Learning Objectives:

• Describe mechanisms, kinematics and degrees of freedom.

• Kinematic pair: Two links or elements of a machine, which are in contact with each other are said to form a pair. If the relative motion between them is completely or successfully constrained (in a definite manner), the pair is known as a kinematic pair. A kinematic pair can be sliding pair, turning pair, rolling pair, screw pair or spherical pair.


• Kinematic chain: if the kinematic pairs are coupled in such a way that the last link is joined with the first link to transmit definite motion, it is called kinematic chain.


• Mechanism: When one of the links of a kinematic chain is fixed, the chain is known as mechanism. Mechanisms are used for transmitting or transforming motion. e.g. typewriters, engine indicators.


• Inversion: The method of obtaining different mechanisms by fixing different links in a kinematic chain, is known as inversion of mechanism.


• Structure: If an assemblage of a number of resistant bodies (known as members) having no relative motion between them and meant for carrying loads having straining action. e.g. a railway bridge, a roof truss, machine frames, etc. Link: Each part of a machine, which moves relative to some other part, is known as kinematic link. A kinematic link may be rigid or flexible.


• A Machine is a mechanism or combination of mechanisms which, apart from imparting definite motions to the parts, also transmits and modifies the available mechanical energy into some kind of desired work.

This animation shows a six-position Geneva Mechanism in operation.
Mike1024, Public domain, via Wikimedia Commons

Solved Example: 34-1-01

The inversion of a mechanism is:

A. Changing of a higher pair to a lower pair

B. Obtained by reversing the input and output motion

C. Obtained by fixing different links in a kinematic chain

D. Turning its upside down

The process of fixing different links of a kinematic chain one at a time to produce distinct mechanisms is called kinematic inversion.

Correct Answer: C

Solved Example: 34-1-02

Consider the following:

Statement I: Mating gear is a higher pair

Statement II : Revolute pair is a lower pair

A. Both statements are correct.

B. I is correct, but II is incorrect.

C. I is incorrect, but II is correct.

D. Both are incorrect.

A higher pair is a kinematic pair in which the links have point or line contact. Ball bearings, cam and follower are examples of higher pair.

A kinematic pair is said to be a lower pair if the links in the pair have surface or area contact between them.

A revolute pair allows only a relative rotation between two elements, which can be expressed by a single coordinate angle $\theta$. Thus a revolute pair has a single degree of freedom. It is lower pair because it has area contact between the elements.

A mating (meshing) gear has only point contact (in 2-D) or a line contact (if 3-D is considered). Hence it is a higher pair.

Correct Answer: A

Solved Example: 34-1-03

The purpose of a link is to:

A. Transmit motion

B. Guide other links

C. Act as a support

D. All of the above.

A link is defined as a rigid body having two or more pairing elements which connect it to other bodies for the purpose of transmitting force or motion.

In every machine, at least one link either occupies a fixed position relative to the earth or carries the machine as a whole along with it during motion. This link is the frame of the machine and is called the fixed link. So it acts as a support.

Also, in certain mechanisms, such as elliptical trammel, the sliding components are guided by fixed links, so option (B) is also correct.

Correct Answer: D

Solved Example: 34-1-04

A universal joint is an example of:

A. Higher pair

B. Lower pair

C. Rolling pair

D. Sliding pair

Universal joint, also referred as Hooke's joint, is used to connect two nonparallel but intersecting shafts. The universal joint can transmit power between two shafts intersecting with an angular misalignment.

A lower pair is one in which there occurs a surface or area contact between two members, e.g. nut and screw, universal joint used to connect two propeller shafts.

Correct Answer: B

Solved Example: 34-1-05

A circular bar moving in a round hole is an example of:

A. Incompletely constrained motion

B. Partially constrained motion

C. Completely constrained motion

D. Successfully constrained motion

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 moving in a round hole can have translation motion as well as rotational motion.

Correct Answer: A

Solved Example: 34-1-06

If some links are connected such that motion between them can take place in more than one direction, it is called:

A. Incompletely constrained motion

B. Partially constrained motion

C. Completely constrained motion

D. Successfully constrained motion

Correct Answer: A

Solved Example: 34-1-07

The example of spherical pair is:

A. Bolt and nut

B. Lead screw of a lathe

C. Ball and socket joint

D. Ball bearing and roller bearing

Correct Answer: C

Solved Example: 34-1-08

Kinematic pairs are those which have two elements that:

A. Have line contact

B. Have surface contact

C. Permit relative motion

D. Are held together

In kinematic pairs, the links are held together in such a way that relative motion is permitted between them. The relative motion can be partially constrained or the contact may be surface or line contact. If there is absolutely no relative motion, then the links are a part of 'structure'.

Correct Answer: C

Solved Example: 34-1-09

In higher pair, the relative motion is:

A. Purely turning

B. Purely sliding

C. Purely surface contact

D. Combination of sliding and turning.

Higher pair is a joint between two links having point or line contact. Hence, they can have sliding as well as turning motion. In lower pairs, the links have surface contact.

Correct Answer: D

Solved Example: 34-1-10

Which of the following has sliding motion:

A. Crank

B. Connecting rod

C. Crank pin

D. Cross-head

Correct Answer: D

Solved Example: 34-1-11

The example of higher pair is:

A. Belt, rope and chain drives

B. Gears, cams

C. Ball and roller bearings

D. All of the above.

Higher pairs are those where the contact between the links occurs along a line or a finite number of points.

Correct Answer: D

Solved Example: 34-1-12

For a kinematic chain to be considered as mechanism:

A. Two links should be fixed.

B. One link should be fixed.

C. None of the links should be fixed.

D. There is no such criterion.

When one of the links of kinematic chain is fixed, it is called a mechanism.

Correct Answer: B

Solved Example: 34-1-13

Which of the following is false statement in respect of differences between machine and structure:

A. Machines transmit mechanical work, whereas structures transmit forces

B. In machines, relative motion exists between its members, whereas same does not exist in case of structures

C. Machines modify movement and work, whereas structures modify forces

D. Efficiency of machines as well as structures is below 100%

Machines are created to tranmit motion and relative motion exists between members. On the other hand, structures are created to resist forces and deflection and there is no relative motion between members.
Machine modify and transmit motions, whereas structure modify, resist and transmit forces.

Correct Answer: D

Solved Example: 34-1-14

Kinematic pairs are those which have:

A. Point or line contact between the two elements when in motion

B. Surface contact between the two elements when in motion

C. Elements of pairs not held together mechanically

D. Two elements that permit relative motion

Correct Answer: D

Solved Example: 34-1-15

Any point on a link connecting double slider crank chain will trace a:

A. Straight line

B. Circle

C. Ellipse

D. Parabola

The Elliptical Trammel is a mechanism consisting of two shuttles which are confined (trammelled) to perpendicular channels or rails, and a rod which is attached to the shuttles by pivots at fixed positions along the rod. which can trace an exact elliptical path. As the shuttles move back and forth, each along its channel, the end of the rod moves in an elliptical path.

Correct Answer: C

Solved Example: 34-1-16

The values of velocity and acceleration of piston at near dead center for a slider-crank mechanism will be:

A. 0, and more than $\omega^2$r

B. 0, and less than $\omega^2$r

C. 0, 0

D. $\omega_2$r, 0

At top and bottom dead centers, (TDC and BDC) the piston stops for a brief moment before reversing its direction and hence, has a zero velocity.
However, acceleration at these points is not zero, as the velocity is changing. \[a_p = \omega^2 r \left(\cos \theta + \dfrac{\cos 2\theta}{n}\right)\] When $\theta$ = 0 \[a_p = \omega^2 r \left(1 + \dfrac{1}{n}\right)\] which is more than $\omega^2 r$.

Correct Answer: A

Solved Example: 34-1-17

If there are L number of links in a mechanism then number of possible inversions is equal to:

A. L + 1

B. L - 1

C. L

D. L + 2

In a kinematic chain, if one of the links is fixed, then it is called Mechanism. Since, there are L links, all can be fixed one by one and hence, we can have L such inversions. (variations)

Correct Answer: C

Solved Example: 34-1-18

A mechanism is an assembly of:

A. Two links

B. Three links

C. Four or more links

D. All of the above.

Two links with relative motion is a kinematic pair.

Three links connected together does not allow relative motion, hence it is a structure rather than a mechanism.

Four or more links allow transmission of motion and forces, hence it is a mechanism.

Correct Answer: C

Solved Example: 34-1-19

Rectangular bar in a rectangular hole is the following type of pair:

A. Completely constrained motion

B. Partially constrained motion

C. Incompletely constrained motion

D. Freely constrained motion

Correct Answer: A

Solved Example: 34-1-20

A foot step bearing and rotor of a vertical turbine form examples of:

A. Incompletely constrained motion

B. Partially constrained motion

C. Completely constrained motion

D. Successfully constrained motion

Correct Answer: B

Solved Example: 34-1-21

A slider crank chain consists of following numbers of turning and sliding pairs:

A. I, 3

B. 2, 2

C. 3, 1

D. 4, 0

Correct Answer: C

Solved Example: 34-1-22

Relationship between the number of links (L) and number of pairs (P) is:

A. P = 2L-4

B. P = 2L + 4

C. P = 2L +2

D. P = 2L-2

Correct Answer: C

Solved Example: 34-1-23

The type of coupling used to join two shafts whose axes are neither in same straight line nor parallel, but intersect is:

A. Flexible coupling

B. Universal coupling

C. Chain coupling

D. Oldham's coupling

Correct Answer: B

Solved Example: 34-1-24

Flexible coupling is used because:

A. It is easy to disassemble

B. Is easy to engage and disengage

C. It transmits shocks gradually

D. It prevents shock transmission and eliminates stress reversals

Correct Answer: D

Solved Example: 34-1-25

With single Hooke's joint it is possible to connect two shafts, the axes of which have an angular misalignment up to:

A. 10$^\circ$

B. 20$^\circ$

C. 30$^\circ$

D. 40$^\circ$

Correct Answer: D

Solved Example: 34-1-26

The Hooke's joint consists of:

A. Two forks

B. One fork

C. Three forks

D. Four forks

A universal joint is a joint or coupling in a rigid rod whose axis is inclined to each other, and is commonly used in shafts that transmit rotary motion. It consists of a pair of hinges located close together, oriented at 90$^\circ$ to each other, connected by a cross shaft.

Correct Answer: A

Solved Example: 34-1-27

It is required to connect two parallel shafts, the distance between whose axes is small and variable. The shafts are coupled by:

A. Universal joint

B. Knuckle joint

C. Oldham's coupling

D. Flexible coupling

Correct Answer: C

Solved Example: 34-1-28

In a mechanism, usually one link is fixed. If the fixed link is changed in a kinematic chain, then relative motion of other links:

A. Will remain same

B. Will change

C. Could change or remain unaltered depending oh which link is fixed

D. Will not occur

Correct Answer: A

Solved Example: 34-1-29

In a four-bar chain it is required to give an oscillatory motion to the follower for a continuous rotation of the crank. For the lengths of 50 mm of crank and 70 mm of the follower, determine theoretical maximum length of coupler. The distance between fixed pivots of crank and followers is:

A. 95 mm

B. Slightly less than 95 mm

C. Slightly more than 95 mm

D. 45 mm

Correct Answer: B

Solved Example: 34-1-30

In above example, the minimum length of the coupler will be:

A. 45 mm

B. Slightly less than 45 mm

C. Slightly more than 45 mm

D. 95 mm

Correct Answer: C

Solved Example: 34-1-31

The number of links and instantaneous centers in a reciprocating engine mechanism are:

A. 4, 4

B. 4, 5

C. 5, 4

D. 4, 6

Correct Answer: D

Solved Example: 34-1-32

In a rigid link OA, velocity of A w.r.t. O will be:

A. Parallel to OA

B. Perpendicular to OA

C. At 45$^\circ$ to OA

D. Along AO

Correct Answer: B

Solved Example: 34-1-33

The velocity of any point in mechanism relative to any other point on the mechanism on velocity polygon is represented by the line:

A. Joining the corresponding points

B. Perpendicular to line as per (A)

C. Not possible to determine with these data

D. At 45$^\circ$ to line as per (A)

Correct Answer: A

Solved Example: 34-1-34

The absolute acceleration of any point P in a link about center of rotation O is:

A. Along PO

B. $\perp$ to PO

C. Along OP

D. None of the above.

Correct Answer: D

Solved Example: 34-1-35

Angular acceleration of a link can be determined by dividing the:

A. Centripetal component of acceleration with length of link

B. Tangential component of acceleration with length of link

C. Resultant acceleration with length of link

D. All of the above.

Correct Answer: B