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position analysis
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9/13/2013
1
Chapter 1Introduction
Dr. Aria Alasty, Sharif U. of Tech.
Mechanics
Statics Dynamics
Kinematics Kinetics
Dr. Aria Alasty, Sharif U. of Tech.
9/13/2013
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Mechanism:Transforms motion to some desirable pattern.Develops very low forces.Transmits little power.
Machine:Contains mechanisms which are designed to provide significant forces and transmits significant power.
Dr. Aria Alasty, Sharif U. of Tech.
Link:An rigid body which possesses at least two nodes.
Node:Point for attachment to other links.
Binary link Ternary link Quaternary link
Nodes
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Joint:A connection between two or more links
a) Classification of joints:a) By the number of degrees of freedom.b) By the type of contact between the elements.c) By the type of physical closure of the joint.d) By the number of links joined.
Dr. Aria Alasty, Sharif U. of Tech.
One DOFThree DOFOne or Two DOF
Dr. Aria Alasty, Sharif U. of Tech.
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Lower pair (Full joint):Joints with surface contacts
Higher pair(Half joint):Joints with point or line contact
Dr. Aria Alasty, Sharif U. of Tech.
Form closed:Is kept together or closed By its geometry.
Force closed:Requires some externalforce to keep it together or closed.
Dr. Aria Alasty, Sharif U. of Tech.
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Second order pin joint
First order pin joint
Dr. Aria Alasty, Sharif U. of Tech.
Kinematic chain:An assemblage of links and joints,interconnected in a way to provide a controlled outputmotion In response to a supplied input motion.
Open kinematic chain Closed kinematic chain
Dr. Aria Alasty, Sharif U. of Tech.
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Constrained kinematic chain: A kinematic chain which one link has been grounded.
Mechanism: A closed constrained kinematic chain.
Dr. Aria Alasty, Sharif U. of Tech.
Inversion
Dr. Aria Alasty, Sharif U. of Tech.
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Planar mechanism:All particlesdescribe plane curves in space andall these curves lie in parallel planes.
Spatial mechanism:No restrictionon the relative motion of the particles.
Dr. Aria Alasty, Sharif U. of Tech.
Spherical mechanism: Each link has some point whichremains stationary as the linkage moves and in which thestationary points of all links lie at a common location.the locus of each point is a curve contained in a sphericalsurface , and the spherical surfaces defined by severalarbitrarily chosen points , are all concentric.
Dr. Aria Alasty, Sharif U. of Tech.
9/13/2013
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Degree of freedom(DOF):The number of inputs which need to be provided in order to create a predictable output.
1
2
J :J :J :
J :Number of single degree of freedom pairs.
J :Number of two degree of freedom pairs.
n:Number of links.
3
4
5
Dr. Aria Alasty, Sharif U. of Tech.
Kutsbach criterion:
Dr. Aria Alasty, Sharif U. of Tech.
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Grublers criterion
Grublers criterion:
Dr. Aria Alasty, Sharif U. of Tech.
Some examples:
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Mechanism DOF=+1 Structure DOF=0
Preloaded structure DOF= -1 Dr. Aria Alasty, Sharif U. of Tech.
Paradoxes :Because the kutzbach criterion pays no attention to link sizes or shapes it can give misleading results in the face of unique geometric configurations .
Kutsbach predicts DOF=0DOF=0
Same connections
Kutsbach predicts DOF=0DOF=1
Kutsbach predicts DOF=0DOF=1
Dr. Aria Alasty, Sharif U. of Tech.
9/13/2013
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Dr. Aria Alasty, Sharif U. of Tech.
4 binaries
and
2 ternaries
Isomers
Isomers
Watts sixbar isomer
Stephensons sixbar isomer An invalid sixbar isomerDr. Aria Alasty, Sharif U. of Tech.
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Introduction to some famous mechanisms
Dr. Aria Alasty, Sharif U. of Tech.
Intermittent motion:A sequence of motion and dwells.
Dwell :A period in which the output link remainsstationary while the input link continues to move.
Geneva mechanism.
Dr. Aria Alasty, Sharif U. of Tech.
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Cam and follower mechanism
Dr. Aria Alasty, Sharif U. of Tech.
Swinging or rocking mechanisms:The out put memberrocks or swings through angles which are generally less Than 360.o
Dr. Aria Alasty, Sharif U. of Tech.
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Reciprocating mechanisms:
FOffset
Workingstroke
Returnstroke
Dr. Aria Alasty, Sharif U. of Tech.
Time ratio =Q= Time of advance strokeTime of return stroke
Quick return mechanismsWith high Q
Dr. Aria Alasty, Sharif U. of Tech.
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The Grashof condition
Dr. Aria Alasty, Sharif U. of Tech.
In order for any four-bar linkageto operate,the following conditions must exist:
A
B
D C
AB < BC + CD + DABC < CD + DA + ABCD < DA + AB + BCDA < AB + BC + CD
Dr. Aria Alasty, Sharif U. of Tech.
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S
P
L
Q
S = Length of shortest linkL = Length of longest linkP = Length of one remaining linkQ = Length of other remaining link
L + S < P + QOne of the links will rotate
continuously relative tothe other three links .
Dr. Aria Alasty, Sharif U. of Tech.
L+S=P+Q
L+S=P+Q
L+SP+Q
Dr. Aria Alasty, Sharif U. of Tech.