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72 ~~_____________--TeXVtKO XPOVIKO

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Figure 7 PM Step Motor with Half Step Motion Figure 8 A Conventional PM Step Motor with Bipolar Winding

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Figure 9 Cut-away View of a PM Motor Figure 10 Schematic Diagram of a PM Motor

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72 ~~_____________--TeXVtKO XPOVIKO

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Figure 7 PM Step Motor with Half Step Motion Figure 8 A Conventional PM Step Motor with Bipolar Winding

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r

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Figure 17 50 Step Angle VR Motor

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Figure 20 Rotation Diagram of 18deg Hydrid Moshytor

Figure 215deg Hydrid Motor

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ClgtAIIKH ANTIITAIH H ovrloroOTl TOU TuAiVIlOTOC OTOV o BK eivOl oroIlOTl1IlampVOt 0Tl1 gepIJOKpaaio nEpll3ciMoshyVTOt Iuvn8wc lleTpIampTOI orout 25degC Ko8opi~el TO peushy110 nou Tpol3ciel 0 BK oroIlOTl1llevot IJE Tl1V OVOIJOorlKri TOOTlmiddot

ClgtAIIKH EnArOriKH ANTIITAIII Elvoll1 oUTenovwvn TWV cpoalKwv TuAIYlJciTWV Ile TOUe noAoue TOU TUllncivou ae eu8uvpcill1J10Tl lJe TOUt aVTloroIXOUC noAouc TOU orashyTOpa ITOUt BK MeTaaAI1nt MOVVI1T1Kric AVTloroOTlt npenEI va npoolovpacpeTol VIO Tl1 8eOTl EAilXlaTl1t JlaYVl1shyTlKric ovrloroOTltmiddot

74_________________T_ampXV1KO XpOV1KO________~___1_n~tlltT_a_K_T11_e_K(5_0_0_n

c

Figure 134 Phase VR Motor with one Phase On Figure 14 4 Phase VR Motor with 2 Phases On

r

Figure 15 4 Phase VR Motor with 1 Phase On Figure 16 4 Phase VR Motor with 2 Phase On Wound for Alternate Polarity Wound for Alternate Polarity

Figure 17 50 Step Angle VR Motor

--75 TeXVIKO XPOVIKO

---- ~----------------------

--2 1 bull 1J11~

IX17pa 18 BK MeraJAT]nt( paVVT]TlK17( aVTiaraQT]( y(Uvia( J17paTO( 18deg 200 J17para ava arpCXP17 360deg

(a) (b)

(d)(c)

OUiPUT s~FT

PtRIIAMEfo(T tVcfo(poundT 1=~vx

Figure 20 Rotation Diagram of 18deg Hydrid Moshytor

Figure 215deg Hydrid Motor

IX17IJa 19 BK YJPIOIKOU Tunou Bf]paTiKOi KIVf]ntpe( UJPIOIKOU TUTTOU

76 TeXVIKO XPOVIKO

TomOIl TOU TUllnovou TOU H KOllnuAIl ouTiJ XPIlOlIlOshynOleiTOI Via va npooolopl06ouv TO e~~lt

1 lqgtaAllo Seoewlt hOvw TPt~~lt 2 TIlV llevioTIl evepvelo nou on06i6el 0 BK OTO OVOIlOshy

OTlKO qgtopTio KOI KOVOVIKtlt ouvS~Kelt AeITouPviolt 3 To qgtopTio pon~lt orpe4Jewlt Ile lleViOTIl TPII3~ nou

Ilnopei va Klv~oel 0 BK 4 Til qgtUOIKr OUXVOTI1Ta TOAovTwoewlt OTOV eivOl vvwoTiJ

11 oopovelo TOU TUllnavou

H KOllnuAI1 TI1lt Ponrlt KpOTl1anlt (PK) 6ivel TI1 ponti Eshy

navafPopac nou ovonruooeTOl OTOV TO TUllnovo lleTOTOshymoSei anD TIlV KOVOVI~ ~111l0TlK~ TOU Seol1 H PK evepshyvei Via va enovaqgtepel TO TUllnovo OTI1 OToSep~ Seol1 TI1lt Pon~lt AKlvllOiolt (PA) r MI16eVIK~lt Pon~lt OAelt 01 XOshyPOKTI1PIOTlKelt ponwv OTpe4JeW4 npoepXOVTOI anD TI1V KOllnUAI1 TI1lt PK

H KOllnUAI1 TI1lt PK oloqgtepet OVclAOVO Ile TOV Tuno TOU BK luxvo oxeolo~eTol KOTO npooeYYlol1 wlt ilia I1IlITOVOshyeI6rlt ouvopTIlOll lTllt napoKOrW KallnuAelt ilia lleToToshyman TOU TUllnovou Ile TOUlt 6eiKTelt TOU POAOVIOU napashyvel ilia apVI1TlKr pon~ enavaqgtopalt

----~--~~~-----

Bifilar Jinding

Stator

A

cmiddot

Figure 22 BT]jJaTIKOt KIVT]Trjpat U3P~KOU Turrou

PRESSURE IN

ROTARY-LINEAR TRANS HYDRAULIC MOTOR

STEP MOTOR

-OUTPUT SHAFT

FEEDBACK SHAFT

RETURN OUT

H)eKTpojj~paU)IKot 3T]jJaTIKOt KIVT]rr7pat

EmAoyi) BK IJamp anA~ npo61aypaqnl 01 mo ouv~Sellt rwvielt B~IlOTOlt eivol

H emAov~ evolt BK Ile anAri npoolovpaqgt~ aMo Kat eshy rQNIA BHMATOI BHMATA ANA ITPO(J)H nopKeilt AenrOllepelelt entTpenel TI1v OIKOVOlllKri Aelshy _(MOIPEl)TOUPvia TOU npolt xPriol1 BK TI1V 6uvaT0Tl1Ta avopolt TOU

18 200 BK anD 6Ioqgtopoult npOll11geuTelt Kat TeAOlt TI1V 6uvaTOshy

25 144 TI1TO emSewprioewlt TOU BK oro KOTOOKeuoonJ nplV anD

36 100 TI1V nopaha~ri TOU 375 96 To ~aOlKa llevtSI1 nou nP0610VpaqgtOVTOI eivat Kupiwlt TO 500 72 e~tilt 60 60

75 48 100 36

rQNIA BHMATOP = BHMATA ANA ITPO(J)H 150 24

-----77111 EKTOKT11 EKi500Tl TeXVIKO XPOVIKO -------~-----~---~---~ ~--

poundxrjjlO 1 POrTrj KpaTT]Ol7r BK oro8spou jlOyvrjTOU TUjlrTaVou

20

15 gt l o

10

sect o

-2 -I

-10

-15

-20

poundxrjjlO 2 POrTrj KpaTT]Ol7r UfjPIOIKOU B-K

BHMATIKH AKPIBEIA H noooonoio nopEKKAIOTl ana TllV OVOIlOOTlKi rwvia BilloTOe Ile TO BK xwpie cpopTio H BI1IlOTIK AKpi3elo ouvSwe npoi5lovpocpeTat anD plusmn 1 EWe plusmn 5

AKPIBEIA 6EIEQI H nopeKKAloll ono Tllv opS Seoll onolov15inoTe 311J10TlKWV Seoewv lleTo anD neploTpocpi 360 0 Ile TOV BK xwpie cpopTio Eivo (5UVOT 11 ouoowshy

2Q

-1$

- lO 4

poundxrjjlO 3 POrTrj KpaTT]Ol7r BK jlsTOfjAl7njr jl0yvl7TlshyKrjr oVTloraoswr TUjlrTaVOu (400 fjrjjlOTO ova orporprj)

a

6 0

~ 4

-30

poundxrjjlO 4 Ponrj KpGTT]Ol7r BK TPlrpOOIKOU Tunou MMA T - IISITOupyio jllar rpaoswr

peuol1 nopEKKAIOI1e lleXPI KOI 3 BI11l0TWV VIO tvo TeTposhyCPOOtKO BK IuvSwc 11 AKpi3elo 6eoewe eivot KOAtJTepl1 anD TI1V BI11l0TlK AKpi3eIO

AAPANEIA H nploTpOQ)tKij A15poVEIO TOU TUllnovou KOt TOU olovo EnIlPEOeuroE1 TllV ponij OTpEljIEWe VIO TllV EntTOshyXUVOIl TOU cpopTiou TOU BK KOSWC Kat TI1V OUXVOT11TO ushynEp3aoewc (overshoot) Kat TOAOVTWoewc IuvijSwc 0shy

78 TEXVIKO XpovlKa 11 ampKTOKT1 ampKliOOTl ------------------------------------~----~------------------------~

20

-2 -1

-I

I

o

g o =

Ro~or 01plcen~ degyebullbull 1

c t

-20

-lD

Ixtjpa 6 POT1tj KpoTTlOTlr Yla TpupaolKo BK ycvviar 15deg TLJT10U perapAI7Ttjr payvl7T aVTOTOshyoecvr TUpT10VOU

VVOEiTOl11 olipavlto TWV eopOvwv TOU BK

ponH KPATHIHI npampnEI vo Ko8oPlogei 0 apI81J0t TWV evepvonoll1lJampVWV cpoaewv KOI TOU peUIJOTOt oro orOTOshypo Iuvl8wt npoolovpocpeTol IJIO eAilXIOTl1 T11l1 oMo KOI

eKooroTE 1110 IlampVIOTl1 KOI IJIO eAilXIOTl1 Tlllrl H npoliloshyVpaCPrl oum Exel IJEVQ)11 OTlJloaio VIO Tl1v op8r AelToupshyvia TOU BK

POnH AKINHIIAI Aun ocpopa TOUt BK Ira8epou MoshyVVrlTl1 KOI onoTeAei evliell1 Tl1t IOXUOe TOU oro8epou JlOvvrlTl1 revlKa BK lJe llevoAI1 Ponr) AKIVl10iot liev eivol KOTOMI1Aol VIO noAu IJIKpO arllJOTO (Micro-Stepping) H Ponr AKIVl1oiot TOU BK lleToaAl1mt JlOVVl1T1Knt OVTIshyoroOTlt eivol JllMv

ClgtAIIKH TAIII 01 BK AEITOUPVouv auxvci ae lleVOAUTEshypEt ana TIt OVOlJoorlKec TaCEIt To peullo npenel Vo neplopl~ETOI ewTeplKa VIO vo onocpeuveTOl 11 unep8epshyIJOvOTl TOU BK OTOV OUTOC eivOl or0Jl0Tl1lJevot

ClgtAIIKH ANTIITAIH H ovrloroOTl TOU TuAiVIlOTOC OTOV o BK eivOl oroIlOTl1IlampVOt 0Tl1 gepIJOKpaaio nEpll3ciMoshyVTOt Iuvn8wc lleTpIampTOI orout 25degC Ko8opi~el TO peushy110 nou Tpol3ciel 0 BK oroIlOTl1llevot IJE Tl1V OVOIJOorlKri TOOTlmiddot

ClgtAIIKH EnArOriKH ANTIITAIII Elvoll1 oUTenovwvn TWV cpoalKwv TuAIYlJciTWV Ile TOUe noAoue TOU TUllncivou ae eu8uvpcill1J10Tl lJe TOUt aVTloroIXOUC noAouc TOU orashyTOpa ITOUt BK MeTaaAI1nt MOVVI1T1Kric AVTloroOTlt npenEI va npoolovpacpeTol VIO Tl1 8eOTl EAilXlaTl1t JlaYVl1shyTlKric ovrloroOTltmiddot

--75 TeXVIKO XPOVIKO

---- ~----------------------

--2 1 bull 1J11~

IX17pa 18 BK MeraJAT]nt( paVVT]TlK17( aVTiaraQT]( y(Uvia( J17paTO( 18deg 200 J17para ava arpCXP17 360deg

(a) (b)

(d)(c)

OUiPUT s~FT

PtRIIAMEfo(T tVcfo(poundT 1=~vx

Figure 20 Rotation Diagram of 18deg Hydrid Moshytor

Figure 215deg Hydrid Motor

IX17IJa 19 BK YJPIOIKOU Tunou Bf]paTiKOi KIVf]ntpe( UJPIOIKOU TUTTOU

76 TeXVIKO XPOVIKO

TomOIl TOU TUllnovou TOU H KOllnuAIl ouTiJ XPIlOlIlOshynOleiTOI Via va npooolopl06ouv TO e~~lt

1 lqgtaAllo Seoewlt hOvw TPt~~lt 2 TIlV llevioTIl evepvelo nou on06i6el 0 BK OTO OVOIlOshy

OTlKO qgtopTio KOI KOVOVIKtlt ouvS~Kelt AeITouPviolt 3 To qgtopTio pon~lt orpe4Jewlt Ile lleViOTIl TPII3~ nou

Ilnopei va Klv~oel 0 BK 4 Til qgtUOIKr OUXVOTI1Ta TOAovTwoewlt OTOV eivOl vvwoTiJ

11 oopovelo TOU TUllnavou

H KOllnuAI1 TI1lt Ponrlt KpOTl1anlt (PK) 6ivel TI1 ponti Eshy

navafPopac nou ovonruooeTOl OTOV TO TUllnovo lleTOTOshymoSei anD TIlV KOVOVI~ ~111l0TlK~ TOU Seol1 H PK evepshyvei Via va enovaqgtepel TO TUllnovo OTI1 OToSep~ Seol1 TI1lt Pon~lt AKlvllOiolt (PA) r MI16eVIK~lt Pon~lt OAelt 01 XOshyPOKTI1PIOTlKelt ponwv OTpe4JeW4 npoepXOVTOI anD TI1V KOllnUAI1 TI1lt PK

H KOllnUAI1 TI1lt PK oloqgtepet OVclAOVO Ile TOV Tuno TOU BK luxvo oxeolo~eTol KOTO npooeYYlol1 wlt ilia I1IlITOVOshyeI6rlt ouvopTIlOll lTllt napoKOrW KallnuAelt ilia lleToToshyman TOU TUllnovou Ile TOUlt 6eiKTelt TOU POAOVIOU napashyvel ilia apVI1TlKr pon~ enavaqgtopalt

----~--~~~-----

Bifilar Jinding

Stator

A

cmiddot

Figure 22 BT]jJaTIKOt KIVT]Trjpat U3P~KOU Turrou

PRESSURE IN

ROTARY-LINEAR TRANS HYDRAULIC MOTOR

STEP MOTOR

-OUTPUT SHAFT

FEEDBACK SHAFT

RETURN OUT

H)eKTpojj~paU)IKot 3T]jJaTIKOt KIVT]rr7pat

EmAoyi) BK IJamp anA~ npo61aypaqnl 01 mo ouv~Sellt rwvielt B~IlOTOlt eivol

H emAov~ evolt BK Ile anAri npoolovpaqgt~ aMo Kat eshy rQNIA BHMATOI BHMATA ANA ITPO(J)H nopKeilt AenrOllepelelt entTpenel TI1v OIKOVOlllKri Aelshy _(MOIPEl)TOUPvia TOU npolt xPriol1 BK TI1V 6uvaT0Tl1Ta avopolt TOU

18 200 BK anD 6Ioqgtopoult npOll11geuTelt Kat TeAOlt TI1V 6uvaTOshy

25 144 TI1TO emSewprioewlt TOU BK oro KOTOOKeuoonJ nplV anD

36 100 TI1V nopaha~ri TOU 375 96 To ~aOlKa llevtSI1 nou nP0610VpaqgtOVTOI eivat Kupiwlt TO 500 72 e~tilt 60 60

75 48 100 36

rQNIA BHMATOP = BHMATA ANA ITPO(J)H 150 24

-----77111 EKTOKT11 EKi500Tl TeXVIKO XPOVIKO -------~-----~---~---~ ~--

poundxrjjlO 1 POrTrj KpaTT]Ol7r BK oro8spou jlOyvrjTOU TUjlrTaVou

20

15 gt l o

10

sect o

-2 -I

-10

-15

-20

poundxrjjlO 2 POrTrj KpaTT]Ol7r UfjPIOIKOU B-K

BHMATIKH AKPIBEIA H noooonoio nopEKKAIOTl ana TllV OVOIlOOTlKi rwvia BilloTOe Ile TO BK xwpie cpopTio H BI1IlOTIK AKpi3elo ouvSwe npoi5lovpocpeTat anD plusmn 1 EWe plusmn 5

AKPIBEIA 6EIEQI H nopeKKAloll ono Tllv opS Seoll onolov15inoTe 311J10TlKWV Seoewv lleTo anD neploTpocpi 360 0 Ile TOV BK xwpie cpopTio Eivo (5UVOT 11 ouoowshy

2Q

-1$

- lO 4

poundxrjjlO 3 POrTrj KpaTT]Ol7r BK jlsTOfjAl7njr jl0yvl7TlshyKrjr oVTloraoswr TUjlrTaVOu (400 fjrjjlOTO ova orporprj)

a

6 0

~ 4

-30

poundxrjjlO 4 Ponrj KpGTT]Ol7r BK TPlrpOOIKOU Tunou MMA T - IISITOupyio jllar rpaoswr

peuol1 nopEKKAIOI1e lleXPI KOI 3 BI11l0TWV VIO tvo TeTposhyCPOOtKO BK IuvSwc 11 AKpi3elo 6eoewe eivot KOAtJTepl1 anD TI1V BI11l0TlK AKpi3eIO

AAPANEIA H nploTpOQ)tKij A15poVEIO TOU TUllnovou KOt TOU olovo EnIlPEOeuroE1 TllV ponij OTpEljIEWe VIO TllV EntTOshyXUVOIl TOU cpopTiou TOU BK KOSWC Kat TI1V OUXVOT11TO ushynEp3aoewc (overshoot) Kat TOAOVTWoewc IuvijSwc 0shy

78 TEXVIKO XpovlKa 11 ampKTOKT1 ampKliOOTl ------------------------------------~----~------------------------~

20

-2 -1

-I

I

o

g o =

Ro~or 01plcen~ degyebullbull 1

c t

-20

-lD

Ixtjpa 6 POT1tj KpoTTlOTlr Yla TpupaolKo BK ycvviar 15deg TLJT10U perapAI7Ttjr payvl7T aVTOTOshyoecvr TUpT10VOU

VVOEiTOl11 olipavlto TWV eopOvwv TOU BK

ponH KPATHIHI npampnEI vo Ko8oPlogei 0 apI81J0t TWV evepvonoll1lJampVWV cpoaewv KOI TOU peUIJOTOt oro orOTOshypo Iuvl8wt npoolovpocpeTol IJIO eAilXIOTl1 T11l1 oMo KOI

eKooroTE 1110 IlampVIOTl1 KOI IJIO eAilXIOTl1 Tlllrl H npoliloshyVpaCPrl oum Exel IJEVQ)11 OTlJloaio VIO Tl1v op8r AelToupshyvia TOU BK

POnH AKINHIIAI Aun ocpopa TOUt BK Ira8epou MoshyVVrlTl1 KOI onoTeAei evliell1 Tl1t IOXUOe TOU oro8epou JlOvvrlTl1 revlKa BK lJe llevoAI1 Ponr) AKIVl10iot liev eivol KOTOMI1Aol VIO noAu IJIKpO arllJOTO (Micro-Stepping) H Ponr AKIVl1oiot TOU BK lleToaAl1mt JlOVVl1T1Knt OVTIshyoroOTlt eivol JllMv

ClgtAIIKH TAIII 01 BK AEITOUPVouv auxvci ae lleVOAUTEshypEt ana TIt OVOlJoorlKec TaCEIt To peullo npenel Vo neplopl~ETOI ewTeplKa VIO vo onocpeuveTOl 11 unep8epshyIJOvOTl TOU BK OTOV OUTOC eivOl or0Jl0Tl1lJevot

ClgtAIIKH ANTIITAIH H ovrloroOTl TOU TuAiVIlOTOC OTOV o BK eivOl oroIlOTl1IlampVOt 0Tl1 gepIJOKpaaio nEpll3ciMoshyVTOt Iuvn8wc lleTpIampTOI orout 25degC Ko8opi~el TO peushy110 nou Tpol3ciel 0 BK oroIlOTl1llevot IJE Tl1V OVOIJOorlKri TOOTlmiddot

ClgtAIIKH EnArOriKH ANTIITAIII Elvoll1 oUTenovwvn TWV cpoalKwv TuAIYlJciTWV Ile TOUe noAoue TOU TUllncivou ae eu8uvpcill1J10Tl lJe TOUt aVTloroIXOUC noAouc TOU orashyTOpa ITOUt BK MeTaaAI1nt MOVVI1T1Kric AVTloroOTlt npenEI va npoolovpacpeTol VIO Tl1 8eOTl EAilXlaTl1t JlaYVl1shyTlKric ovrloroOTltmiddot

76 TeXVIKO XPOVIKO

TomOIl TOU TUllnovou TOU H KOllnuAIl ouTiJ XPIlOlIlOshynOleiTOI Via va npooolopl06ouv TO e~~lt

1 lqgtaAllo Seoewlt hOvw TPt~~lt 2 TIlV llevioTIl evepvelo nou on06i6el 0 BK OTO OVOIlOshy

OTlKO qgtopTio KOI KOVOVIKtlt ouvS~Kelt AeITouPviolt 3 To qgtopTio pon~lt orpe4Jewlt Ile lleViOTIl TPII3~ nou

Ilnopei va Klv~oel 0 BK 4 Til qgtUOIKr OUXVOTI1Ta TOAovTwoewlt OTOV eivOl vvwoTiJ

11 oopovelo TOU TUllnavou

H KOllnuAI1 TI1lt Ponrlt KpOTl1anlt (PK) 6ivel TI1 ponti Eshy

navafPopac nou ovonruooeTOl OTOV TO TUllnovo lleTOTOshymoSei anD TIlV KOVOVI~ ~111l0TlK~ TOU Seol1 H PK evepshyvei Via va enovaqgtepel TO TUllnovo OTI1 OToSep~ Seol1 TI1lt Pon~lt AKlvllOiolt (PA) r MI16eVIK~lt Pon~lt OAelt 01 XOshyPOKTI1PIOTlKelt ponwv OTpe4JeW4 npoepXOVTOI anD TI1V KOllnUAI1 TI1lt PK

H KOllnUAI1 TI1lt PK oloqgtepet OVclAOVO Ile TOV Tuno TOU BK luxvo oxeolo~eTol KOTO npooeYYlol1 wlt ilia I1IlITOVOshyeI6rlt ouvopTIlOll lTllt napoKOrW KallnuAelt ilia lleToToshyman TOU TUllnovou Ile TOUlt 6eiKTelt TOU POAOVIOU napashyvel ilia apVI1TlKr pon~ enavaqgtopalt

----~--~~~-----

Bifilar Jinding

Stator

A

cmiddot

Figure 22 BT]jJaTIKOt KIVT]Trjpat U3P~KOU Turrou

PRESSURE IN

ROTARY-LINEAR TRANS HYDRAULIC MOTOR

STEP MOTOR

-OUTPUT SHAFT

FEEDBACK SHAFT

RETURN OUT

H)eKTpojj~paU)IKot 3T]jJaTIKOt KIVT]rr7pat

EmAoyi) BK IJamp anA~ npo61aypaqnl 01 mo ouv~Sellt rwvielt B~IlOTOlt eivol

H emAov~ evolt BK Ile anAri npoolovpaqgt~ aMo Kat eshy rQNIA BHMATOI BHMATA ANA ITPO(J)H nopKeilt AenrOllepelelt entTpenel TI1v OIKOVOlllKri Aelshy _(MOIPEl)TOUPvia TOU npolt xPriol1 BK TI1V 6uvaT0Tl1Ta avopolt TOU

18 200 BK anD 6Ioqgtopoult npOll11geuTelt Kat TeAOlt TI1V 6uvaTOshy

25 144 TI1TO emSewprioewlt TOU BK oro KOTOOKeuoonJ nplV anD

36 100 TI1V nopaha~ri TOU 375 96 To ~aOlKa llevtSI1 nou nP0610VpaqgtOVTOI eivat Kupiwlt TO 500 72 e~tilt 60 60

75 48 100 36

rQNIA BHMATOP = BHMATA ANA ITPO(J)H 150 24

-----77111 EKTOKT11 EKi500Tl TeXVIKO XPOVIKO -------~-----~---~---~ ~--

poundxrjjlO 1 POrTrj KpaTT]Ol7r BK oro8spou jlOyvrjTOU TUjlrTaVou

20

15 gt l o

10

sect o

-2 -I

-10

-15

-20

poundxrjjlO 2 POrTrj KpaTT]Ol7r UfjPIOIKOU B-K

BHMATIKH AKPIBEIA H noooonoio nopEKKAIOTl ana TllV OVOIlOOTlKi rwvia BilloTOe Ile TO BK xwpie cpopTio H BI1IlOTIK AKpi3elo ouvSwe npoi5lovpocpeTat anD plusmn 1 EWe plusmn 5

AKPIBEIA 6EIEQI H nopeKKAloll ono Tllv opS Seoll onolov15inoTe 311J10TlKWV Seoewv lleTo anD neploTpocpi 360 0 Ile TOV BK xwpie cpopTio Eivo (5UVOT 11 ouoowshy

2Q

-1$

- lO 4

poundxrjjlO 3 POrTrj KpaTT]Ol7r BK jlsTOfjAl7njr jl0yvl7TlshyKrjr oVTloraoswr TUjlrTaVOu (400 fjrjjlOTO ova orporprj)

a

6 0

~ 4

-30

poundxrjjlO 4 Ponrj KpGTT]Ol7r BK TPlrpOOIKOU Tunou MMA T - IISITOupyio jllar rpaoswr

peuol1 nopEKKAIOI1e lleXPI KOI 3 BI11l0TWV VIO tvo TeTposhyCPOOtKO BK IuvSwc 11 AKpi3elo 6eoewe eivot KOAtJTepl1 anD TI1V BI11l0TlK AKpi3eIO

AAPANEIA H nploTpOQ)tKij A15poVEIO TOU TUllnovou KOt TOU olovo EnIlPEOeuroE1 TllV ponij OTpEljIEWe VIO TllV EntTOshyXUVOIl TOU cpopTiou TOU BK KOSWC Kat TI1V OUXVOT11TO ushynEp3aoewc (overshoot) Kat TOAOVTWoewc IuvijSwc 0shy

78 TEXVIKO XpovlKa 11 ampKTOKT1 ampKliOOTl ------------------------------------~----~------------------------~

20

-2 -1

-I

I

o

g o =

Ro~or 01plcen~ degyebullbull 1

c t

-20

-lD

Ixtjpa 6 POT1tj KpoTTlOTlr Yla TpupaolKo BK ycvviar 15deg TLJT10U perapAI7Ttjr payvl7T aVTOTOshyoecvr TUpT10VOU

VVOEiTOl11 olipavlto TWV eopOvwv TOU BK

ponH KPATHIHI npampnEI vo Ko8oPlogei 0 apI81J0t TWV evepvonoll1lJampVWV cpoaewv KOI TOU peUIJOTOt oro orOTOshypo Iuvl8wt npoolovpocpeTol IJIO eAilXIOTl1 T11l1 oMo KOI

eKooroTE 1110 IlampVIOTl1 KOI IJIO eAilXIOTl1 Tlllrl H npoliloshyVpaCPrl oum Exel IJEVQ)11 OTlJloaio VIO Tl1v op8r AelToupshyvia TOU BK

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bull AlvoTepol OKpoOeuroKTelt bull AlvoTepelt cpooellt

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INERTIA CONVERSION (Mass x radius of Gyration2l

Lb Ft2 Ozln2 Lb FU

Lbln2 Lb Ft Sec Lbln Sec2 144 3108 x 10-2 373 2304 x 1031

6944 x 10-3 2590 X 10-32158 x 10-Lbln2 1 16 4633 x 103 bull 12 7413 x 1043217 1Lb Ft Sec2

8333 x 10-2 6177 X 1032681 3861 1Lb In Sec 1619x10-4434 x 10- 625 X 10-2 1349 x 10-5Ozln2 1

5208 x 10-3 625 X 10-21676 2413 3861Oz In Sec2 3417 x 1032373 07376 5467 x 104kg m2 (SI)middot 8851 3351 x 10 5362 x 105kg m sec2 2327 7233 868

gr cm2 273 x 10-6 3417 X 10-4 7376 x 10-8 8851 X 10-1 5467 x 10-3

7233 x 10-5gr cm sec2 2327 x 10-3 3351 8680 x 10- 5362

gr cm2 gr c sec2

Lb Ft2

kg m2 (SI)middotOz In Sec kg m sec

4214 x 1054214 x 10-2 42974297 X 10-35968 2926 X 103 29842926 X 10-4 2984 x 10-54144 x 10-2Lbln2

2934 x 105 2926 x 103 29842926 x 1044144 x 10-2Lb Ft Sec2

1383 x 10-13561356 01383Lb In Sec2 192 1152 X 1031130 X 1061152 x 10-20113016Oz 1829 X 105 18651865 X 10-6 1829259 x 10-3Oz In

7062 x 10 72017062 x 10-3 7201 x 10-41Oz In Sec2

101 102 x 10middot 105

1416 x 102 0102kg m2 SW 1 9807 x 1071389 9807 1kg m sec

102 X 10-3102 X 10-8 11416 x 10-5 10-1gr cm 110-5 98071389 x 10-2 9807 x 10-5gr cm sec

bull International System

TORQUE CONVERSION

Lb Ft

LbFt Lb In Oz In Dyne-Cm

1 12 192 1356 x 107

Lb In 8333 x 102 1 16 1 1298 x 105

Oz In 5208 x 10-3 6250 X 10-2 1 7062 x 104

Dyne Cm 7376 x 10-5 8851 X 10-7 1416 x 10-5 1 Nm 07376 88509 14161 x 102 107

Ncm 7376 x 10-3 88509 x 1 0-2 14161 105 Kpm grcm

7233 7233 x 10-5

86796 8680 x 10-

1389 x 103

1389 X 10-2 98067 X 107

98067

Lb Ft Lb In

Nm Ncm Kpm (kgfm) grcm

1356 01130

1356 x 102 1130

01383 1152 x 10-2

~ 383 x 10 1152 X 103

Oz In 7062 x 10-3 7062 7201- 7201 Dyne Cm 10-7 10-5 10197 X 10-8 10197x 10-3

Nm 1 102 010197 10197x10 Ncm 10-2 1 10197 X 10-3 010197 Kpm 98066 980665 1 105

grcm 98066 x 10-5 98066 10-5 1

To Convert Find known unit in the left hand column Move across and find the number in the column headed by the desired unit Multiply the known unit by this number for the desired unit

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