Part II Kinematics Fundamental Concepts_printer Friendly

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Part II: Kinematics, the fundamentals

This section will provide an overview of the fundamental concepts in kinematics. This will

include the following topics:

1. What is Kinematics?

2. Kinematics within mechanics

3. Key definitions. !otion and kinematic pairs

". Transmission of motion

#. !o$ility%. &eview of some general classes of !echanisms

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1: What is Kinematics?

/Kinematics is the study of 0000000000000000000000000000000000000000000000000

This is kinematics

and this is kinematics

This is *,T kinematics



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Why Kinematics? Why !achines?

)reate harness energy non+human energy4

!anufacturing agriculture

5ssistive serve humans

What is the future of kinematics and machinery?

!iniature micro and perhaps even nano+scale machines motion at a micro or molecular level4

!edical reha$ilitative prosthetic

6elf+replication of machinery machines design machines

!achines $ecome more $iological in nature compliant $iological muscles intelligent4.



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!echanics

6tatics 7ynamics

Kinematics Kinetics

!echanics of materials

2. Kinematics within Mechanics

Kinematics and the theory $ehind machines have a long history. Kinematics has evolved to

$ecome a uni8ue component within !echanics as demonstrated in this figure

3. A few key definitins:

Kinematics

7ynamics

!echanism

!achine

7egrees of freedom

)onstraint

!o$ility

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!. Mtin of a rigid $ody4: displacement of a rigid $ody w.r.t. a fi9ed frame or reference framefor dynamics needs to $e an &4.

Translation:

&otation:

-lanar:

6patial:

Kinematic -airs: Two mem$ers links4 are ;ointed through a connection ;oint4 that defines the

relative motion $n the two.

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JointsLinks

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!ore a$out ;oints:)lassically classified into a couple classes: arious types of ;oints:

&evolute:

-rismatic slider4

)am or gear

&olling contact

6pring

,thers?

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*

t>2

2

>3

,3,2

K

". #ransmissin f Mtin: The motion of a mechanism is defined $y its constraintskinematic4. The following e9ample shows one of the most general cases of motion $etween two

$odies and demonstrates some key elements in understanding the $ehavior of motion. )onsider

two general kinematic $odies rigid $odies known geometric properties4 in contact at point P.'ach $ody rotates a$out a fi9ed point ,2 and ,3.

*otes:

14 5 common *ormal and tangent * t4 e9ist and are defined $y the 2 surfaces24 /)ondition of contact: no relative motion can occur along the common normal

34 5ll sliding takes place along the common tangent

4 The result of these rules plus some geometric construction4:

PO

V

PO

V

3

3

3

2

22

==

KO

KO

3

2

2

3=

"4 &e8uirement for constant velocity:

#4 &e8uirement for no sliding:

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,2 ,3K

5 few special cases may $e mentioned: can $e treated in the more special case a$ove4:=inkage:

@elt and -ulley )hain drive:

$. M%ility Analysis:

!o$ility is defined as the num$er of dof. !o$ility is calculated as the total num$er of possi$le

degrees of freedom minus the num$er of constraints. The following diagrams will demonstratethe process:

tem 7iagram 7,

,ne $ody

Two @odies

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Two $odies connected$y a revolute

Bround it is a $ody4

Writing these rules as e8uations yields:

Which is known as Bru$lerCs or the KutD$ach e8uation.

*ote: when ! E ( 6tructure statically determinant

! F ( ndeterminant structure

! G ( !echanism with ! dof

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M%ility &'am(leslist +# e9amples for in+class practice 3 line drawings 3 photos4

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M%ility as a synthesis tl:6ketch a 1 dof mechanism having e9actly " links:



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). *e+iew f sme eneral classes f Mechanisms

!ore a$out each of these general mechanism types to follow later in the course4

1. =inkages:The most famous types of linkages include the +$ar slider crank. ollowed $y five+$ars and si9

$ars.

The four+$ar:

6lider )rank:

2. )am mechanisms:

3. Bear !echanisms

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. )hain and 6procket @elt and -ulley

". ntermittent motion devices: Beneva Wheel

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