius R and r, where the circle with radius r having a fixed point roll outside the circle with radius R along its circumference forming epicycloid. What is the equation of epicycloid in X(θ)?
a) X(θ) = (R+r)cos(θ)-rcos($$\frac{R+r}{r}$$ θ)
b) X(θ) = (R+r)cos(θ)+rcos($$\frac{R+r}{r}$$ θ)
c) X(θ) = (R-r)cos(θ)-rcos($$\frac{R+r}{r}$$ θ)
d) X(θ) = (R+r)cos(θ)-rcos($$\frac{R-r}{r}$$ θ)

Explanation: Epicycloid is formed by the path traced by the fixed point on a circle rolling outside a circle along its circumference. It is represented as X(θ) = (R+r)cos(θ)-rcos($$\frac{R+r}{r}$$ θ), where R is the radius of a direct circle, and r is the radius of the rolling circle.

8. Two circles of radius R and r, where the circle with radius r having a fixed point roll outside the circle with radius R along its circumference forming epicycloid. What is the equation of epicycloid in Y(θ)?
a) Y(θ) = (R+r)sin(θ)-rsin($$\frac{R+r}{r}$$ θ)
b) Y(θ) = (R+r)cos(θ)+rsin($$\frac{R+r}{r}$$ θ)
c) Y(θ) = (R-r)sin(θ)-rsin($$\frac{R+r}{r}$$ θ)
d) Y(θ) = (R+r)cos(θ)+rsin($$\frac{R-r}{r}$$ θ)

Explanation: Epicycloid is formed by the path traced by the fixed point on a circle rolling outside a circle along its circumference. It is represented as Y(θ) = (R+r)sin(θ)-rsin($$\frac{R+r}{r}$$ θ), where R is the radius of a direct circle, and r is the radius of the rolling circle.

9. If the radius of a rolling circle is r and radius of a direct circle is R. And R = kr and K is an integer, how many cusps does the epicycloid?
a) R-r
b) 1
c) k
d) r/k

Explanation: Epicycloid is formed by the path traced by the fixed point on the rolling/generating circle with radius r, along the circumference of a circle with radius R, outside the circle. If R = kr, then the epicycloid will have k number of cusps if the k is an integer.

10. If the radius of a rolling circle is r and radius of a direct circle is R. And R = kr and K is a rational number p/q, how many cusps does the epicycloid?
a) R-r
b) q
c) p
d) r/k

Explanation: Epicycloid is formed by the path traced by the fixed point on the rolling/generating circle with radius r, along the circumference of a circle with radius R, outside the circle. If R = kr and k is a rational number p/q then we will have p number of cusps. For example k = 21/10, then we will have 21 cusps.

11. Two circles of radius R and r, where the circle with radius r having a fixed point roll inside the circle with radius R along its circumference forming epicycloid. What is the equation of hypocycloid in X(θ)?
a) X(θ) = (R-r)cos(θ)-rcos($$\frac{R-r}{r}$$ θ)
b) X(θ) = (R+r)cos(θ)+rcos($$\frac{R+r}{r}$$ θ)
c) X(θ) = (R-r)cos(θ)+rcos($$\frac{R-r}{r}$$ θ)
d) X(θ) = (R+r)cos(θ)-rcos($$\frac{R-r}{r}$$ θ)

Explanation: Hypocycloid is formed by the path traced by the fixed point on a circle rolling inside a circle along its circumference. It is represented as X(θ) = (R-r)cos(θ)+rcos($$\frac{R-r}{r}$$ θ), where R is the radius of a direct circle, and r is the radius of the rolling circle.

12. Two circles of radius R and r, where the circle with radius r having a fixed point roll inside the circle with radius R along its circumference forming hypocycloid. What is the equation of epicycloid in Y(θ)?
a) Y(θ) = (R+r)sin(θ)-rsin($$\frac{R+r}{r}$$ θ)
b) Y(θ) = (R+r)cos(θ)+rsin($$\frac{R+r}{r}$$ θ)
c) Y(θ) = (R-r)sin(θ)-rsin($$\frac{R-r}{r}$$ θ)
d) Y(θ) = (R+r)cos(θ)+rsin($$\frac{R-r}{r}$$ θ)

Explanation: Hypocycloid formed by the path traced by the fixed point on the rolling circle with radius r, outside the direct circle, with radius R, along its circumference, then the hypocycloid is represented by the equation Y(θ) = (R-r)sin(θ)-rsin($$\frac{R-r}{r}$$ θ).

13. What will be the hypocycloid when the radius of the rolling circle is half the radius of the direct circle?
a) A straight line equal to the length of the diameter of the direct circle
b) A semicircle with a radius equal to the direct circle
c) A semicircle with a radius equal to the rolling circle
d) A straight line equal to the length of the diameter of the rolling circle

Explanation: When a point on the rolling circle is fixed and having radius half the radius of the direct circle, results in a path of straight which is having a length equal to the length of the direct circle diameter.

14. How many numbers of cusps the epicycloid has if the radius of the rolling circle is 10 and the radius of a direct circle is 20?
a) 20
b) 2
c) 10
d) 10/20

Explanation: The given radius of rolling circle r = 10, and radius direct circle R = 20. Then the number of cusps the epicycloid has is equal to R/r = 20/10 = 2. Hence the given epicycloid has 2 cusps.

15. How many numbers of cusps the epicycloid has if the radius of the rolling circle is 3 and the radius of the direct circle is 5?
a) 15
b) 3
c) 5
d) 5/3

Explanation: The given radius of rolling circle r = 3, and radius direct circle R = 5. Then the number of cusps the epicycloid has is equal to 5. It is because the R = kr, where k = 5/3 which is ration number hence we take the numerator that is 5. Hence the given epicycloid has 5 cusps.

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