Program 60-710—Involute Splines And Inspection Introduction
Program 60-710—Involute Splines and InspectionIntroductionThe primary purpose of this model is to provide data from ANSI Standard B92.11970 for Involute Splines and Inspection. This is the standard for inch-series splinesbased on a stub diametral pitch design. It is possible to use the model to convert thedimensions to metric, but the basic calculations are always based on diametral pitchand the inch system.The model will automatically calculate data for splines and gages in accordance withthe standard. If data is entered for a modified spline, the model will indicate that thespline is not standard and will then calculate data for measurements and gages forthe modified spline.Plots of the assembled and individual splines are available on the Plot Sheet of theTK Solver model. The plots are of the mean actual tooth thickness.For information on the proper use and interchangeability of splines and gages referto the standard.In some cases the dimension given by the software will be slightly different than thedata in the tables in the standard. The software uses the equations given inAppendix A of the standard and the user must decide which value should be used.
UTS Integrated Gear SoftwareExamplesExample 1The first example is a 26 tooth, 10/20 diametral pitch, side fit, fillet root spline. AClass 5 tolerance is desired on both the internal and external splines. (Differenttolerance classes can be used on each spline if desired.) The spline length is 1.5inches, which we enter in order to obtain analytical checking data for the toothalignment. We also wish to use the “Standard” gaging method and will print all dataneeded to manufacture the gages including tapered external masters to calibrate thering gages for the external spline.Enter the data as shown in Figure 1-1. Click “Yes” when prompted for spline lengthvalues and for plot tic marks. Report 1 gives the input and output values for thesolved model.Fig. 1-12
60-710—Involute Splines and InspectionReport 1Model Title :Program 60-710Unit System:USCOMMONNumber of Teeth26Diametral Pitch10.000000 1/in Stub Pitch20.0000 1/in Spline Pitch10/20Standard Pressure Angle30.0000 degType of Fit ('maj or 'side Def 'side)sidePitch Diameter2.6000000 inBase Dia2.2516660 inMax Effective Clearance0.0028 inMin Effective Clearance0.0000 inCOMMON: Theoretical from Measured TeethMax Actual Clearance0.0064 inMin Actual Clearance0.0036 inRadial Form Clearance (Standard)0.0026 inINTERNAL SPLINEInternal Spline ANSI B92.1-1970 Std?YesFillet or Flat Root ('fil/'flt)filMajor Diameter - Min, roundedNA inMajor Diameter - Max, rounded2.8010 inForm Diameter, rounded2.7050 in3
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USRoll Angle at Form Diameter38.144 degMinor Diameter - Min, rounded2.5000 inMinor Diameter - Max, rounded2.5050 inTolerance Class5Machining Tolerance0.0014 inVariation Allowance0.0018 inMin Effective Space Width0.1571 inSpecification Required or ReferenceRequiredPlug Gage - Composite or SectorGO CmpMax Effective Space Width0.1585 inSpecification Required or ReferenceReferencePlug Gage - Composite or SectorNoneMin Actual Space Width0.1589 inSpecification Required or ReferenceReferencePlug Gage - Composite or SectorNoneMax Actual Space Width0.1603 inSpecification Required or ReferenceRequiredPlug Gage - Composite or SectorNO GO SecINTERNAL SPLINE: Size Between PinsPin Diameter0.14400 inMin Between 2 Pins2.4431 inMax Between 2 Pins2.4456 inMin Diameter Under 3 Pins2.4431 inMax Diameter Under 3 Pins2.4456 inMin Pin Contact Diameter2.6610 in4
60-710—Involute Splines and InspectionModel Title :Program 60-710Unit System:USMax Pin Contact Diameter2.6637 inINTERNAL SPLINE: Analytical InspectionTotal Index Variation0.0018 inProfile Variation0.0004 inProNI-0.0006 inSpline Length1.50 inLead Variation0.0005 inEXTERNAL SPLINEExternal Spline ANSI B92.1-1970 Std?YesFillet or Flat Root ('fil/'flt)filMajor Diameter - Max2.7000 inMajor Diameter - Min2.6950 inMajor Diameter Chamfer - MaxinMajor Diameter Chamfer - MininForm Diameter2.4950 inRoll Angle at Form Diameter27.347 degMinor Diameter - Min2.3990 inTolerance Class5Machining Tolerance0.0014 inVariation Allowance0.0018 inMax Eff Tooth Thickness0.1571 inSpecification Required or ReferenceRequiredRing Gage - Composite or SectorGO CmpMin Eff Tooth Thickness0.1557 inSpecification Required or ReferenceReference5
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USRing Gage - Composite or SectorNoneMax Actual Tooth Thickness0.1553 inSpecification Required or ReferenceReferenceRing Gage - Composite or SectorNoneMin Actual Tooth Thickness0.1539 inSpecification Required or ReferenceRequiredRing Gage - Composite or SectorNO GO SecEXTERNAL SPLINE: Size Over PinsPin Diameter0.19200 inMax Over 2 Pins2.8951 inMin Over 2 Pins2.8930 inMax Pin Contact Diameter2.6018 inMin Pin Contact Diameter2.5998 inEXTERNAL SPLINE: Analytical InspectionTotal Index Variation0.0018 inProfile Variation0.0004 inProNX-0.0006 inSpline Length1.50 inLead Variation0.0005 inPLOTS DATAMark mod/inv/fil intersections?yNumber of teeth on plot16
60-710—Involute Splines and InspectionModel Title :Program 60-710Unit System:USGAGESDimensioning Method (Def 'std, 'A, 'B)stdINTERNAL SPLINE GAGES: GO Composite Plug Gage: Front SectionMajor Diameter2.7055 inODxfGOi2.7050 inINTERNAL SPLINE GAGES: GO Composite Plug Gage: Rear SectionMajor Diameter - NewinODxrGOiinMajor Diameter - Wear LimitinINTERNAL SPLINE GAGES: GO Composite Plug Gage: ChamferDiameter to Chamfer, maxinChamfer Cutting Angle fr CL SpacedegForm Diameter2.4948 inMinor Diameter, Max2.4948 inTooth Thickness, New (REF)0.1574 inTooth Thickness, Wear Limit (REF)0.1571 inPin Diameter0.1920 inMax Size Over Pins - New2.89858 inMin Size Over Pins - New2.89843 inSize Over Pins - Wear Limit2.89796 inINTERNAL SPLINE GAGES: NOT GO Sector Plug GageMajor Diameter2.6710 inODxSi2.6690 in7
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USForm Diameter2.4948 inMinor Diameter, Max2.4948 inTooth Thickness, New (REF)0.1603 inPin Diameter0.1920 inMax Size Over Pins - New2.90295 inMin Size Over Pins - New2.90279 inNumber of Teeth in Sector2EXTERNAL SPLINE GAGES: GO Composite Ring GageBushing Bore, MaxinBushing Bore, MininMinor Diameter, Max2.4950 inMinor Diameter, Min2.4945 inForm Diameter2.7052 inMajor Diameter, Min2.7056 inSpace Width, New (REF)0.1568 inSpace Width, Wear Limit (REF)0.1571 inPin Diameter0.1728 inMin Size Between Pins - New2.34928 inMax Size Between Pins - New2.34947 inSize Between Pins - Wear Limit2.35004 inEXTERNAL SPLINE GAGES: NOT GO Sector Ring GageMinor Diameter, Max2.5310 inMinor Diameter, Min2.5290 inForm Diameter2.7000 inMajor Diameter, Min2.7000 in8
60-710—Involute Splines and InspectionModel Title :Program 60-710Unit System:USSpace Width0.1539 inPin Diameter0.1728 inMin Size Between Pins2.34387 inMax Size Between Pins2.34406 inNumber of Teeth in Sector2EXTERNAL SPLINE GAGES: GO Composite Ring Gage: Tapered External MasterMajor Diameter2.6950 inODGORMi2.6945 inForm Diameter2.4850 inMinor Diameter, Max2.4850 inEXTERNAL SPLINE GAGES: GO Composite Ring Gage: Tooth ThicknessEnd of Lead Length, XX0.1567 inEnd of Fit Range, YY0.1568 inEnd of Wear Range, ZZ0.1571 inPin Diameter0.1920 inSize Over Pins at XX2.89733 inSize Over Pins at YY2.89749 inSize Over Pins at ZZ2.89796 inEXTERNAL SPLINE GAGES: NOT GO Composite Ring Gage: Tooth ThicknessEnd of Lead Length, XXinEnd of Fit Range, YYinPin DiameterinSize Over Pins at XXinSize Over Pins at YYin9
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USEXTERNAL SPLINE GAGES: NOT GO Sector Ring Gage: Tapered External MasterMajor Diameter2.6950 inODSERMi2.6945 inForm Diameter2.5200 inMinor Diameter, Max2.4990 inEXTERNAL SPLINE GAGES: NOT GO Sector Ring Gage: Tooth ThicknessEnd of Lead Length, XX0.1539 inEnd of Fit Range, YY0.1540 inPin Diameter0.1920 inSize Over Pins at XX2.89295 inSize Over Pins at YY2.89311 inA plot of the teeth in assembly is available on the Plot Sheet or on the drop-downplots list in the Toolbar of the TK Solver model. (See Figure 1-2.) Individual plots ofthe internal and external splines are also available in the TK Solver model.10
60-710—Involute Splines and InspectionFig. 1-211
UTS Integrated Gear SoftwareExample 2This is a 12 tooth, 5/10 diametral pitch, major diameter fit spline. A Class 5tolerance is desired on both the internal and external splines. The spline length is 2”which we will enter in order to obtain analytical checking data for tooth alignment.We also wish to use the “A” gaging method and will print all data needed tomanufacture the gages, including tapered external masters to calibrate the ringgages for the external spline.Enter the data in the data input form as shown in Figure 2-1. The inputs andoutputs for the solved model are shown in Report 2.Fig. 2-112
60-710—Involute Splines and InspectionReport 2Model Title :Program 60-710Unit System:USCOMMONNumber of Teeth12Diametral Pitch5.000000 1/in Stub Pitch10.0000 1/in Spline Pitch5/10Standard Pressure Angle30.0000 degType of Fit ('maj or 'side Def 'side)majPitch Diameter2.4000000 inBase Dia2.0784610 inMax Effective Clearance0.0048 inMin Effective Clearance0.0018 inCOMMON: Theoretical from Measured TeethMax Actual Clearance0.0090 inMin Actual Clearance0.0060 inRadial Form Clearance (Standard)0.0024 inINTERNAL SPLINEInternal Spline ANSI B92.1-1970 Std?YesFillet or Flat Root ('fil/'flt)fltMajor Diameter - Min, rounded2.6000 inMajor Diameter - Max, rounded2.6017 in13
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USForm Diameter, rounded2.5610 inRoll Angle at Form Diameter41.246 degMinor Diameter - Min, rounded2.2120 inMinor Diameter - Max, rounded2.2200 inTolerance Class5Machining Tolerance0.0015 inVariation Allowance0.0021 inMin Effective Space Width0.3142 inSpecification Required or ReferenceRequiredPlug Gage - Composite or SectorGO CmpMax Effective Space Width0.3157 inSpecification Required or ReferenceRequiredPlug Gage - Composite or SectorNO GO CmpMin Actual Space Width0.3163 inSpecification Required or ReferenceReferencePlug Gage - Composite or SectorNoneMax Actual Space Width0.3178 inSpecification Required or ReferenceRequiredPlug Gage - Composite or SectorNO GO SecINTERNAL SPLINE: Size Between PinsPin Diameter0.28800 inMin Between 2 Pins2.0833 inMax Between 2 Pins2.0860 inMin Diameter Under 3 Pins2.0833 inMax Diameter Under 3 Pins2.0860 in14
60-710—Involute Splines and InspectionModel Title :Program 60-710Unit System:USMin Pin Contact Diameter2.5226 inMax Pin Contact Diameter2.5258 inINTERNAL SPLINE: Analytical InspectionTotal Index Variation0.0018 inProfile Variation0.0006 inProNI-0.0008 inSpline Length2.00 inLead Variation0.0005 inEXTERNAL SPLINEExternal Spline ANSI B92.1-1970 Std?YesFillet or Flat Root ('fil/'flt)fltMajor Diameter - Max2.5999 inMajor Diameter - Min2.5991 inMajor Diameter Chamfer - Max0.0340 inMajor Diameter Chamfer - Min0.0220 inForm Diameter2.2070 inRoll Angle at Form Diameter20.460 degMinor Diameter - Min2.1140 inTolerance Class5Machining Tolerance0.0015 inVariation Allowance0.0021 inMax Eff Tooth Thickness0.3124 inSpecification Required or ReferenceRequiredRing Gage - Composite or SectorGO CmpMin Eff Tooth Thickness0.3109 in15
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USSpecification Required or ReferenceRequiredRing Gage - Composite or SectorNO GO CmpMax Actual Tooth Thickness0.3103 inSpecification Required or ReferenceReferenceRing Gage - Composite or SectorNoneMin Actual Tooth Thickness0.3088 inSpecification Required or ReferenceRequiredRing Gage - Composite or SectorNO GO SecEXTERNAL SPLINE: Size Over PinsPin Diameter0.38400 inMax Over 2 Pins2.9803 inMin Over 2 Pins2.9782 inMax Pin Contact Diameter2.3861 inMin Pin Contact Diameter2.3843 inEXTERNAL SPLINE: Analytical InspectionTotal Index Variation0.0018 inProfile Variation0.0006 inProNX-0.0008 inSpline Length2.00 inLead Variation0.0005 inPLOTS DATAMark mod/inv/fil intersections?yNumber of teeth on plot116
60-710—Involute Splines and InspectionModel Title :Program 60-710Unit System:USGAGESDimensioning Method (Def 'std, 'A, 'B)AINTERNAL SPLINE GAGES: GO Composite Plug Gage: Front SectionMajor Diameter2.5612 inODxfGOi2.5610 inINTERNAL SPLINE GAGES: GO Composite Plug Gage: Rear SectionMajor Diameter - New2.6004 inODxrGOi2.6002 inMajor Diameter - Wear Limit2.6000 inINTERNAL SPLINE GAGES: GO Composite Plug Gage: ChamferDiameter to Chamfer, max2.5610 inChamfer Cutting Angle fr CL Space76.9 degForm Diameter2.2072 inMinor Diameter, Max2.2072 inTooth Thickness, New (REF)0.3145 inTooth Thickness, Wear Limit (REF)0.3142 inPin Diameter0.3840 inMax Size Over Pins - New2.98653 inMin Size Over Pins - New2.98638 inSize Over Pins - Wear Limit2.98595 inINTERNAL SPLINE GAGES: NOT GO Composite Plug GageMajor Diameter2.5083 inODxNGi2.5063 in17
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USForm Diameter2.2072 inMinor Diameter, Max2.2072 inTooth Thickness, New (REF)0.3157 inPin Diameter0.3840 inMax Size Over Pins - New2.98811 inMin Size Over Pins - New2.98797 inINTERNAL SPLINE GAGES: NOT GO Sector Plug GageMajor Diameter2.5083 inODxSi2.5063 inForm Diameter2.2072 inMinor Diameter, Max2.2072 inTooth Thickness, New (REF)0.3178 inPin Diameter0.3840 inMax Size Over Pins - New2.99113 inMin Size Over Pins - New2.99098 inNumber of Teeth in Sector2INTERNAL SPLINE GAGES: GO Major Dia Fit Plug GageMajor Diameter2.6004 inODxGOPi2.6002 inMajor Diameter - Wear Limit2.6000 inMinor Diameter, Max2.1363 inTooth Thickness0.2687 intGOPi0.2657 inPin Diameter0.3840 inMax Size Over Pins2.9189 in18
60-710—Involute Splines and InspectionModel Title :Program 60-710Unit System:USMin Size Over Pins2.9143 inINTERNAL SPLINE GAGES: NOT GO Major Dia Fit Plug GageMajor Diameter2.6017 inODxNGPi2.6015 inMinor Diameter, Max2.1380 inTooth Thickness0.2698 intNGPi0.2668 inPin Diameter0.3840 inMax Size Over Pins2.9205 inMin Size Over Pins2.9160 inEXTERNAL SPLINE GAGES: GO Composite Ring GageBushing Bore, Max2.5997 inBushing Bore, Min2.5996 inMinor Diameter, Max2.2070 inMinor Diameter, Min2.2065 inForm Diameter2.6047 inMajor Diameter, Min2.6047 inSpace Width, New (REF)0.3121 inSpace Width, Wear Limit (REF)0.3124 inPin Diameter0.3456 inMin Size Between Pins - New1.88148 inMax Size Between Pins - New1.88172 inSize Between Pins - Wear Limit1.88244 in19
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USEXTERNAL SPLINE GAGES: NOT GO Sector Ring GageMinor Diameter, Max2.2723 inMinor Diameter, Min2.2703 inForm Diameter2.5999 inMajor Diameter, Min2.5999 inSpace Width0.3088 inPin Diameter0.3456 inMin Size Between Pins1.87367 inMax Size Between Pins1.87392 inNumber of Teeth in Sector2EXTERNAL SPLINE GAGES: GO Composite Ring Gage: Tapered External MasterMajor Diameter2.5311 inODGORMi2.5309 inForm Diameter2.1970 inMinor Diameter, Max2.1970 inEXTERNAL SPLINE GAGES: GO Composite Ring Gage: Tooth ThicknessEnd of Lead Length, XX0.3120 inEnd of Fit Range, YY0.3121 inEnd of Wear Range, ZZ0.3124 inPin Diameter0.3840 inSize Over Pins at XX2.98278 inSize Over Pins at YY2.98293 inSize Over Pins at ZZ2.98336 in20
60-710—Involute Splines and InspectionModel Title :Program 60-710Unit System:USEXTERNAL SPLINE GAGES: NOT GO Composite Ring GageMinor Diameter, Max2.2723 inMinor Diameter, Min2.2703 inForm Diameter2.6047 inMajor Diameter, Min2.6047 inSpace Width0.3109 inPin Diameter0.3456 inMin Size Between Pins1.87882 inMax Size Between Pins1.87906 inEXTERNAL SPLINE GAGES: NOT GO Composite Ring Gage: Tapered ExternalMasterMajor Diameter2.5311 inODNGRMi2.5309 inForm Diameter2.2613 inMinor Diameter, Max2.2032 inEXTERNAL SPLINE GAGES: NOT GO Composite Ring Gage: Tooth ThicknessEnd of Lead Length, XX0.3109 inEnd of Fit Range, YY0.3110 inPin Diameter0.3840 inSize Over Pins at XX2.98119 inSize Over Pins at YY2.98134 inEXTERNAL SPLINE GAGES: NOT GO Sector Ring Gage: Tapered External MasterMajor Diameter2.5311 inODSERMi2.5309 inForm Diameter2.2613 in21
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USMinor Diameter, Max2.2002 inEXTERNAL SPLINE GAGES: NOT GO Sector Ring Gage: Tooth ThicknessEnd of Lead Length, XX0.3088 inEnd of Fit Range, YY0.3089 inPin Diameter0.3840 inSize Over Pins at XX2.97816 inSize Over Pins at YY2.97830 inA plot of the teeth in assembly is available on the Plot Sheet of the TK Solver model.(See Figure 2-2) Note the chamfer required at the tips of the external spline teeth toclear the radii in the corners of the internal spline teeth. Individual plots of theinternal and external splines are also available.22
60-710—Involute Splines and InspectionFig. 2-223
UTS Integrated Gear SoftwareExample 3This is a 6 tooth, 20/40 diametral pitch, 45 degree pressure angle, side fit, fillet rootspline. A Class 7 tolerance will be allowed on both splines. The spline length is .25inch, which we enter in order to obtain analytical checking data for tooth alignment.We use the “B” gaging method and will print all data needed to manufacture thegages, including tapered external masters to calibrate the ring gages for the externalspline.Enter the data shown in the data input form, Figure 3-1, as described in previousexamples. Note that this time we will plot 6 teeth. The inputs and outputs for thesolved model are shown in Report 3.Fig. 3-124
60-710—Involute Splines and InspectionReport 3Model Title :Program 60-710Unit System:USCOMMONNumber of Teeth6Diametral Pitch20.000000 1/in Stub Pitch40.0000 1/in Spline Pitch20/40Standard Pressure Angle45.0000 degType of Fit ('maj or 'side Def 'side)sidePitch Diameter0.3000000 inBase Dia0.2121320 inMax Effective Clearance0.0046 inMin Effective Clearance0.0000 inCOMMON: Theoretical from Measured TeethMax Actual Clearance0.0100 inMin Actual Clearance0.0054 inRadial Form Clearance (Standard)0.0020 inINTERNAL SPLINEInternal Spline ANSI B92.1-1970 Std?YesFillet or Flat Root ('fil/'flt)filMajor Diameter - Min, roundedNA inMajor Diameter - Max, rounded0.3800 in25
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USForm Diameter, rounded0.3540 inRoll Angle at Form Diameter76.545 degMinor Diameter - Min, rounded0.2700 inMinor Diameter - Max, rounded0.2750 inTolerance Class7Machining Tolerance0.0023 inVariation Allowance0.0027 inMin Effective Space Width0.0885 inSpecification Required or ReferenceRequiredPlug Gage - Composite or SectorGO CmpMax Effective Space Width0.0908 inSpecification Required or ReferenceRequiredPlug Gage - Composite or SectorNO GO CmpMin Actual Space Width0.0912 inSpecification Required or ReferenceReferencePlug Gage - Composite or SectorNoneMax Actual Space Width0.0935 inSpecification Required or ReferenceReferencePlug Gage - Composite or SectorNoneINTERNAL SPLINE: Size Between PinsPin Diameter0.09600 inMin Between 2 Pins0.1540 inMax Between 2 Pins0.1570 inMin Diameter Under 3 Pins0.1540 inMax Diameter Under 3 Pins0.1570 in26
60-710—Involute Splines and InspectionModel Title :Program 60-710Unit System:USMin Pin Contact Diameter0.3117 inMax Pin Contact Diameter0.3158 inINTERNAL SPLINE: Analytical InspectionTotal Index Variation 10 Teeth inProfile Variation0.0006 inProNI-0.0010 inSpline Length0.25 inLead Variation0.0004 inEXTERNAL SPLINEExternal Spline ANSI B92.1-1970 Std?YesFillet or Flat Root ('fil/'flt)filMajor Diameter - Max0.3500 inMajor Diameter - Min0.3450 inMajor Diameter Chamfer - MaxinMajor Diameter Chamfer - MininForm Diameter0.2660 inRoll Angle at Form Diameter43.347 degMinor Diameter - Min0.2400 inTolerance Class7Machining Tolerance0.0023 inVariation Allowance0.0027 inMax Eff Tooth Thickness0.0885 inSpecification Required or ReferenceRequiredRing Gage - Composite or SectorGO CmpMin Eff Tooth Thickness0.0862 in27
UTS Integrated Gear SoftwareModel Title :Program 60-710Unit System:USSpecification Required or ReferenceRequiredRing Gage - Composite
60-710—Involute Splines and Inspection 3 Report 1 Model Title : Program 60-710 Unit System: US COMMON Number of Teeth 26 Diametral Pitch 10.000000 1/in Stub Pitch 20.0000 1/in Spline Pitch 10/20 Standard Pressure Angle 30.0000 deg Type of Fit ('maj or 'side Def 'side) side Pitch Diameter 2.6000000 in Base Dia 2.2516660 in Max_Effective Clearance 0.0028 in
with mating keys machined onto a shaft. There are two major types of splines used in industry: 1) straight-sided splines, and 2) involute splines. Splines provide a more uniform ci
Cable Pack Sony Cable Pack P/Oly Cable Fuji. CAPTUR Compatibility Part No. 1000 710.0 1000 710.1 1000 710.4 1000 710.3 1000 710.2 1000 708.1 1000 708.3 1000 710.5 1000 710.6 1000 710.7 1000 711.0 1000 710.8 Range Up to 100m Up to 100m Up to 100m Up to 100m Up to 100m Up to 100m Up to 100m Up to 100m
A study of trigonometric splines has been made by a number of authors, [1,4,5,7,10]. It was found that problems of scattered data interpolation over spherical surfaces can be better handled in terms of accuracy, computational convenience and smoothness of the resulting surface using trigonometric splines. Trigonometric splines
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Keywords: Frenet frames; Involute-evolute curves; Hyperbolic space; De Sitter space. Mathematics Subject Classification (2010). 53A25, 53C50. Introduction The idea of a string involute is due to, who is also known for his . geometry for Frenet frame in hyperbolic 2-space, hyperbolic 3-space and de Sitter 3-space [3-8].
Herringbone gear pair is composed of two matched herringbone gears. It can be classified into two types: external herringbone gear pair and internal herringbone gear pair. Involute herringbone gear pair of external gearing with parallel axes It consists of two matched involute herringbone gears of external gearing.
ANSI Y14.5-73 ANSI Y14.5M-82 ANS Y14. 6-78 ANSI Y14. 6AM Surface Texture (Surface roughness, and lay) Involute Splines and Inspection Knurling of the cited waviness, Flowchart Symbols and their Usage in Information Processing. S
Albert woodfox Arthur Kinoy Award A Message from NYU PILC At every NLG #Law4thePeople Convention, we honor members and friends of the Guild whose exemplary work and activism capture the spirit of “law for the people,” and speak to the Guild’s philosophy of human rights over property interests. Please join us in congratulating our 2016 honorees! Workshops Tentative Schedule Felon .
