Category: Machine Kinematics Objective Questions

Machine Kinematics Multiple Choice Questions on “Systems of Gear Teeth”.

1. The face of the tooth is the
a) surface of the top of tooth
b) surface of tooth above the pitch surface
c) width of tooth below the pitch surface
d) width of tooth measured along the pitch circle
Answer: b
Clarification: Face of tooth is the surface of the gear tooth above the pitch surface.
Flank of tooth is the surface of the gear tooth below the pitch surface.

2. The flank of the tooth is the surface of the tooth _____________ the pitch surface.
a) above
b) below
c) on
d) none of the mentioned
Answer: b
Clarification: Face of tooth is the surface of the gear tooth above the pitch surface.
Flank of tooth is the surface of the gear tooth below the pitch surface.

3. The ratio of the number of teeth to the pitch circle diameter in millimeters, is called
a) circular pitch
b) diametral pitch
c) module
d) none of the mentioned
Answer: b
Clarification: Diametral pitch is the ratio of number of teeth to the pitch circle diameter in millimetres.
Circular pitch is the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth.

4. The ratio of the pitch circle diameter in millimeters to the number of teeth, is called circular pitch.
a) True
b) False
Answer: b
Clarification: Diametral pitch is the ratio of number of teeth to the pitch circle diameter in millimetres.
Circular pitch is the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth.

5. The product of the diametral pitch and circular pitch is equal to
a) 1
b) 1/п
c) п
d) 2п
Answer: c
Clarification: None.

6. The product of the diametral pitch and module is equal to one.
a) True
b) False
Answer: a
Clarification: None.

7. The module is the reciprocal of diametral pitch.
a) True
b) False
Answer: a
Clarification: Diametral pitch is the ratio of number of teeth to the pitch circle diameter in millimetres.
Module is the ratio of the pitch circle diameter in millimeters to the number of teeth.

8. The dedendum circle diameter is equal to
a) pitch circle dia. x cosɸ
b) addendum circle dia. x cosɸ
c) clearance circle dia. x cosɸ
d) pitch circle dia. x sinɸ
Answer: a
Clarification: It is the circle drawn through the bottom of the teeth. It is also called root circle.
Root circle diameter = Pitch circle diameter × cos φ, where φ is the pressure angle.

9. The contact ratio is the ratio of
a) length of pair of contact to the circular pitch
b) length of arc of contact to the circular pitch
c) length of arc of approach to the circular pitch
d) length of arc of recess to the circular pitch
Answer: b
Clarification: The ratio of the length of arc of contact to the circular pitch is known as contact ratio i.e. number of pairs of teeth in contact.

10. According to law of gearing, the common normal at the point of contact between a pair of teeth must always pass through the pitch point.
a) True
b) False
Answer: a
Clarification: None.

Machine Kinematics Puzzles on “Path of Contact”.

1. Which of the following is a commonly used pressure angle in gears?
a) 20
b) 10
c) 12
d) 17
Answer: a
Clarification: The pressure angle is the angle between the tangent to the pitch circles and the line drawn normal (perpendicular) to the surface of the gear teeth. It has a set of standard values which is accepted globally, 20° is one of them.

2. Addendum circle of the gear wheel has the shortest radius.
a) True
b) False
Answer: b
Clarification: Addendum circle of the gear wheel has the largest radius, the base circle has the smallest radius. Addendum of the gear plays a vital role in determining whether interference will take place or not.

3. Which of the following is true for Length of arc of contact?
a) Sum of Arc of recess and Arc of approach
b) Difference of arc of approach and arc of recess
c) Twice the arc of approach
d) Twice the arc of recess
Answer: a
Clarification: The arc of contact is given by the sum of Length of arc of approach and length of arc of recess. Numerically it is the ratio of length of path of contact and the cosine of the pressure angle.

4. Which of the following is true for Length of path of contact?
a) Sum of path of recess and path of approach
b) Difference of path of approach and path of recess
c) Twice the arc of approach
d) Twice the path of recess
Answer: a
Clarification: The path of contact is given by the sum of Length of path of approach and length of path of recess. Numerically it is dependent on pitch radius, addendum radius and the sine of pressure angle.

5. From the following data, find the addendum in mm:
Teeth on each wheel: 40
Pressure angle: 20°
Module: 6mm
Arc of contact/ pitch: 1.75
a) 6.12
b) 6.51
c) 6.61
d) 6.81
Answer: a
Clarification: Pc = πm = 18.85mm
Arc of contact = 1.75xp = 33mm
Length of path of contact = cosΦx Arc of contact
From another relation of length of path of contact we get
Ra = 126.12 mm
R = 120mm
Therefore addendum = 6.12mm.

6. From the following data:
Teeth on pinion: 30
Teeth on gear: 80
Pressure angle: 20°
Module: 12mm
Addendum: 10mm
Find the length of path of contact in mm.
a) 52.3
b) 55.4
c) 53.2
d) 54.5
Answer: a
Clarification: R = mT/2 = 480mm
r = mt/2 = 180mm
Addendum radius of pinion = 190mm
Addendum radius of gear = 490mm
Using the relation for length of path of approach
We get path of approach = 27.3mm
Path of recess = 25mm
adding both we get total length of path of contact
= 52.3mm.

7. From the following data:
Teeth on pinion: 30
Teeth on gear: 80
Pressure angle: 20°
Module: 12mm
Addendum: 10mm
Find the length of arc of contact in mm.
a) 52.333
b) 55.66
c) 53.22
d) 54.55
Answer: b
Clarification: R = mT/2 = 480mm
r = mt/2 = 180mm
Addendum radius of pinion = 190mm
Addendum radius of gear = 490mm
Using the relation for length of path of approach
We get path of approach = 27.3mm
Path of recess = 25mm
adding both we get total length of path of contact
= 52.3mm
Length of arc of contact = length of path of contact / cosΦ
= 55.66mm.

8. Maximum sliding velocity is the sum of angular velocities and its product with the length of path of contact.
a) True
b) False
Answer: b
Clarification: Maximum sliding velocity is the sum of angular velocities and its product with the length of path of appraoch.
Vs = (ω₂ + ω₁)x(length of path of approach).

9. From the following data:
Teeth on pinion: 30
Teeth on gear: 80
Pressure angle: 20°
Module: 12mm
Addendum: 10mm
Find the contact ratio.
a) 1.5
b) 1.75
c) 2
d) 1,33
Answer: b
Clarification: R = mT/2 = 480mm
r = mt/2 = 180mm
Addendum radius of pinion = 190mm
Addendum radius of gear = 490mm
Using the relation for length of path of approach
We get path of approach = 27.3mm
Path of recess = 25mm
adding both we get total length of path of contact
= 52.3mm
Length of arc of contact = length of path of contact / cosΦ
Contact ratio = Length of arc of contact/Pc
=1.75.

10. Find maximum sliding velocity in cm/s from the given data
addendum = 1 module = 5mm
Pitch line speed = 1.2m/s
Pressure angle of involute profile: 20 degrees
Tp = 20
Gear ratio = 2
a) 45.5
b) 46.8
c) 45.1
d) 47.2
Answer: a
Clarification: We know that
V = ω₁r = ω₂R
120/(mt/2) = ω₁
ω₁ = 24 rad/s
similarly
ω₂ = 12 rad/s
Now maximum sliding velocity = (ω₂ + ω₁)x(length of path of approach)
= 455.4 mm/s
= 45.5 cm/s.

To practice all Puzzles on Machine Kinematics,

Machine Kinematics Multiple Choice Questions on “Acceleration of a Particle along a Circular Path”.

1. A wheel accelerates uniformly from rest to 2000 r.p.m. in 20 seconds. What is its angular acceleration?
a) 10.475 rad/s²
b) 12 rad/s²
c) 14 rad/s²
d) 15 rad/s²
Answer: a
Clarification: Solution. Given : N₀ = 0 or ω = 0 ; N = 2000 r.p.m. or ω = 2π × 2000/60 = 209.5 rad/s ; t = 20s
Angular acceleration
Let α = Angular acceleration in rad/s²
We know that
ω = ω₀ + α.t
or 209.5 = 0 + α × 20
or α = 209.5 / 20 = 10.475 rad/s²

2. A wheel accelerates uniformly from rest to 2000 r.p.m. in 20 seconds. How many revolutions does the wheel make in attaining the speed of 2000 r.p.m.?
a) 400
b) 300
c) 333.4
d) 200
Answer: c
Clarification: Solution. Given : N₀ = 0 or ω = 0 ; N = 2000 r.p.m. or ω = 2π × 2000/60 = 209.5 rad/s ; t = 20s
We know that the angular distance moved by the wheel during 2000 r.p.m. (i.e. when ω = 209.5 rad/s),
θ = (ω₀ + ω )t/2
= (0 + 209.5)20/2
= 2095 rad
Since the angular distance moved by the wheel during one revolution is 2π radians, therefore number of revolutions made by the wheel,
n = θ /2π = 2095/2π = 333.4

3. The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known
a) tangential component
b) normal component
c) parallel component
d) none of the mentioned
Answer: a
Clarification: The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known tangential component.
The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path, is known as normal component.

4. The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path, is known as
a) tangential component
b) normal component
c) parallel component
d) none of the mentioned
Answer: b
Clarification: The acceleration of a particle at any instant moving along a circular path in a direction tangential to that instant, is known tangential component.
The acceleration of a particle at any instant moving along a circular path in a direction normal to the tangent at that instant and directed towards the centre of the circular path, is known as normal component.

5. When a particle moves along a straight path, then the radius of curvature is
a) infinitely small
b) zero
c) infinitely great
d) none of the mentioned
Answer: c
Clarification: When a particle moves along a straight path, then the radius of curvature is infinitely great. This means that v²/r is zero.

6. When a particle moves with a uniform velocity, then dv/dt will be
a) infinitely small
b) zero
c) infinitely great
d) none of the mentioned
Answer: b
Clarification: When a particle moves with a uniform velocity, then dv/dt will be zero. In other words, there will be no tangential acceleration; but the particle will have only normal or radial or centripetal acceleration.

7. A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the linear velocity at the beginning of the interval ?
a) 188.6 m/s
b) 235.5 m/s
c) 300 m/s
d) 400 m/s
Answer: a
Clarification: Given : r = 1.5 m ; N₀ = 1200 r.p.m. or ω₀ = 2 π × 1200/60 = 125.7 rad/s ;
N = 1500 r.p.m. or ω = 2 π × 1500/60 = 157 rad/s ; t = 5 s
Linear velocity at the beginning
We know that linear velocity at the beginning,
v₀ = r . ω₀ = 1.5 × 125.7 = 188.6 m/s

8. A horizontal bar 1.5 metres long and of small cross-section rotates about vertical axis through one end. It accelerates uniformly from 1200 r.p.m. to 1500 r.p.m. in an interval of 5 seconds. What is the linear velocity at end of the interval ?
a) 188.6 m/s
b) 235.5 m/s
c) 300 m/s
d) 400 m/s
Answer: b
Clarification: Given : r = 1.5 m ; N₀ = 1200 r.p.m. or ω₀ = 2 π × 1200/60 = 125.7 rad/s ;
N = 1500 r.p.m. or ω = 2 π × 1500/60 = 157 rad/s ; t = 5 s
Linear velocity at the end of 5 seconds
We also know that linear velocity after 5 seconds,
v₅ = r . ω = 1.5 × 157 = 235.5 m/s

Machine Kinematics Multiple Choice Questions on “Kinematic Link or Element”.

1. In a reciprocating steam engine, which of the following forms a kinematic link?
a) cylinder and piston
b) piston and connecting rod
c) crankshaft and flywheel
d) flywheel and engine frame
Answer: c
Clarification: Each part of a machine which moves relative to some other part, is known as a kinematic link. The piston and cylinder in a steam engine, form a pair and the motion of the piston is limited to a definite direction relative to the cylinder irrespective of the direction of motion of the crank.

2. A link or element need not to be a rigid body, but it must be a resistant body.
a) True
b) False
Answer: a
Clarification: A body is said to be a resistant body if it is capable of transmitting the required forces with negligible deformation. A link or element need not to be a rigid body, but it must be a resistant body.

3. A railway bridge is an example of a machine.
a) True
b) False
Answer: b
Clarification: When a mechanism is required to transmit power or to do some particular type of work, then it becomes a machine. A railway bridge remains static and there is no motion in it. Hence, it is not a machine.

4. The motion between a pair when limited to a definite direction, irrespective of the direction of force applied, is known as
a) completely constrained motion
b) incompletely constrained motion
c) successfully constrained motion
d) none of the mentioned
Answer: a
Clarification: When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion.

5. The motion between a pair which takes place in ____________ is known as incompletely constrained motion.
a) one direction only
b) more than one direction
c) opposite direction
d) none of the mentioned
Answer: b
Clarification: When the motion between a pair can take place in more than one direction, then the motion is called an incompletely constrained motion.

6. When the connection between the elements forming a pair is such that the constrained motion is not completed by itself, but by some other means, the motion is said to be a completely constrained motion.
a) True
b) False
Answer: b
Clarification: When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion.
When the connection between the elements forming a pair is such that the constrained motion is not completed by itself, but by some other means, the motion is said to be a successfully constrained motion.

7. The example of completely constrained motion is
a) motion of a piston in the cylinder of a steam engine
b) motion of a square bar in a square hole
c) motion of a shaft with collars at each end in a circular hole
d) all of the mentioned
Answer: d
Clarification: When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the motion is said to be a completely constrained motion. In all the above mechanism, motion is limited, so they all are examples of completely constrained motion.

8. The motion of a shaft in a circular hole is an example of
a) completely constrained motion
b) incompletely constrained motion
c) successfully constrained motion
d) none of the mentioned
Answer: b
Clarification: When the motion between a pair can take place in more than one direction, then the motion is called an incompletely constrained motion. A circular bar or shaft in a circular hole, is an example of an incompletely constrained motion as it may either rotate or slide in a hole.

9. The example of successfully constrained motion is a
a) motion of an I.C. engine valve
b) motion of the shaft between a foot-step bearing
c) piston reciprocating inside an engine cylinder
d) all of the mentioned
Answer: d
Clarification: When the connection between the elements forming a pair is such that the constrained motion is not completed by itself, but by some other means, the motion is said to be a successfully constrained motion. so, the above examples have successfully constrained motion.

10. Which of the following statement is wrong?
a) A round bar in a round hole form a turning pair
b) A square bar in a square hole form a sliding pair
c) A vertical shaft in a foot step bearing forms a successful constraint
d) All of the mentioned
Answer: c
Clarification: None

Machine Kinematics written test Questions & Answers on “Double Slider Crank Chain & its Inversions”.

1. Which of the following instruments is used to draw ellipses?
a) Elliptical trammels
b) Slotted lever and crank
c) Gnome engine
d) Oldham’s coupling
Answer: a
Clarification: Elliptical trammel is an instrument which is an inversion of a double slider crank chain. It is mainly used to draw ellipses.

2. Elliptical trammels are used to convert reciprocating motion into rotary motion.
a) True
b) False
Answer: b
Clarification: Elliptical trammels are used to draw ellipses; scotch yoke mechanisms are used to convert rotary motion into reciprocating motion.

3. How inversion is obtained in an elliptical trammel?
a) Fixing the slotted plate
b) Fixing the sliders
c) Fixing the turning pairs
d) Fixing the pin
Answer: a
Clarification: An elliptical trammel is an instrument which is an inversion of a double slider crank chain, here the inversion is obtained by fixing the slotted plate. It is used to draw ellipses.

4. In the given figure, 1 and 2 are sliders, 3 is a bar and 4 is a fixed slotted plate, identify the mechanism.

a) Elliptical trammel
b) Scotch yoke mechanism
c) Oldham’s coupling
d) Gnome engine
Answer: a
Clarification: In the given figure, the slotted lever is fixed and there are two sliders, hence it is a double slider crank chain, since the slotted plate is fixed, it is an inversion. This inversion is known as elliptical trammels.

5. In the given figure if P is not the midpoint of the line connecting 1 and 2, what is the locus of P?

a) Ellipse
b) Straight line
c) Parabola
d) Rectangular hyperbola
Answer: a
Clarification: The given figure represents an elliptical trammel, in an elliptical trammel any point on the bar traces a path which is an ellipse, hence the locus of P is ellipse.

6. In the given figure if P is the midpoint of the line connecting 1 and 2, what is the locus of P?

a) Ellipse
b) Circle
c) Parabola
d) Rectangular hyperbola
Answer: b
Clarification: The given figure represents an elliptical trammel, in an elliptical trammel any point on the bar traces a path which is an ellipse, hence the locus of P is ellipse, but in this case P is the midpoint hence, the locus of P will be a circle.

7. Which of the mechanism is used to convert rotary motion into a reciprocating motion?
a) Elliptical trammel
b) Scotch yoke mechanism
c) Oldham’s coupling
d) Gnome engine
Answer: b
Clarification: Scotch yoke mechanism is an example of an inversion of a double slider crank chain, this mechanism is used to convert rotary motion into reciprocating motion.

8. In Scotch yoke mechanism, the crank is fixed in order to obtain the inversion.
a) True
b) False
Answer: b
Clarification: In scotch yoke mechanism there are in total 4 links, one is Crank and one is frame. Inversion can be obtained by fixing either of the remaining two links.

9. Which of the following mechanism is used for connecting two parallel shafts whose axes are at a small distance apart?
a) Elliptical trammel
b) Scotch yoke mechanism
c) Oldham’s coupling
d) Gnome engine
Answer: c
Clarification: Oldham’s coupling is an instrument which is an inversion of double slider crank chain, this is used to connect two parallel shafts whose axes are at a small distance apart.

10. Which of the following link is fixed to obtain inversion in Oldham’s coupling?
a) Driving shaft
b) Flange
c) Supporting frame
d) Driven shaft
Answer: c
Clarification: The shafts are coupled in such a way that if one shaft rotates, the other shaft also rotates at the same speed. This inversion is obtained by fixing the link which corresponds to Supporting frame.

11. How many turning pairs are there in a double slider crank chain?
a) 1
b) 2
c) 3
d) 4
Answer: b
Clarification: Double slider crank chain is a kinematic chain which consists of two turning pairs, as a result it is called double slider crank chain.

12. A double slider crank chain has one pair of each sliding and turning pairs.
a) True
b) False
Answer: b
Clarification: In a double slider crank chain, there are two turning pairs and two sliding pairs. In a single slider crank chain there is one sliding pair and three turning pairs.

13. How many sliding pairs are there in a double slider crank chain?
a) 1
b) 2
c) 3
d) 4
Answer: b
Clarification: Double slider crank chain is a kinematic chain which consists of two sliding pairs, as a result it is called double slider crank chain.

14. In which of the following mechanisms inversion is obtained by fixing the cylinder?
a) Pendulum pump
b) Gnome engine
c) Double slider crank chain
d) Oscillating cylinder
Answer: a
Clarification: Pendulum pump also known as the bull engine is an inversion of single slider crank chain, here inversion is obtained by fixing the cylinder.

15. Which of the following is not an inversion of double slider crank chain?
a) Elliptical trammels
b) Scotch yoke mechanism
c) Oldham’s coupling
d) Gnome engine
Answer: d
Clarification: Gnome engine is an example of inversion of single slider crank chain, whereas Elliptical trammels, Scotch yoke mechanism and Oldham’s coupling are inversions of double slider crank chain.

To practice all written questions on Machine Kinematics,

Machine Kinematics Question Paper on “Exact Straight Line Motion Consisting of One Sliding Pair”.

1. Which of the following is an exact straight line mechanism?
a) Scott Russell’s mechanism
b) Watt’s mechanism
c) Grasshopper mechanism
d) Robert’s mechanism
Answer: a
Clarification: Scott Russell’s mechanism is an exact straight line mechanism, however this mechanism is not so useful for practical purposes as friction and wear of sliding pair is more than that of turning pair.

2. Scott Russell’s mechanism is very important for practical purposes.
a) True
b) False
Answer: b
Clarification: Scott Russell’s mechanism is not so useful for practical purposes as friction and wear of sliding pair is more than that of turning pair.

3. Which of the following mechanisms is an approximate straight line mechanism?
a) Scott Russell’s mechanism
b) Watt’s mechanism
c) Gnome engine
d) Oscillating engine
Answer: b
Clarification: Watt’s mechanism is an approximate straight line mechanism. It is a crossed four bar chain mechanism used in early steam engines.

4. Which of the following mechanism forms an elliptical trammel?
a) Modified Scott Russell’s mechanism
b) Watt’s mechanism
c) Gnome engine
d) Oscillating engine
Answer: a
Clarification: Modified Scott Russell’s mechanism is similar to Scott russell’s mechanism but in this case the path traced by an arbitrary point P on the link is an ellipse.

5. Which of the following mechanisms has the form of trapezium in its mean position?
a) Scott Russell’s mechanism
b) Watt’s mechanism
c) Grasshopper mechanism
d) Robert’s mechanism
Answer: d
Clarification: Robert’s mechanism is a four bar chain mechanism, which, in its mean position, has the form of a trapezium.

6. Which of the following mechanisms was used in early days to give long stroke with a very short crank?
a) Scott Russell’s mechanism
b) Watt’s mechanism
c) Grasshopper mechanism
d) Robert’s mechanism
Answer: c
Clarification: The Grasshopper mechanism was used in early days as an engine mechanism which gave long stroke with a very short crank.

7. In Scott Russell’s mechanism the straight line motion is generated.
a) True
b) False
Answer: b
Clarification: In Scott Russell’s mechanism, straight line motion is not generated but merely copied and this mechanism is not much of practical value due to wear and friction in sliding pair.

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