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

1. ___________ is a curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line.

a) Cycloid

b) Epicycloid

c) Epitrochoid

d) Trochoid

View Answer

Explanation: Cycloid form if generating point is on the circumference of generating a circle. Epicycloid represents generating circle rolls on the directing circle. Epitrochoid is that the generating point is within or outside the generating circle but generating circle rolls on directing circle.

2. ___________ is a curve generated by a point on the circumference of a circle, which rolls without slipping along another circle outside it.

a) Trochoid

b) Epicycloid

c) Hypotrochoid

d) Involute

View Answer

Explanation: Trochoid is curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line. ‘Hypo’ represents the generating circle is inside the directing circle.

3. __________ is a curve generated by a point on the circumference of a circle which rolls without slipping on a straight line.

a) Trochoid

b) Epicycloid

c) Cycloid

d) Evolute

View Answer

Explanation: Trochoid is curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line. Cycloid is a curve generated by a point on the circumference of a circle which rolls along a straight line. ‘Epi’ represents the directing path is a circle.

4. When the circle rolls along another circle inside it, the curve is called a __________

a) Epicycloid

b) Cycloid

c) Trochoid

d) Hypocycloid

View Answer

Explanation: Cycloid is a curve generated by a point on the circumference of a circle which rolls along a straight line. ‘Epi’ represents the directing path is a circle. Trochoid is a curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line. ‘Hypo’ represents the generating circle is inside the directing circle.

5. Match the following

1. | Generating point is within the circumference of circle and generating circle rolls on straight line. | i. | Inferior trochoid |
---|---|---|---|

2. | Generating point is on the circumference of circle and generating circle rolls on straight line. | ii. | Epicycloid |

3. | Generating point is outside the circumference of circle and generating circle rolls on straight line. | iii. | Cycloid |

4. | Generating point is on the circumference of circle and generating circle rolls along another circle outside it. | iv. | Superior trochoid |

a) 1, i; 2, iii; 3, iv; 4, ii

b) 1, ii; 2, iii; 3, i; 4, iv

c) 1, ii; 2, iv; 3, iii; 4, i

d) 1, iv; 2, iii; 3, ii; 4, i

View Answer

Explanation: Trochoid is curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line. Inferior or superior depends on whether the generating point in within or outside the generating circle. If directing path is straight line then the curve is cycloid.

6. Match the following

1. | Generating point is within the circumference of circle and generating circle rolls on another circle outside it | i. | Superior Epitrochoid |

2. | Generating point is within or outside the circumference of circle and generating circle rolls inside another circle. | ii. | Inferior Epitrochoid |

3. | Generating point is outside the circumference of circle and generating circle rolls on another circle outside it. | iii. | Hypotrochoid |

4. | Generating point is on the circumference of circle and generating circle rolls along another circle inside it. | iv. | Hypocycloid |

a) 1, i; 2, iii; 3, iv; 4, ii

b) 1, ii; 2, iii; 3, i; 4, iv

c) 1, ii; 2, iv; 3, iii; 4, i

d) 1, iv; 2, iii; 3, ii; 4, i

View Answer

Explanation: Inferior or superior depends on whether the generating point in within or outside the generating circle. ‘Hypo’ represents the generating circle is inside the directing circle. Trochoid is curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line.

7. Steps are given to find the normal and tangent for a cycloid. Arrange the steps if C is the centre for generating circle and PA is the directing line. N is the point on cycloid.

i. Through M, draw a line MO perpendicular to the directing line PA and cutting at O.

ii. With centre N and radius equal to radius of generating circle, draw an arc cutting locus of C at M.

iii. Draw a perpendicular to ON at N which is tangent.

iv. Draw a line joining O and N which is normal.

a) iii, i, iv, ii

b) ii, i, iv, iii

c) iv, ii, i, iii

d) i, iv, iii, ii

View Answer

Explanation: The normal at any point on a cycloidal curve will pass through the corresponding point of contact between the generating circle and the directing line. So with help of locus of centre of generating circle we found the normal and the tangent.

8. Steps are given to find the normal and tangent to an epicycloid. Arrange the steps if C is the centre for generating circle and O is the centre of directing cycle. N is the point on epicycloid.

i. Draw a line through O and D cutting directing circle at M.

ii. Draw perpendicular to MN at N. We get tangent.

iii. With centre N and radius equal to radius of generating circle, draw an arc cutting the locus of C at D.

iv. Draw a line joining M and N which is normal.

a) iii, i, iv, ii

b) ii, i, iv, iii

c) iv, ii, i, iii

d) i, iv, iii, ii

View Answer

Explanation: The normal at any point on an epicycloidal curve will pass through the corresponding point of contact between the generating circle and the directing circle. And also with help of locus of centre of generating circle we found the normal and the tangent.

9. The generating circle will be inside the directing circle for _________

a) Cycloid

b) Inferior trochoid

c) Inferior epitrochoid

d) Hypocycloid

View Answer

Explanation: The generating circle will be inside the directing circle for hypocycloid or hypotrochoid. Trochoid is a curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line or over circle if not represented with hypo as a prefix.

10. The generating point is outside the generating circle for____________

a) Cycloid

b) Superior Trochoid

c) Inferior Trochoid

d) Epicycloid

View Answer

Explanation: If the generating point is on the circumference of generating circle then the curve formed may be cycloids or hypocycloids. Trochoid is a curve generated by a point fixed to a circle, within or outside its circumference, as the circle rolls along a straight line or a circle. But here given is outside so it is superior trochoid.

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