(Under the guidance of Prof. Rangaraj M Desai)

Prepared by: Syed Zabuilla

Chunkyraj KhRU1441MDD007

RU1441MDD008

A Presentation onKINEMATIC CHAIN, MECHANISM, INVERSION & GRASHOFF’s LAW

Contents

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Kinematic ChainMechanismInversionGrashoff’s Law

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KINEMATIC CHAIN:Kinematic chain may be defined as a combination of kinematic

pairs, joined in such a way that each link forms a part of two pairs and the relative motion between the links or elements is completely or successfully constrained.

For example, the crankshaft of an engine forms a kinematic pair with the bearings which are fixed in a pair, the connecting rod with the crank forms a second kinematic pair, the piston with the connecting rod forms a third pair and the piston with the cylinder forms a fourth pair. The total combination of these links is a kinematic chain.

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Kinematic chain may be Open or Closed. In a closed kinematic chain, the distal segment is fixed and the end segments are

unite to form a ring or a circuit. When one link moves all the other links will move in a predictable pattern.

In an open kinematic chain, the distal segment terminates free in space. Each segment of an open chain has a characteristic degree of freedom of motion; the distal possessing a higher degree of freedom than the proximal ones.

Link 1

Joint 1 Link 2 Joint 2

Joint 3

Link 3

Link 4Open Kinematic Chain

Link 1

Link 2

Link 3

Link 4

Link 5Link 6

J1

J2J3

J4

J6

J7

Closed Kinematic Chain

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Types of Kinematic Chains Four bar chain or quadric cyclic chain, Single slider crank chain, and Double slider crank chain.

Fig 1. Four bar chain or quadric cyclic chain,

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Fig 2. Single slider crank chain,

Fig 3. Double slider crank chain.

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MECHANISM: When one of the links of a kinematic chain is fixed, the chain

is known as mechanism. It may be used for transmitting or transforming motion

E.g. Slider-crank mechanism etc.

Robotic arm ( Open type mechanism) Slider-Crank mechanism( Closed type mechanism)

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INVERSION: Method of obtaining different mechanism by fixing

different links in a kinematic chain, is Inversion . Inversions will have same relative motion between the

links but absolute motion will change. No. of inversion = No. of links in kinematic chain. Example of Slider-crank Inversion:

1

2

3

4

Inversion #1 :Slider block translates

1

2

3

4

Inversion #2 :Slider block has complex motion

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GRASHOFF’s LAW: It states that for a Planar 4-bar linkage, Sum of the Shortest and

the longest link lengths must be less than or equal to Sum of the remaining link lengths, if there is to be a continuous relative motion between 2 members.

i.e.

1

2

3

4

Inversion #4 :Link 3 reciprocates

1

2

3

4

Inversion #3 :Slider block translates

s

l

p q

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There are 3 inversions of 4-bar mechanisms, which are obtained by fixing different links of the kinematic chain. They are: Double Crank Mechanism Crank Rocker Mechanism Double Rocker Mechanism

Double Crank mechanism:- When the shortest link is fixed, it gives double crank

mechanism. A double crank converts rotary motion from a crank to a second crank or link in a different plane or axis. It is also known as crank-crank, drag-crank or rotary-rotary converter. The links p and l shown rotate through one complete revolution. This is one of the first inversions of four-bar mechanisms.

- Application: Coupling rod of locomotive(train wheels) etc.

p

ls q

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Crank-Rocker mechanism:- When any of the link adjacent to the shortest link is fixed, it gives crank

rocker mechanism. A crank-rocker converts rotary motion from a crank to a reciprocating link in a different plane or axis or vice cersa. It is also known as crank-lever mechanism or a crank-rocker mechanism or a rotary-oscillating converter . The links s rotates and q reciprocates.

- Application: Reciprocating engines/IC engines, Compressors etc.

Double Rocker mechanism:- When the link opposite to the shortest link is fixed, it gives double rocker

mechanism. A double rocker converts reciprocating motion from one link to another link in a different plane or axis. The links p and l reciprocates.

- Application:Windshield wipers, Quick return mechansism etc.

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References:Theory of Machines by R.S. KhurmiKinematic of MachinesKinematic FundamentalsMechanism by Ken Youssefiwww.wikipedia.com

THANK YOU

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