Kinematic Couplings Gus Hansen Phil Wayman Sunny Ng.

Kinematic CouplingsKinematic Couplings

Gus HansenGus Hansen

Phil WaymanPhil Wayman

Sunny NgSunny Ng

AgendaAgenda

Coupling DefinitionCoupling Definition

Methods of CouplingMethods of Coupling

Kinematic Coupling DesignKinematic Coupling Design

Critical Design IssuesCritical Design Issues

Compliant Kinematic CouplingsCompliant Kinematic Couplings

ConclusionConclusion

What is a “Coupling”What is a “Coupling”

For the purposes of this discussion, a For the purposes of this discussion, a “coupling” is a device with the following “coupling” is a device with the following characteristics:characteristics: A coupling connects two parts or assembliesA coupling connects two parts or assemblies It can be separated and rejoined at willIt can be separated and rejoined at will The resulting connection will have some level The resulting connection will have some level

of stiffness.of stiffness. The specific locating features of the The specific locating features of the

connection will result in some level of connection will result in some level of accuracy and repeatability.accuracy and repeatability.


Pin/Hole MethodPin/Hole Method

Elastic Averaging MethodElastic Averaging Method

Quasi-Kinematic MethodQuasi-Kinematic Method

Planar-Kinematic MethodPlanar-Kinematic Method

Kinematic MethodKinematic Method

Pinned JointsPinned Joints

AdvantagesAdvantages A seal between the coupling componentsA seal between the coupling components

DisadvantagesDisadvantages Jamming & Wedging = high assembly/mfg Jamming & Wedging = high assembly/mfg

costcost ““Slop” = component relative location not Slop” = component relative location not

uniquely defined.uniquely defined. Repeatability ↑ Tolerance↑Repeatability ↑ Tolerance↑

Elastic AveragingElastic AveragingAdvantage:Advantage:

Capability of withstanding high loadsCapability of withstanding high loads Large amount of contact area allow for a stiff joint Large amount of contact area allow for a stiff joint

design.design. Better repeatability than pin jointBetter repeatability than pin joint

Disadvantage:Disadvantage: Grossly over constrainedGrossly over constrained Susceptible to surface finish & contaminantsSusceptible to surface finish & contaminants Repeatability requires an extended period of “wear-in”Repeatability requires an extended period of “wear-in”

Quasi-Kinematic CouplingQuasi-Kinematic Coupling

Advantage = DisadvantageAdvantage = Disadvantage Near kinematicNear kinematic Improve load capacity over K.C.Improve load capacity over K.C. Not as over constraint as Elastic AveragingNot as over constraint as Elastic Averaging Less sensitive in placements of their locating Less sensitive in placements of their locating

features = mfg. cost lowerfeatures = mfg. cost lower

Planar Kinematic CouplingPlanar Kinematic Coupling

Extension to QKCExtension to QKC Mixed nature of couplingMixed nature of coupling

Large contact surface with line or point to constraint Large contact surface with line or point to constraint degrees of freedomdegrees of freedom

High stiffness and load capacityHigh stiffness and load capacity Good repeatabilityGood repeatability

Kinematic CouplingKinematic CouplingAdvantageAdvantage Low cost Sub-micron Low cost Sub-micron

repeatabilityrepeatability Less sensitive to contaminationLess sensitive to contamination

DisadvantagesDisadvantages High stress concentrationHigh stress concentration Does not allow for sealing jointsDoes not allow for sealing joints


Coupling Coupling TypeType

Contact Contact TypeType

RepeatabilityRepeatability Stiffness/Load Stiffness/Load CapacityCapacity

Industrially Industrially IdealIdeal

Basic Pin Basic Pin JointJoint

SurfaceSurface PoorPoor

(~5 (~5 m)m)

HighHigh FairFair

Elastic Elastic AveragingAveraging

SurfaceSurface FairFair

(~1 (~1 m)m)

HighHigh GoodGood

Planar Planar KinematicKinematic

MixedMixed GoodGood HighHigh GoodGood

Quasi-Quasi-KinematicKinematic

LineLine GoodGood

(~0.5 (~0.5 m)m)

Medium to HighMedium to High GoodGood

KinematicKinematic PointPoint ExcellentExcellent

(~0.01 (~0.01 m)m)

VariesVaries

(Usually Low)(Usually Low)

PoorPoor

Found at http://pergatory.mit.edu/kinematiccouplings/html/design_process/define.html

Kinematic CouplingKinematic Coupling

History:History: (from “Optimal Design Techniques for Kinematic Couplings”, L.C. Hale, A.H. Slocum)(from “Optimal Design Techniques for Kinematic Couplings”, L.C. Hale, A.H. Slocum)

James Clerk Maxwell (1876, 3-vee)James Clerk Maxwell (1876, 3-vee) Lord Kelvin (“Kelvin Clamp”)Lord Kelvin (“Kelvin Clamp”) Professor Robert Willis (~1849)Professor Robert Willis (~1849)

Other Advantages:Other Advantages: EconomicalEconomical No wear in periodNo wear in period ContaminatesContaminates

Geometry

CouplingSystem

Others

MaterialKinematics

Kinematic Coupling Design ProcessKinematic Coupling Design Process

DisturbanceRequirementsInputs

•Displacement•Force

Desire Outputs•Desired Location

Improvement

Actual Outputs•Actual Location

Geometry

CouplingSystem

Others

MaterialKinematics

Kinematic Coupling Design ProcessKinematic Coupling Design ProcessDisplacementDisturbance

RequirementsInputs

•Displacement•Force


Improvement


RequirementsRequirements

Identify the various parameter for the coupling Identify the various parameter for the coupling systemsystem AccuracyAccuracy RepeatabilityRepeatability InterchangeabilityInterchangeability

Understanding constrain & bounds of these Understanding constrain & bounds of these parameterparameter

Place priority on requirements – helps identify Place priority on requirements – helps identify critical path to a successful solutioncritical path to a successful solution

InputsInputs

Coupling ForceCoupling Force

DisplacementDisplacement

ThermalThermal

DisturbancesDisturbances VibrationVibration Temperature fluctuationTemperature fluctuation

Geometry

Coupling SystemOthers

MaterialKinematics


ForceDisturbance

Inputs•Displacement

•Force


Improvement


Error/Source AnalysisError/Source AnalysisKinematic/Geometry/MaterialsKinematic/Geometry/Materials Example: Three-Groove K.C.Example: Three-Groove K.C.

Balls diameters, groove radiiBalls diameters, groove radii

Coordinate location of ballsCoordinate location of balls

Contact force directionContact force direction

Preload force magnitude and directionPreload force magnitude and direction

External load magnitude and directionExternal load magnitude and direction

Young’s modulus & Poisson’s Ratio of materialsYoung’s modulus & Poisson’s Ratio of materials

Error/Source AnalysisError/Source AnalysisStress and deflection at contact pts. Stress and deflection at contact pts.

Force and momentum equilibriumForce and momentum equilibrium

Six error motion termsSix error motion terms

Geometry

CouplingSystem

Others

MaterialKinematics


ForceDisturbance


•Force


Improvement


Improvements → Desire OutputImprovements → Desire OutputSpreadsheet – instantaneous resultsSpreadsheet – instantaneous resultsAssembly techniques & calibrationAssembly techniques & calibration Refine procedures w/ minor alignment adjustRefine procedures w/ minor alignment adjust Symmetric torque patternSymmetric torque pattern Apply stepped preload (25%–50%–75%–100%)Apply stepped preload (25%–50%–75%–100%)

Lubricate the fasteners and the contact surfacesLubricate the fasteners and the contact surfaces

Solid LubricantSolid Lubricant MoSMoS22, PTFE, PTFE Polyamide, PolyethylenePolyamide, Polyethylene GraphiteGraphite

SprayableSprayable Water Dilute-ableWater Dilute-able Non-combustibleNon-combustible Low in SolventsLow in Solvents

Geometry

CouplingSystem

Others

MaterialKinematics


ForceDisturbance


•Force


Improvement


Actual OutputActual OutputAlignment error with

galaxy NGC383 must be less than

2 micron!!!!

Made byLockheed Martin SSC

Ooo…..Challenging…

.NOT!!!!


Material SelectionMaterial Selection

Geometry SpecificationGeometry Specification


Material SelectionMaterial SelectionSteel vs. CeramicsSteel vs. Ceramics

Cycle count considerationsCycle count considerations

Fracture toughness considerationsFracture toughness considerations

Repeatability considerationsRepeatability considerations

SteelSteel SiliconSiliconNitrideNitride

RepeatabilityRepeatability

InitialInitial Worn InWorn In

Ball & GrooveBall & Groove 0.1 0.1 mm 10 10 mm

GrooveGroove BallBall 50 nm50 nm 0.1 0.1 mm

Ball & GrooveBall & Groove < 0.1 < 0.1 mm < 0.1 < 0.1 mm

Adapted from “Design of three-groove kinematic couplings”, Slocum, Alexander


Material SelectionMaterial SelectionSteel vs. Silicon CarbideSteel vs. Silicon Carbide

From “Kinematic Couplings for Precision Fixturing-Part 1:Formulation of design parameters”, Slocum, Alexander


Geometry SpecificationGeometry Specification Ball-Mounting MethodsBall-Mounting Methods

Grind flat Grind flat Annular grooves Annular grooves

Grind/machine a shaped seatGrind/machine a shaped seat HemisphereHemisphere ConeCone TetrahedronTetrahedron

SymmetrySymmetryReduces manufacturing costsReduces manufacturing costs

Simplifies designSimplifies design

Allows coupling for rotary jointsAllows coupling for rotary joints

Combining Kinematic & ElasticCombining Kinematic & Elastic

Compliant Kinematic Couplings (CKC’s) Compliant Kinematic Couplings (CKC’s) combine features of Elastic Averaging combine features of Elastic Averaging Couplings and Pure Kinematic CouplingsCouplings and Pure Kinematic Couplings

The merger of concepts combines The merger of concepts combines strengths from both, with some strengths from both, with some compromisescompromises

Types of CKC’sTypes of CKC’s

Flexural Ball & ConeFlexural Ball & Cone• Tangential flexures allow spheres to

seat in three cones. This has the following advantages:

• Over-constrained condition which would occur if solid arms were used does not occur.

• Load between ball and cones is thru line contact, instead of point contact—load capability is increased.

• Load limit defined by lesser of flexure load limit and Hertzian contact at balls.

• Requirement for precision location of cones and balls is relaxed.

Tangential Flexure, 3 Pl

(Hale 1999)

Sphere in Cone ContactSphere in Cone Contact

Can we approximate the line contact of a sphere in a cone as contact between 2 parallel cylinders? If so, can we use the following contact

stress from Rourke? Max = 0.798*[p/(KDCE)]1/2

Where CE = (1-2)/E1 – (1-2)/E2

D2 = ball diameter

KD = D2 for D1 = = cross section of cone

p = load per unit length of contact = PN/L.

Hale (1999) has posed this as a possible method, without above stress formula

D2

Line of contact (L)

P PN

Needs further validation, but contact area is larger than ball in V or on FlatNeeds further validation, but contact area is larger than ball in V or on Flat

D1=

Conical Seat


V-Groove Beam Flexures (“Kineflex”V-Groove Beam Flexures (“Kineflex”TMTM))• Balls mating with V-grooves through

beam flexures locate and clock coupling. This has the following advantages:

• Location and clocking geometry same as kinematic 3 ball & V groove (6 contact points)

• Flexures allow plates to be adjusted, or clamped together after location is set.

• The distance between the two plates is no longer determined by the tolerances of the balls and V grooves—this removes an over-constraint if spacing between the plates or clamping are desired attributes.

(Culpepper, Slocum)


V-Groove Beam FlexuresV-Groove Beam Flexures

(Culpepper, Slocum)


Axial Spring Ball PlungerAxial Spring Ball Plunger• Balls mating with V-grooves through

spring force locate and clock coupling. This has the following advantages:


• Springs allow spacing between the coupling plates to be adjusted, or clamped together.

• The distance between the two plates is no longer determined by the tolerances of the balls and V grooves—this removes an over-constraint if spacing between the plates or clamping are desired attributes.

(Culpepper, Slocum)


Axial Spring Ball PlungerAxial Spring Ball Plunger

Cheaper version, with less accuracy…?

High accuracy, at reasonable cost?(Culpepper, Slocum)


Actively Controlled CKC’sActively Controlled CKC’s• Balls mate in V-grooves whose

spacing can be actively controlled. This has the following advantages:


• Translation and rotation (6 DOF) of the pallet can be adjusted by changing groove plate spacing.

• Electronic feedback can provide closed loop control of pallet location.

• Tested accuracy of 60 nm/2 micro-radians under closed loop control.

• $$$ ??? (Culpepper, Varadaranjan)

CKC Repeatability ComparisonCKC Repeatability Comparison

CKC repeatability falls between pinned joints and CKC repeatability falls between pinned joints and elastic averaging.elastic averaging.

Different sources show CKC Different sources show CKC repeatabilities between 5 and .25 repeatabilities between 5 and .25 mm

(Culpepper, Slocum)

CKC SummaryCKC Summary

CKC’s are a compromise between elastic CKC’s are a compromise between elastic averaged and kinematic connectionsaveraged and kinematic connections Load capabilityLoad capability

Similar to elastic averagingSimilar to elastic averaging Moderate accuracy and repeatabilityModerate accuracy and repeatability

Accuracy similar to pinned elastic averaged Accuracy similar to pinned elastic averaged connectionsconnections

Lower cost of kinematic connectionsLower cost of kinematic connections

CKC’s features are useful for applications requiring moderate CKC’s features are useful for applications requiring moderate repeatability of elastic averaged connections, at lower costrepeatability of elastic averaged connections, at lower cost

ConclusionsConclusions

Pinned & Elastic Averaging methods can result Pinned & Elastic Averaging methods can result in couplings with high load capacity, but limited in couplings with high load capacity, but limited repeatability and accuracy, and higher cost.repeatability and accuracy, and higher cost.

Kinematic coupling methods can result in Kinematic coupling methods can result in couplings with extremely high accuracy, but with couplings with extremely high accuracy, but with limited load capability, at potentially lower cost.limited load capability, at potentially lower cost.

Quasi-kinematic and Compliant Kinematic Quasi-kinematic and Compliant Kinematic methods can result in couplings with cost, load methods can result in couplings with cost, load capability and accuracy between the extremes of capability and accuracy between the extremes of elastic averaging and kinematic methods.elastic averaging and kinematic methods.

BibliographyBibliographyA. C. Weber, A. C. Weber, Precision Passive Alignment of WafersPrecision Passive Alignment of Wafers, Master’s Thesis, Massachusetts , Master’s Thesis, Massachusetts Institute of Technology, February 2002. Institute of Technology, February 2002. http://pergatory.mit.edu/kinematiccouplings/documents/Theses/weber_thesis/Precision passivhttp://pergatory.mit.edu/kinematiccouplings/documents/Theses/weber_thesis/Precision passive alignment of wafers.pdfe alignment of wafers.pdfM. L. Culpepper, M. L. Culpepper, Design and Application of Compliant Quasi-Kinematic Couplings, Design and Application of Compliant Quasi-Kinematic Couplings, Master’s Master’s Thesis, Massachusetts Institute of Technology, February 2000. Thesis, Massachusetts Institute of Technology, February 2000. http://pergatory.mit.edu/kinematiccouplings/documents/Theses/culpepper_thesis/quasi_kinemhttp://pergatory.mit.edu/kinematiccouplings/documents/Theses/culpepper_thesis/quasi_kinematic_couplings.pdfatic_couplings.pdfM. L. Culpepper, A. H. Slocum, M. L. Culpepper, A. H. Slocum, Kinematic Couplings for Precision Fixturing and AssemblyKinematic Couplings for Precision Fixturing and Assembly , , Lecture notes. Lecture notes. http://pergatory.mit.edu/kinematiccouplings/documents/Presentations/kinematic_couplings_forhttp://pergatory.mit.edu/kinematiccouplings/documents/Presentations/kinematic_couplings_for_precision_precisionM. L. Culpepper, K. M. Varadaranjan, M. L. Culpepper, K. M. Varadaranjan, Active Compliant Fixtures for NanomanufacturingActive Compliant Fixtures for Nanomanufacturing, , December 2004. December 2004. http://pergatory.mit.edu/kinematiccouplings/documents/Papers/Active_Compliant_Fixtures_forhttp://pergatory.mit.edu/kinematiccouplings/documents/Papers/Active_Compliant_Fixtures_for_Nanomanufacturing.pdf_Nanomanufacturing.pdfL. C. Hale, L. C. Hale, Principles and Techniques for Designing Precision MachinesPrinciples and Techniques for Designing Precision Machines , Ph. D. Thesis, , Ph. D. Thesis, Massachusetts Institute of Technology, February 1999. Massachusetts Institute of Technology, February 1999. http://www.llnl.gov/tid/lof/documents/pdf/235415.pdfhttp://www.llnl.gov/tid/lof/documents/pdf/235415.pdfM. L. Culpepper, M. L. Culpepper, Design of Quasi-kinematic CouplingsDesign of Quasi-kinematic Couplings, Precision Engineering, December , Precision Engineering, December 2002. http://psdam.mit.edu/2_76/Reading/QKC%20Theory.pdf2002. http://psdam.mit.edu/2_76/Reading/QKC%20Theory.pdfCarr-Lane Manufacturing Company on-line catalog, Carr-Lane Manufacturing Company on-line catalog, http://www.carrlane.com/Catalog/index.cfm/27025071F0B221118070C1C512D020609090C0http://www.carrlane.com/Catalog/index.cfm/27025071F0B221118070C1C512D020609090C0015482013180B041D1E173C3B2853524459015482013180B041D1E173C3B2853524459M. L. Culpepper, A. H. Slocum, F. Z. Shaikh, M. L. Culpepper, A. H. Slocum, F. Z. Shaikh, Compliant Quasi-Kinematic Couplings for Use in Compliant Quasi-Kinematic Couplings for Use in Manufacturing and AssemblyManufacturing and AssemblyW. C. Youg,W. C. Youg, Rourke’s Formulas for Stress and Strain, Rourke’s Formulas for Stress and Strain, McGraw Hill Book Company, 1989.McGraw Hill Book Company, 1989.

BibliographyBibliographyA.H.Slocum, A.H.Slocum, Design of three-groove kinematic couplings, Design of three-groove kinematic couplings, found in “Precision Engineering”, found in “Precision Engineering”, April 1992 Vol 14 No 2April 1992 Vol 14 No 2http://pergatory.mit.edu/kinematiccouplings/documents/Papers/http://pergatory.mit.edu/kinematiccouplings/documents/Papers/three_ball_and_groove_couplings/Design_of_Three-groove_kinematic_couplings.pdfthree_ball_and_groove_couplings/Design_of_Three-groove_kinematic_couplings.pdfA. H. Slocum, A. H. Slocum, Kinematic Couplings for Precision Fixturing – Part 1: Formulation of design Kinematic Couplings for Precision Fixturing – Part 1: Formulation of design parametersparameters, Massachusetts Institute of Technology, April 1988. , Massachusetts Institute of Technology, April 1988. http://pergatory.mit.edu/kinematiccouplings/documents/http://pergatory.mit.edu/kinematiccouplings/documents/L. C. Hale, A. H. Slocum, L. C. Hale, A. H. Slocum, Optimal Design Techniques for kinematic Couplings, “Optimal Design Techniques for kinematic Couplings, “Precision Precision Engineering” 2001Engineering” 2001http://pergatory.mit.edu/kinematiccouplings/documents/Papers/http://pergatory.mit.edu/kinematiccouplings/documents/Papers/three_ball_and_groove_couplings/Optimal_design_techniques_for_kcs.pdfthree_ball_and_groove_couplings/Optimal_design_techniques_for_kcs.pdf

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