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CubesinaSphere
byFredHolder
IntheJuly/August2004issueofTheWoodturnerMagazine,publishedin
England,therewasanadvertisementfortheStoneleighTurningcompetition
for2004.ThefeaturedpictureatthetopofthepageintriguedmeandIhadto
knowhowtodoit.Itwasobviousfromthephotothattheoriginalblankwasa
spherewithsixequallyspacedsteppedholes.Thisgavetheeffectof
decreasing-sizedcubesinsidethesphere.Thesphereinthephotohadsix
levelsofcubes.
Apparentlytheballinthephotographwassomewhereintheneighborhoodof
3-1/2"indiameter.Thereareatleastacoupleofwaystodothisproject:drill
stepswithForstnerdrillsordrawcirclesoftheappropriatesizeandthen,
usingasquareendscraper,cuttheholestotheproperdepth.
SinceInormallymaketheChineseBallfrom2-1/2"spheresandhaveachuck
toholdthatsizesphere,Ioptedtousethatsize.Ihadnoideawhatsizedrills
touse,soIbegantoexperiment.MyRirstattemptprovidedaballwiththree
stepsplusaholeinthemiddle,buttheholesdidn’tintersectoneanotherto
givethedesiredeffectofcubesinsidethesphere.IRinallyworkedoutthatthe
properdepthforastepwas1/2of3/8"or3/16"andthediameterchangeof
drillsizeneededtochangeby3/8"asthedrillsizechangeslargerorsmaller.
AtRirstthisdidn’tseemtowork.ThenIrealizedthattheoriginalsizeofthe
sphereshouldhavebeenabout2-1/4".IcompensatedanddrilledtheRirst
hole5/16"deepandalloftheothers3/16"deepfromthebottomofthe
precedinghole.
Picture1:Thiswasmy2irstsuccessfulattempttomakethisproject.Itis
madefromElmandhasanAfricanBlackwoodbase.Allholeswere
drilledwithForstnerbits.
IntheBeginning
Tobeginthisproject,youmustchooseaspotontheendgraintobethenorth
pole.Then,usingthisasthestartingpoint,layoutsixequallyspacedholeson
thesurfaceofthesphere.AsshowninFigure1,astraightlinefromthenorth
polepositiontotheequatorofthesphereisdeterminedbytheformulax
(radiusonxaxis)squaredplusy(radiusontheyaxis)squaredequalsz
squared.“z”isthelengthofastraightlinefromthenorthpoletoanypointon
theequator.
Figure1.Thisshowsamethodofdeterminingthedimensiontosetyour
pencilcompasstolayoutthesixequallyspacedholes.
ThisformulasimpliRiesdowntozequalstheradiustimesthesquarerootof2
(or1.414).Forthe2-1/2"sphere,setyourpencilcompasstothe1/2ofthe
diameterofthesphere;i.e.,1.25"times1.414,toobtainavalueof1.7675".
HereiswhereoneoftheRirstinaccuraciescancomeintoplay.Itisunlikely
thatonecansetapencilcompasstothatprecisenumber.ImadeupaRlexible
cardboardtemplateofthatlengthasdeterminedwithmydigitalcalipers.
Layingthetemplatefromthenorthpoleacrossthesurface,Imarkedthree
locationsabout120degreesapartonwhatwouldbetheequator.Then
measuringfromeachoftheselocations,Imadeamarknearthesouthpole.I
selectedthecenterofthesethreemarkstobethesouthpole.
Ithenmountedthespherebetweencentersonthelatheanddrewacircle
arounditattheequatorlocation.Iengagedtheindexingpinandmarkedone
oftheholes.Imoved90degrees(sixholesonmyNovaDVR3000indexhead)
andmadeanothermark.TwomoreequalmovesandIhadfourequallyspaced
holesmarkedontheequatorline.Atthispoint,Iwasreadytostartdrilling
holes.Ifyoucanmanagetosetyourpencilcompasstothe1.7675"dimension,
youcaneasilylayouttheholeswiththecompass.Selectapolepositionand
insertthepoint.Drawalinearoundthesphere.Onthatlineselectsomepoint
anddrawanothercircularlinearoundthesphere.Nowatoneofthe
intersectionsofthesetwolines,drawanotherlinearoundthesphere.This
givesyoualocationfortheotherpolepositionandfourequallyspacedlines
ontheequatorline.Ofcourse,allofthisassumesthattheballisperfectly
round.
Picture2.Inthisphoto,thetailcenterisbeingusedtoaligntheballoncenterbefore
thechuckistightened.
Mountyoursphereinthechuckwithoneofthepositionsalignedwiththeaxis
ofrotationofthelathedeterminedbyinsertingthetailstockcenterintothe
intersectionofthelines.Lockthechuckdownandreplacethetailstockcenter
withthedrillchuckanda1-1/2"Forstnerdrillbitmountedinit.Drillintothe
sphereuntiltheoutsideedgesoftheForstnerdrillbitisreadytocutthe
surfaceofthesphere.Makeamarkonthesideofthedrillbitthatis5/16"
fromthesurfaceofthesphere.Drilldowntothisline.Checktomakesurethat
yourholeis5/16"deep.Ifitis,useaRinepointpentomarkalineonthedrill
bittoindicatethedepthofcut.ThisisforuseontheotherRiveoutsideholes.
Figure2showstherelationshipofanyfourholesdrilledontheequatorat
eachdrilldepth.
Figure2.Thisdrawingshowswhatishappeninginsidethesphereifa
crosssectionwastakenthroughthecenterofanyfourholes.
Note:Ifthewoodisfairlyhardandheatsupwhiledrilling,Isuggestthatyou
arrangetoRlowairontothewoodanddrillbitwhiledrillingtopreventheat
cracksandpossiblefailureoftheproject.
Younowhaveadecisiontomake.Youcanaligneachoftheotherholesand
drillthe
1-1/2"holeforeachofthembeforechangingtothenextsmallersizedrill.Or
youcandrillholeswithallofthedrillswiththissetup.I’mpersonallynotsure
whichisthesafest.Ihavedoneitbothwaysandhadfailuresdoingitboth
ways.
Picture3:Thissetupshowstheoperationofdrillingthe2irststepatany
givenposition.Notethemarkonthedrillwhichwasmadeafterthe2irst
holewasdrilledintheball.
Picture4:Bydrillingtwoadjacentholes,youcanchecktoensurethat
youaredrillingtotheproperdepthtoobtaintheoptimaloverlapofthe
holestocreatetheeffectofcubes.
Alloftherestoftheholestobedrilledmustbe3/16"deepfromthebottom
surfaceofthepreviousholeandineachcasetheyare3/8”smallerthanthe
precedinghole.Therefore,thenextsizedowndrillis1-1/8”indiameter.I
recommendthatyoubackoffyourtailstockspindleasfarasitwillgoand
makeamarkonittoindicatezero.Thenmakeamarkagainwhenthetailstock
spindlehasmovedout3/16".WiththetailstockspindlesettotheRirstmark,
movethetailstockassemblyinuntilthedrillbottomsagainstthesurfaceof
theprevioushole.Lockdownthetailstockassemblyanddrillinuntilthe
3/16"markappears.Retractthedrillandcheckthedepthofthehole.Ifthe
drillslipsinthechuckorthetailstockslipsonitsmounting,yourholewillnot
betherightdepth.Therefore,Irecommendcheckingeachholefordepth.The
nextholetodrillisthe3/4"hole.Itshouldalsobedrilled3/16"deep.Repeat
thisoperationforthe3/8"drillandyouarereadyforthenextholelocation.
Picture5.Thisphotoshowsthatallofthe2irstholeshavebeendrilled
andthentheotherlevelsonthisholehavealsobeendrilled.
Whenallholesaredrilled,youshouldbeabletolookintotheholesandsee
whatlookslikedecreasingsizesofcubesallconnectedtothepreviouslayerat
theirpoints.Aprojectsuchasthisrequiresastand.Youcouldsimplymakea
littleeggcup-typestandtosetitin;however,itwouldbehardtokeeptheitem
orientedproperlyusingthistypeofmounting.Therefore,Ifeltapermanently
attachedbasewouldbebetter.Iturnedthebasefortheoneillustratedinthe
photoatthebeginningofthisarticleoutofAfricanBlackwood.Iturneda
smalltenononthetopofthebaseanddrilledamatchingholeinthesphere.
Thisholeneedstobelocatedinthecenterofoneofthetriangulararea
betweenthreeholes.Thisgivesthebestorientation,inmyopinion,forthe
Rinishedproject.WhatI’vejustdescribedishowIdidtheRirstoneofthese,
madeoutofa2-1/2”sphere.Unfortunately,my40+yearoldmathematics
doesn’tseemtoallowmetoworkouttheformulatodeterminehowdeepthe
Rirstholeneedstobedrilledonanysizeofsphereandwhatsizediameterhole
isrequired.IthoughtIcouldjustusethesameformulagoingupinsizeasIdo
ingoingdowninsize,butsomethingdidn’tseemtoworkhereeither.WhatI
havedeterminedisthatbydrillingtwoadjacentholesofanestimatedsize,I
candetermineatwhatdepththatsizeholewilloverlapandgivethedesired
openingattheinterception.Usingthismethod,Iwasabletoincreasethesize
ofthesphereslightlytogivefourstepsinthesphere.Ihadtouseadifferent
sizestartingdrill,whichchangedalloftheotherdrillsused.Eachdrillstillhad
tobe3/8”smallerthanthepreviousoneandwasdrilledintothesphere3/16”
deepfromthepreviouslevel.Inthiscase,thelastholedrilledwas1/2”instead
of3/8”asforthesmallersphere.Thisprojectrequiredmetomakeupalarger
chuckoutofthreeinchPVCcompressionRitting.
Picture6.Thisphotoillustratesthe2irstsuccessfulversionofthisproject
andthenumbertwoversionwhichismadefromalargersphereand
containsfourstepsinsideeachhole.
MakingtheBallChuck
Picture7.ThisphotoshowsthebasiccomponentsoftheballchuckthatI
use.Lefttoright:screwoncap,plywoodwasherto2itbetweenthesphere
andthecap,malepartofthePVCcompression2ittingis2ittedwitha
hardwoodblockwithasphericalrecess.Thisonehassandpapergluedin
togrip.
MyRirstchuckofthistypewasmadefroma3”PVCcompressioncoupling.I
cutoffoneendtomakeaverynicechuck.Iglueda1inch,8tpinutintoa
blockofelmandturnedittoRitinsidethecoupling,gluedthewoodintothe
coupling,insertedfourscrewstohelptheglue,turnedahemispherical
depressionfora2-1/2”sphereintheelm,turnedapieceof1/4”plywoodto
Ritinsidethelid,putthelidandplywoodontothechuckbodyandturneda
holeintheplywoodtoRitontoa2-1/2”ball.Ithendrilledaholetoinserta
pieceof3/8”doweltouseasaleverfortighteningandlooseningthecap,
glueda3”sandingdiskintothebottomofthehole(aftercuttingslotsallofthe
wayaround),andIhadaveryserviceableballchuck.Theonlyproblemwas
thatthecapwastoobigformyhandandIhadproblemsscrewingitdownand
looseningit.Irepeatedtheoperationwitha2”compressioncouplingandused
aOnewayChuckinsertinsteadofa1inch8tpinut.NowIhaveachuckwitha
screw-onlidthatIcanhandtightenandloosenandthatcanbeadaptedtoany
lathethatIcanbuyaOnewayChuckinsertfor.Itworksgreat.
Thesechucksareveryeasytomake.Ittakesmeaboutanhourtomakeone.
I’vefoundthateitheraOnewayStrongholdChuckInsertorapieceofcross
grainoakwith8tpithreadstoRitaNovaChuckInsertworkverywellforme.
However,youcanmountthewoodenblockontoadedicatedfaceplatetoRit
yourlathe.
AnotherthingthatI’mdoingthesedaysistocoatthesphericalhollowwith
hotmeltglue.Ithentakearoundnosescraperandspreadtheglueevenlyon
thesurfaceofthesphericalhollow.WhenI’mreadytochuckupasphere,I
turnonthelatheandsandthesphericalhollowlightlywith80-gritsandpaper.
Thisslightlywarmsthegluesurfaceandallowsittogripthespherevery
Rirmly.Ishouldcaution,donotwarmittoomuchoryoumayRindyoursphere
permanentlyattachedtoyourchuck.
Havefunwiththisnewwaytodecorateasphere!