Introduction to Kinematics and Mechanisms

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MACHINE THEORY

Bachelor in Mechanical Engineering

INTRODUCTION TO KINEMATICS ANDMECHANISMS

Ignacio Valiente BlancoJos Luis Prez DazDavid Mauricio Alba LuceroEfrn Dez Jimnez


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Machine Definition

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DEFINITIONS Kinematic chain: It is a linkage of elements and joints that transmit a controlled output

motion related to a given input motion. Mechanism: It is a kinematic chain where one element (or more) are fixed to the

reference framework (which can be in motion) Machine: Group of resistant elements (which usually contain mechanisms) thought to

transmit considerable movement, forces or/and power. Boundary is not completelyclear!!

Source: Wikipedia


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Kinematic pair Existing connection between two

elements of a mechanism that have a relative motionbetween them.Kinematic pairs was classified by Reuleaux as follow: Lower pair two links having a surface contact between

them. Higher pair two links having line or point contact between

them.

Joint - guarantees the contact between

two members and constrains their relative motion

Kinematic Pairs

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Classification of Kinematic Pairs by

Degrees of Freedom

0 DOF

1 DOF

2 DOF

3 DOF

4 DOF

5 DOF

y x

z


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Standard representation UNE-EN ISO 3952:1996.

REPRESENTATION


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REPRESENTATION


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D.O.F

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Degrees of freedom:

1. Number of independent coordinates needed to define the position ofthe element/mechanism...

2. .. or number of parameters needed to determine unambigously the

geometry configuration of a system in space.3. .. or the number ofinputs needed to obtain a predictible output of

a mechanism.

GRBLERS EQUATION

( ) 1 2G = 3 N- 1 - 2 f - f

Kutzbach Criterion for

mobility of a planarmechanism

f1 = n pairs 1 DOF

f2 = n pairs 2 DOF

N = n of elements


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CHEVYCHEF-GRBLER-KUTZBACH

CRITERION

G=0 Structure. No motion G>0 Mechanism. Motion

G < 0 Hyperestatic

Structure. No motion

Example. Obtain the number of DOF ofthe digger arm.

Ground


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CHEVYCHEF-GRBLER-KUTZBACH

CRITERION

G=0 Structure. No motion

G>0 Mechanism. Motion

G < 0 HyperestaticStructure. No motion

Example. Obtain the number of DOF ofthe digger arm.

G=3*(12-1)-2*12(pin joints)-

2*3(slide joints)=3

Ground


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D.O.F

Be careful!!!! Grbler ecuation not always works. As

far as this equation does not consider shape or sizeof links, there are some exceptions:


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FOUR-BAR LINCKAGE

Very simple but very versatile.

First option for design.

Clasification depending on the

task:

Function Generator. Output rules

Path Generator. Path rules

Motion Generator. All important


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4 BAR KINEMATIC INVERSIONS

It is the method of obtaining different mechanisms by fixingdifferent links of the same kinematic chain. POWERFULTOOL. See that with the slider-crank example:

Whitworth mechanism. Gnomeengine

Hand pump

Marine engine


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GEOMETRIC INVERSION

In some mechanisms,

for a given driver position, there are morethan one possibleconfigurations.

DEAD CENTER

POSITION ALWAYSAPPEARS in a four barmechanism.

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GRASHOF CRITERIA

Simple relation that describes the behavior of the kinematic

inversions of a four-bar mechanism.S= lenght of the shortest link

L= lenght of the longest link.

P and Q are the other links.

S+L P+Q

If my condition is satisfied, at

least one link would be able to

do a full revolution with respectto another link.

`

CONTINOUS MOTIONIS ALLOWED


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If s + l < p + q: Four possibilities of Grashof mechanism:

Double Crank or drag-link:Shortest link is the frame.

Crank-rocker: Shortest link is thecrank. Frame is adjacent

Rocker-Crank: The shortest link isthe follower.

GRASHOF CRITERIA


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Double rocker: The link opposite the shortest is the frame.

Where is the full rotation of a link?

GRASHOF CRITERIA


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GRASHOF CRITERIA

Double rocker: link opposite the shortest is the frame

Where is the full rotation of a link? The Coupler


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No Grashof mechanisms

If s + l > p + q: All the kinematic inversions will be

double rocker. No continous relative motion isposible.

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Special Grashof mechanisms.

If s + l = p + q. Grashof Special Mechanisms. All inversions are double-crank or crank-rocker. These mechanisms suffer from the change-point

condition.All links become collinear creating momentarily asecond DOF. OUTPUT RESPONSE IS UNDETERMINED.

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SIX-BAR CHAINS

Use it when a four-bar lickage does not provide the

performance requiered.

Watt Kinematic Chain Stephenson Kinematic Chain


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Six bar kinematic chains also present kinematic

inversions.

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Inversions of Watt and Stephenson kinematic chains

6 BAR KINEMATIC INVERSIONS


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REAL MECHANISMS

See some real examples

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http://www.youtube.com/watch?v=ZiAbpscuJdo


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REAL MECHANISMS

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FOUR BAR MECHANISM SIX BAR MECHANISM: to maintain aconstant distance between the axle and bottom

bracket. It is a Stephenson III six-bar linkage

UCI XGR gravity racer Brake pedal


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INTERMITENT MOTION

Sometimes intermitent motion is needed.

Examples: Geneva mechanism, camshaft, ratchetmechanism.

http://www.youtube.com/watch?v=85BsbncfRqA

http://www.youtube.com/watch?v=eijyLC4ZzQk&feature=related


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LITERATURE

Erdman, A.G., Sandor, G.N. and Sridar Kota Mechanism Design.Prentice Hall, 2001. Fourth Edition.

Robert L. Norton. Diseo de Maquinaria. Ed.Mc Graw Hill 1995. Shigley, J.E. & Uicker, J.J. Teora de mquinas y mecanismos.

McGraw-Hill, 1998.

Mquina y Mecanismo. Ed.UPC, 2001 Mechanism and Machine Theory. Ed. Elsevier.

http://synthetica.eng.uci.edu:16080/~mccarthy/animations.html

http://www.wellnessoptions.ca/html/1/015/1_i15_2_main.html MOVIES

http://www.youtube.com/watch?v=ZiAbpscuJdo

http://synthetica.eng.uci.edu:16080/~mccarthy/animations.html

http://synthetica.eng.uci.edu:16080/~mccarthy/Animations/Convertible-2.gif

http://www.youtube.com/watch?v=85BsbncfRqA

http://www.youtube.com/watch?v=eijyLC4ZzQk&feature=related 25

Documents

Introduction to Kinematics and Mechanisms