5/29/2015 Planetarygearratiocalculations

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PlanetarygearratiocalculationsThisarticlealsoavailableinSpanish

AquestionthatIoftengetishowtoworkoutplanetarygearsusingthegeartemplategenerator

Workingoutthetoothcountsforplanetarygearsisactuallynotthatcomplicated,soIinitiallyneglectedtomentionhowtodoit.Buthavingreceivedthequestionanumberoftimes,I'llelaborate.

Forconvenience,let'sdenoteR,S,andPasthenumberofteethonthegears.

R Numberofteethinringgear

SNumberofteethinsun(middle)gear

P NumberofteethinplanetgearsThefirstconstraintforaplanetarygeartoworkoutisthatallteethhavethesamepitch,ortoothspacing.Thisensuresthattheteethmesh.

Thesecondconstraintis:R=2P+S

Thatistosay,thenumberofteethintheringgearisequaltothenumberofteethinthemiddlesungearplustwicethenumberofteethintheplanetgears.

Inthegearatleft,thiswouldbe30=29+12

Thiscanbemademoreclearbyimagining"gears"thatjustroll(noteeth),andimagineanevennumberofplanetgears.Fromtheillustrationatleft,youcanseethatthediametersofthesungear,plustwoplanetgearsbemustequaltotheringgearsize.

Nowimaginewetakeoutoneofthegreenplanetwheels,andrearrangetheremainingonestobeevenlyspaced.Stillthesamesizegear.

Nowimaginethewheelshaveteeth.Theteethwouldstickoutbeyondthelineofthewheelasmuchastheyindent,sothatthepitchlineofthegearswouldbethelinearoundthegears.Thegeometrystillworksthesame.Ifyougointothegeargeneratorandselect"show

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pitchdiameter",youcanseehowthepitchdiameterisjustacirclethattheteetharecenteredover.

Thepitchdiameterofagearisjustthenumberofteethdividedbydiametricalpitch(largervaluesof"diametricalpitch"meansmallerteeth).Thegeargeneratorprogramtendstorefertotoothspacing.Pitchdiametercanalsobecalculatedastoothspacing*numberofteeth/(2*),where2*=6.283

Here'sanotherplanetarygearset.Themiddlearrangementisremoved...

...andhereitisinserted.

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Inthiscase,theplanetgearshave12teeth,thesungearhas18andtheringgearhas42teeth.

So,applying

R=2P+S

Weget

42=212+18

Thesepicturesarepartofafasincatinglycomplicatedplanetarygear

drivebyRonaldWalters.

Workingoutplanetarygearturnsratios

Workingoutthegearratioofaplanetarygeartraincanbetricky.Let'sdenotethefollowing:Tr TurnsoftheringgearTs TurnsofthesungearTy Turnsoftheplanetarygearcarrier(theYshapedthinginthepreviousphoto)R RinggearteethS SungearteethP PlanetgearteethTheturnsratioisasfollows:

(R+S)Ty=RTr+TsS

Example:

Now,usuallyinaplanetarygear,oneofthegearsisheldfixed.Forexample,ifweholdtheringgearinafixedposition,Trwillalwaysbezero.Sowecanremovethosetermsfromtheaboveformula,andweget:

(R+S)Ty=TsS

Now,ifwedrivethesungear,wecanrearrangetheformulatosolveforturnsoftheYcarrier:

Ty=TsS

R+SSothegearratiois

S/(R+S)

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Constraintsonnumberofteethandplanets

Ifyouwanttheplanetarygearstobeevenlyspaced,andallbeengagingthenexttoothatthesametime,thenbothyoursunandyourringgearneedstobeevenlydivisiblebythenumberofplanets.

Ifyouwantthemtobeevenlyspaced,butdon'tneedthemtoallbeinthesamephasewithrespecttotheirteeth,thenthenthesumoftheringgear'steethandthesungear'steethmustbeevenlydivisiblebythenumberofplanets.Thatis:

(R+S)isevenlydividesbythenumberofplanets.

Ifhoweveryouarewillingtospacetheplanetsunevenly,thisconstraintdoesnotapply.Theanglebetweentheplanetgearsaboutthesungearishoweverstillconstrainedby:

Anglep2p=360

N WhereNisawholenumberR+S

Thatistosay,theanglebetweenplanetgearsisamultipleof360/(R+S).

Finally,here'sanothercoolarrangementofgears,thoughnotreallya"planetary"gearset.

Ifyouplaceagearinsideanothergear,withtheinternalgearhavingatoothcountofhalftheringgear'stoothcount,anypointonthepitchdiameteroftheinsidegearwillmovebackandforthinastraightline.

Thebrassrodinthisphotowillmovestrictlylefttorightintheslot,whilethegearitisattachedtorollsaroundinsidetheringgear.Thatgearisactuallyattachedtoacrankwhichkeepsitrollingaroundtheedge,althoughonlythecenterpartofthatcrankisvisible,soitdoesn'treallylooklikeacrankinthephoto.

Photocredits:Ihaven'tactuallyhadaneedtobuildaplanetarygearsetmyself,soIusedsomephotosthatweresenttomebyreaders.ThefirstandlastphotosweretakenbyBrianKerrThesecondandthirdphotosweresenttomebyRonaldWalters

Seealso:

5/29/2015 Planetarygearratiocalculations

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Geartemplategenerator Cuttingplywoodgears Howtomakewoodengears

Workingoutcompoundgearratios

RonWalters'splanetarygeardrive

Penshakingcontraption

Makingrightanglegears