Figure1:AKEVAcontraptionskitwecouldusetobuildRubeGoldbergmachines.Dyna - PDF document

Figure1:AKEVAcontraptionskitwecoulduseto
Figure1:AKEVAcontraptionskitwecouldusetobuildRubeGoldbergmachines.DynamicBlocksWorlds:WhatCouldBeLearnedFromKEVAcontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionscontraptionsChristopherG.Atkeson,CMUVersion3,October1,20181IntroductionThesenotesexplorewhathighlevelconceptsandabstractions,models,andotherinformationcouldbelearnedinareallifeblocksworldmanipulatedbyanactualrobot.Thegoalistocopy,buildfromhumaninstructions,adjustuntilitworks,andinventnewRubeGoldbergmachines().Thecontraptionskits(Figures1and2)areexplicitlyde-signedtobuildRubeGoldbergmachines,andincludeinstructionstodoso.Thesenotesdiscusshowwecanusethesekitstoexplorehowrobotscanlearnconceptsandabstractions.Wenditusefulto“storyboard”whatmightcomeoutofaresearchprojectbeforeembarkingonit.Hereisthestoryboardforthecontraptionskits.ThemostinterestingpartsareSection8onhowtobuildrobuststructuresandAppendixIII(Section15)onwhatalibrarymightlook

like.2Contraptions:KEVAPlanksUsersofthec
like.2Contraptions:KEVAPlanksUsersofthecontraptionskitsbuildastructureoutofblocks(“planks”)bystackingthem.Thekitin-cludeslightweightballsthatroll,bounce,orslidetotransferenergyandcausechangesinthestructure.Theuserplacesaballtostarttheprocess.Arobotmustbeabletostackblocks,placeballswithinthestructure,andplaceaballthatstartsthemachine.Nofastmovementsorfastperceptionarerequired.Figure2:AnotherKEVAcontraptionskitwecouldusetobuildRubeGoldbergmachines.3LearningRobustGraspsTherobotmayhaveahandwithngersorasuctionorjamminggripper.Asdescribedinanappendix,graspingprimitivesalreadyexist.Herearesomepossibleconceptstolearn:Graspnearthegeometriccenteroftheobject.Amorerenedversionistograspnearthecenterofmass(anotherconcepttobelearned).thegeometriccenteroftheobjectwithcontacts,inthecaseofngerswithunilateralcontacts.Amorerenedversionistodeneapolygonofsupport.theobjectwithcontacts.ItisbettertohavethecontactingpartoftherobotbelowtheInterference:Anynearbysupportsurfaceorobjectsaffectthechoiceofgrasp.Planahead:Itisusefultoanticipatewhatwillbedonewithanobjectwhenchoosingagrasp.Suckfaces:Forsuction

graspers,avoidedgesandpreferatterfaces.
graspers,avoidedgesandpreferatterfaces.Controlgripforce:Forgraspswithngers,thecontactforceisusefultocontrol,ifitcanbecontrolled.Toosmallagripforceandtheobjectslips.Toolargeagripforceandtheobjectmaybedamagedorslipbybeingsqueezedoutofthegrasp.4LearningRobustUngraspsChallengesinungraspingarereleasingtheobjectwithatiltsoitfallsoverorjustwobbles,andhavingtheobjectadheretoangerorsuckerandpullingtheobjectoverasitisreleased.Ungraspalittlebitandthenpausetoestimateiftheobjectisstillincontact.Ifitisstilltouchingapartofthehand,movethehandtoreduceanytilt(typicallyalongadirectionfromthecontacttotheobjectcentroid)andrepeat.Ifthereisnocontact,thengersorhandcancompletetheungraspingmotion.Thisstrategyhelpsreducetheeffectofrobotmotionerrorsorvibrations,aswellasobjecttippingafterrelease.Ungraspdownwards:Toeliminateadhesionbetweenangerorsuckerandtheobject,movethehanddownwardsduringungrasping.Thisensurescontactwiththeground.Movingthehandsidewayscouldcausetheobjecttotilt,andmovingthehandupwardscouldlifttheobjectofftheground.Rotatingthengersaboutthecontactpointscanalsohelpeliminateadhesion.5Learni

ngToStackAndStaticsLearningtostackplanks
ngToStackAndStaticsLearningtostackplanksinvolveslearningtheconceptofcenterofmass(whichisthesameasthecentroidfortheobjectsinthisdomain)andthepolygonofsupportdenedbythecontacts.Italsoinvolvesknowledgeofhowfrictionworksfortiltedobjects.Tippiness:Agoodestimateoftherobustnessoftheposeofablockwithaathorizontalsupportsurfaceisthedistanceofthecenterofmassprojectedontothesupportsurfacetotheclosestedgeofthepolygonofsupport,dividedbytheheightofthecenterofmassabovethesupportsurface.Planksstandingupverticallyontheirsmallestfacecanfallovermoreeasilythanplankslyingdownontheirlargestface,withtheothercongurationintermediateinitsstability(Figure3).ThisconceptcanFigure3:VariousstableposesofaKEVAplank.Lyingat(blueplank)isthemoststable,andvertical(greenplank)istheleaststable.belearnedbyexampleasacatalogofpossiblepositionsandfailurestatistics,ratherthanexplicitlycomputingdistances,centerofmasslocations,ortheproposedratio.Polygonofsupport:Thesystemcouldlearnexplicitlytheconceptofthepolygonofsupport,oratleastestimatethehorizontallyprojecteddistanceofthecenterofmasstotheclosestsupportedge.Understandi

ngthisconceptcanhelpeliminatetheneedfora
ngthisconceptcanhelpeliminatetheneedforalibraryofrobustposes,especiallyinthecaseofsupportcontactsatdifferentheights.Centerofmass:Thesystemcouldlearnexplicitlytheconceptofcenterofmass,oratleastthegeometriccentroid.Understandingthisconceptcanhelpeliminatetheneedforalibraryofrobustposes,especiallyinthecaseofsupportcontactsatdifferentheights.StaticFriction:Thesystemcouldlearnaformulaforstaticfrictionandafrictioncone,justlearnalimitingangleamongsupportingcontacts,orcatalogexamplesofwhenspecicobjectsstickorslideonspecicsetsofcontacttypes,conguration,andlocation.RealfrictionismorecomplicatedthatthesimpleformulasgiveninRoboticsorPhysics101.Contactshapesmatter.Whethercontactsareface-face,face-edge,face-corner,edge-edge,edge-corner,orcorner-cornermatters.Tiltedobjectstypicallyrestonedges.Anotherareawherefrictionisimportantiswhetherobjectswillslideiftheyarehitwithaballoranotherobject.Supportsurfacessuchascarpetshaveahugeeffect.BuildFromTheBottomUp:Stacksarebuiltfromthebottomup.Blocksthataresupportedtypicallyshouldhaveallthesupportingblocksalreadyplaced.6LearningBallDynamics:Rolling,Slidi

ng,Bouncing,Impacts,andTippingCoefcient
ng,Bouncing,Impacts,andTippingCoefcientofrestitution:Howdoballsbounce?Thisismorecomplexifthebouncesurfacemovesduringbouncing.Thecoefcientofrestitutionmodelisonlyapproximateandignoresspin.Rollingvs.Sliding:Afteranimpact,willtheballrollorslideorboth?SlidingtoRolling:Whendoesaslidetransitionintoaroll?Whendoesaballstarttoslideorroll?Whendoesaballstoprollingorsliding?Whathappenswhentwoobjectshit?Tip,slide,roll,...?Tipping:Whathappenswhenablocktipsover?Aninterestingquestioniswhetherthesystemwillinventtheconceptof“force”.Forcescannotbedirectlyobserved.Onlytheeffectsofforcescanmeasured.Itispossibletolearndynamicsandconceptsofmass,momentum,andenergyandpredicttheeffectsofcollisionswithoutinventingtheconceptofforces.Similarly,willthesysteminventtheconceptof“gravity”?Orwillitknowthatslantedslopeshavedynamiceffects,andtippingoverhappens,butthereisnolinkbetweenthetwophenomena?7LearningToTransferEnergyEnergycanbetransferredbymovingballsandchainsofplanksfallingover(likedominos),sliding,ormovinginmorecomplexways.Rampsandrailsareoftenusedtoguideballsduringrollingorsliding(Figure4).Figure4:Twotyp

esoframpswithplanksorientedindifferentwa
esoframpswithplanksorientedindifferentways,walls,impactwalls,aV,andSlopesanddrops:Useslopedplanksanddropstomoveballs.Aatsurfacedoesnotguidetheballalongapath.Herearesomeconceptsthatdoabetterjobreducinguncertainty.Wallshelpguidearollingorslidingobject.Theamountof“play”orexcesswidthbeyondtheballcanaffectballbehavior.Wallscanbetilted(AVwithaoor,forexample).Pathwidthscanchangealongthepath.ImpactWalls:Aseriesofdisconnectedwallscanbeusedtoguideaballrollingdownhill.E4:Ahelpsguidearollingorslidingobject.TheVanglecanchangealongthepath,changingtheinstantaneouscenterofrotationandtherollingvelocityduetoenergyconservationandtheparallelaxistheorem.helpguidearollingorslidingobject.Therailingwidthcanchangealongthepath,changingtheinstantaneouscenterofrotationandtherollingvelocityduetoenergyconservationandtheparallelaxistheorem.Complexchutes:Morecomplexchutescombinedifferenttypesofguides,suchasarailononesideandaoorandwallontheother.Bounceplatformsandsupportsurfacescanbeusedtoguidetheball.Theballcandropfromonechute,andbounceintoanotherchuteorfunnel.Energycanbetransferredbymovingballsandchainsofpl

anksfallingover(Figure5.Figure5:Aballro
anksfallingover(Figure5.Figure5:Aballrollingdownachuteabouttoinitiateachainofdomi-nosfalling.See-saws(inboththeverticalandhorizontalplanes)canbeusedtotransferenergy.Wherethepivotpointiscanbeusedtomodulateenergytransfer.8LearningRobustStructures*Asterisks*mark“Tips”fromthecontraptionsmanual.Quotesindicatedirectquotesfromthetraptions*TrialandError*:“Makefrequenttrialsasyoubuildtoseeiftheballwilldowhatyouexpectittodo.”*EasyDoesIt*:“Gentleslopesandslowerspeedsmakeiteasiertocontroltheballmovements.”*Gentlydropplanksintoplace*:“Leteachplankgentlydropintoplace.Pressingitintoplacemaydisturbtheplanksbeneathit.”*Gentlypushplanksintoplace*:Gentlepushesfromthesidecanbeusedtoalignplanks.:“Useplanksasatooltomakerowsperfectlystraight.”(Figure6)Figure6:Usingplanksastoolstoalignother*LikeSandcastles*:“RememberthatContraptionsaretemporary.Theywilleventuallyfalloutofalignment.ThegoalistosuccessfullygettheballthroughtheContraptiononeormoretimes.”Makeadjustmenteasy:Buildstructuressothatkeyareas(typicallywheretheballrollsorbounces)canbeeasilyadjusted.Thenextconcept,MoveableStructures,isagoodexample.*

MoveableStructures*:“Build[modules]on...
MoveableStructures*:“Build[modules]on...basessotheirpositioncanbeeasilyadjusted.”*TableIt*:“Buildonatabletogainmore[changeof]height.TrymakingtheKEVAballmovefromtabletotheoor.”[Largeblockssuchasbooksandsupportsurfaceslikestairscanbeusedtogainheight.]Figure7:Makingthesupportsperpendicularmakesatrestlemore*TheAngleAdvantage*:“Uprightplanks(likethoseusedonatrestle)aremuchmorestableiftheyareangledratherthanparallel.”(Figure7)*Focusingtheball*:Rollsandwallsthatnarrowachute(afunnel)canbeusedtoreduceuncertaintyofaball.Thiscanhappeninanear-horizontalchute,orwallscannarrowaverticaldrop.Funnelsalsoreduceuncertainty.(Figure8).Figure8:Impactwalls.*WallAndRailPose*:Walls(includingimpactwallsandturns)andrailscanbemadebyhavingtheplankatoronedge(Figure8).Wallsandrailscanbereinforcedusingadditionalplanksontopofthewallsandrails,ornexttothewallsandrails.Thesewallswillmovelessonimpactandbemorebouncy.Wallsandrailscanbestraightorzig-zag.*RailWidth*:“Experimenttondthebestspacingforyourtracks....Ifyoumakethetrackwider,theballgoesslower.[anditisdifculttohavetheballtransitionofftherailswithoutslipping

]...Ifyoumakethetracktoonarrow,theballis
]...Ifyoumakethetracktoonarrow,theballismorelikelytoleavethetrack.”*Crossplanks*:Crossplankscanstabilizewallsandtrestles,preventingadominoeffect(FigureFigure9:Examplesofcrosssup-portsstrengtheningastructure.Ontheright,thecrossplanksalsoactasbouncebafesthatpreventballsbouncingoutofthechutesaftera*Bouncebafes*:Crossplankscanalsopreventaballbouncingoutofaballcatchingstructure(Figure9).Holdingaball:Ablockedchute,especiallywithaVorrails,canholdaballinapreciselocationsoitcanbepickedupbyarobotorhitbyanotherballordomino(Figure10Left).Otherwaystodothisareputtingaballinacrackinaramp(Figure10MiddleandRight).*BouncePlates*:“BounceplatesarefunbecausetheymaketheKEVAballlooklikeithasamindofitsown.Theballappearstoleap[drop]toasmallplatformandthenhop[bounce]toitsnewdestination.”Figure10:Astableandrepeatablewaystopo-sitionaball.*ReliableBounces*:“Atwolayertop[(bounceplate)]createsahigher,moreconsistentbounce.”:Shafts,tunnels,andotherenclosurescanbeusedtoguidedroppingoryingballs.Energytransfertoadominochain:Whatisthebestheightforaballtohitanuprightplanktoinitiateadominochain?Energytransferwithi

nadominochain:Whatisthebestspacingofvert
nadominochain:Whatisthebestspacingofverticalplankstomaintainachainofplanksfalling(likedominochains)?Energytransferoutofadominochain:Whatisthebestverticalandhorizontalspacingbetweenthelastverticalplankandaballtosuccessfullytransferenergytotheball?*Assemblesub-unitsandplacethem*:“Placeanentirestackofplanksatonetime.”[Thisisespeciallytrueforwidespanbeams(Figure11).]Figure11:Examplesofassemblingwithsub-Buildstackshorizontally:Onecanbuildstackshorizontallyandthengraspandplacethestackvertically.Thismakesbuildingstackseasierwhosepartialstacksarenotstable.*Creatingtilts*:Varyingnumbersofstackedplankscanbeusedtocreatearamporotherslopedstructure.Puttingthestacksatthebottomofastructurecanallowalllayersofamultilayerstructuretobetilted.*Changingorcancelingtilts*:Atiltofastructurecanbechangedorcanceledbydifferentheightsofstackedplanksatthetopofthestructuretocreateaplatformwiththedesiredtiltforbuildingabovethestructure.*Addstructureformeasurement*:Additionalstructurecanbeaddedtoprovidereferencesandmeasurementforspacingstructuresliketrestlesupports.Dangletomakeplankvertical:Whentryingtopositiona

graspedplankverticaltoputitdownsupported
graspedplankverticaltoputitdownsupportedbyitssmallestface,itisusefultoholditattheotherendandletitswingfreely.Gravitythenmakesitvertical.SmoothRamps:Theplacementofacrackoverasupportchangesthesizeofthecrack(Fig-ure12).Figure12:Unevennessoframpsdependsonplacementofthesup-9SegmentingStructuresAndBehaviorFunctionalandstructuralanalysisareusefulinguidingreasoningandlearning.Wecanuseobservationofbehaviorandalsohowastructureisbuilt(Figure13)toidentifyfunctionandre-usablepartsorFigure13:Instructionstobuildastructure.modules.Thecontactsequenceoftheballishelpfultodothis.Atiltedatsurfacewithasinglecontinuouscontactbelowtheballdenesaramp.Horizontallinearmotionwithasinglecontactatthebottomofaballwithsidewaysmotionandimpactsonthesidedenesachute.HorizontallinearmotionwithtwocontinuouscontactswithfacesdenesaV.Horizontallinearmotionwithtwocontinuouscontactswithedgesdenesrails/tracks.Animpactandhorizontalchangeofdirectionisaturn.Animpactandverticalchangeofdirectionisabounce.Rollingalongawallisaguidewall.Fallingdenesadrop.Figure14showsarelatedmarblegame(Labyrinth)inwhichamarbleisdriventhrough

amazebytiltingthemaze.Figure15showsanexa
amazebytiltingthemaze.Figure15showsanexampleofthistypeoffunctionalanalysisappliedtothetiltmarblemazegamewherecontinuousmotionofthemarbleissegmentedintoprimitivesbasedonballWecanusethecongurationsofblocksorplankstondreusablemodulesaswell.Supportstacks,trestles,andtowerscontrolheightofastructure,forexample.Tiltedplanescreateramps.Increasesinheightcanbewalls.Decreasesinheightcanbedrops.Figure16showsexamplesofmanualsegmentationthatcouldbegeneratedbyfunctionalandstructuralanalysis.Ultimatelywewillwant3Dsegmentationswithpartsofthestructurethattouchedtheballhighlighted.Figure14:TopLeft:thetiltmarblemazegame(Labyrinth).TopRight:Adenitionofanactionprimitive,Actionprimitives.VideostoexperimentwithofbothbuildingandrunningKEVAcontraptionsmachinesarelistedinanAppendix.10CreatingNewStructuresThereareanumberofoperationsthatcanbeusedtocreatenewstructures.Themostimportantisusingcompositionanddecompositiontocombineelementsordiscoverelementsthatarepartsofobservedstructures.Figure17showsexamplesofcombinationsofmodulespresentedinthetraptionsinstructions.Suchcombinationscanalsobeusedtolearnhowtoseg

mentbyundoingthecombination.Forexample,F
mentbyundoingthecombination.Forexample,Figure17provideslabelledsegmentationsaswell.Thesegmentationde-scribedintheprevioussectioncanbeusedtocreatenewmachinesthataresubsetsofknownmachines.Otherpossibleoperationsincludeextendinglinearelements.Horizontalelementssuchaschutescanbelengthenedorshortenedbyaddingorremovingpieces.Verticalelementssuchasshaftsandtow-erscanbemadetallerorshorterbyaddingorremovingpiecesaswell.Inadditiontoextendingorshorteningturns,turnratescanbeincreasedordecreased.11TheoriesAndModelsTheoriesallowasystemtomakepredictions,asdomodels.Itisnotclearhowtheoriescanbedis-tinguishedfrommodelsinthisdomain.Weexpecttheproposedsystemwillhavemultiplelevelsofmodels,allofwhichcouldbelearned.Structuralmodels:Anabstractstructuralmodelmightdescriberelationshipsamongcomponents:[(CHUTEonTRESTLEonSUPPORT-SURFACE)to-right-of(BOUNCE-PLATEonSUPPORT-SURFACE)to-right-of((FUNNELonBALL-DISPENSOR)next-toSTOP)],Anothertypeofstruc-turalmodelcoulddescribehowtobuildeachcomponentintermsofblocksandqualitativelywhichblocksupportswhichotherblock.Atrestlemightbedescribedas[(top-plankishorizontal),(top

-planksupportedbyleft-plank),(top-planks
-planksupportedbyleft-plank),(top-planksupportedbyright-plank),(left-plankisvertical),(right-plankisvertical),(left-plankissupportedbysupport-surface)and(right-plankissupportedbysupport-surface)].Adetailedstructuralmodelcouldlistthe3Dpositionsandorientationsofeachplank,andFigure15:TopLeft:theobservedpathofthemarbleinthemaze,TopRight:estimateofcontactsindicatedbythickredlines,identiedprimitives.Figure16:Examplesofmanualsegmentation.mightcontactsorsupportrelationships.Functionalmodels:Anabstractmodelmightsimplylistballbehaviorsandcomponents:[ROLLonCHUTEonTRESTLE-DROPonBOUNCE-PLATE-CAUGHTinFUN-NEL-DROPontoBALL-DISPENSER-ROLLintoSTOP](ToprightofFigure17).Detailednu-mericalmodelswouldfocusonasinglebehavior,orasingletransitionbetweenbehaviors,suchasdetailedmodelsofrolling,impactswithwalls,dropping,andbouncing.12ExtensionsVaryblocksize:Differentblocks,suchasJengablocks,areavailableorcanbemade(Figure18).Varyblockfriction:Useblockswithdifferentfrictionduetodifferentcoatingsormaterials,suchassandpaper,metal,orTeon.Varyballs:Ballscanbemadeofdifferentmaterials,havedifferentsurfacespropert

ies,andhavedifferentsizes,massesandmassd
ies,andhavedifferentsizes,massesandmassdistributions(momentofinertia),rangingfrompingpongballstometalballbearingsofvarioussizes.Varysupportsurfacefriction:Teon,airtable,sandpaper.Applyperturbations:Buildonashakertabletoforcestructurestobemorerobust.Applywindwithafan.:Makestructuresmorepermanentbygluingthem,andreducemisalingnmentovertimeandtheeffectsofvibration.Blocksthatattach:Legosandmagneticblockscanbeattached.ForLegosthekeynewfeaturesherearethelossofatfaces,andthepresswithinterlockformofattachment.Unfortunately,attachingLegopiecesrequiressignicantforceandaheavyrobot(sotherobotisnotliftedoffitssupportsurfacewhiletryingtopressdownonapiece)orarobotthatisattachedtoasupportsurface.Magneticattachmentmayexhibitcomplexinteractionbetweenpieces,orbetweenpiecesandmetalpartsoftheSpecialpieces:Varioustoys,includingLegos,providespecialpurposepiecesEXAMPLES.Figure17:Combinationsofmodules.Figure18:AKEVAplankcomparedtoaJENGAblock.Activecomponents:Useservosormotorstomovestructuresatparticulartimes(suchasthewindmillobstacleinmini-golf).Usesensors:Useservosormotorstomovestructuresbasedonsenso

rreadings.Muchwiderrangeofpieces:EXAMPLE
rreadings.Muchwiderrangeofpieces:EXAMPLESOFYOUTUBERUBEGOLDBERG.13AppendixI:PriorKnowledgeInadiscussionaboutwhatislearned,itisusefultobeexplicitaboutwhatisalreadyknown,eitherbecauseitwasprogrammedintothesystemorlearnedpreviously.Herearesomeconceptsweexpectthesystemtoalreadyknow.Environment:Thereisascopewhichcontainseverythingunderconsideration.:Therearewaystomeasuredistance,size,andangles.:Therearesupportsurfacesandpossiblywallsthatarerigidandimmovable.Thereisawaytodescribetheirshape.:Thereareobjectsoratoms.Inthecaseofcontraptionstheseincludeplanksandballs.InthecaseofLegostheseincludeallthepieces.ObjectShapes:Atanytime,andobjecthasashape.Primitiveshapedescriptorsincludewaystodescribeatorcurved“faces”,“edges”,and“corners”.Forexample,aballhasonecurvedface.Ablockhassixatfaces,withcorrespondingedgesandcorners.Theactualshapeofanobjectismeasuredorestimatedbythesystem.:Anobjecthasalocation.Thiscouldbethelocationofareferencepointontheshapesuchasthegeometriccenteroraparticularcorner.Theactuallocationofanobjectismeasuredorestimatedbythesystem.:Anobjecthasanorientation.Someobjectshavesymme

tries,suchasaballoraregularblock.Theactu
tries,suchasaballoraregularblock.Theactualorientationofanobjectismeasuredorestimatedbythesystem.Conceptsmarkedwithdouble**asterisks**aredebatableastowhethertheyshouldbepriorknowledgeorlearnedbytheproposedsystems.:Surfaces,edges,andcornerscancontactothersurfaces,edges,andcornersandmustnotinterpenetrate(butcanhaveelasticorplasticdeformation).Possiblecontactsareestimatedbythesystem.14AppendixII:PriorLearningWeexpectanyrobotswillhavealreadylearned3Dvision(eitherstereoorRGBD)andkinematicrelationshipsbetweenvisualperceptionandsensedjointangles.3DVision:WeexpecttoinstrumentbothrobotsandtheenvironmentwithmultipleRGBDcam-eras,includingcamerasontherobottoreduceocclusionandmeasurerelativeposesofanyendeffec-torsandobjects.3DAction:ForwardJacobians:Therobotknowstheeffectofmovingjointsasmallamountoratavelocityonthedirectionandspeedofanobjectin3Dandinanyimages.3DAction:ForwardKinematics:Therobotknowsthe3Dpositionandorientationofthegrippergivenasetofjointangles,aswellasbeingabletopredicttheappearanceofthegripperinany15AppendixIII:WhatWouldALibraryLookLike?Inadditiontotheguresshownsofar,herearead

ditionalelementsthatmightbeinalibraryof
ditionalelementsthatmightbeinalibraryofFigure19:Ramps.Figure20:V.Figure21:Rails.Figure22:Stacks,trestles,andtowers.Figure23:Chutes.Figure24:Multi-layertrestles,overpasses,andchutes.Figure25:90degreeturns.Figure26:Uturns.Figure27:Wallfunnels.Figure28:Impactwalls.Figure29:Enclosedturningsteps.Whataboutenclosedstraightsteps?Figure30:Drops(typicallyfollowedbyabounce).Figure31:Bounceplatforms.Figure32:Catchersandfunnels.Figure33:Verticalshafts.Therstfourarestraightdrops,thefthistilted,andthelasthasbafesmarkedbyasterisks(*).Figure34:Astablewaytopositionaball.Figure35:Stops.Figure36:Ballsrollingtoinitiateachainofdominosfalling.Figure37:Dominochains.Figure38:Dominochainsthatwilllaunchtheball.Figure39:Lanesforballsandamerge.Figure40:Ballcorral.16AppendixIV:YouTubeVideosYouTubevideosofbothbuildingandrunningKEVAcontraptionsmachinesinclude:https://www.youtube.com/watch?v=3fb-aiSOPJohttps://www.youtube.com/watch?v=rss6JuM-xucYouTubevideosofKEVAcontraptionsmachinesinclude:https://www.youtube.com/watch?v=nxg7Q-6Nzkohttps://www.tes.com/lessons/jdq4FRzEfF4b9Q/keva-contrap