kinematic chain mechanism inversion_grashoff
TRANSCRIPT
(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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