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.
Methods of CouplingMethods of Coupling
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
Methods of CouplingMethods of Coupling
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
Desire Outputs•Desired Location
Improvement
Actual Outputs•Actual Location
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
Kinematic Coupling Design ProcessKinematic Coupling Design ProcessDisplacementDisturbance
ForceDisturbance
Inputs•Displacement
•Force
Desire Outputs•Desired Location
Improvement
Actual Outputs•Actual Location
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
Kinematic Coupling Design ProcessKinematic Coupling Design ProcessDisplacementDisturbance
ForceDisturbance
Inputs•Displacement
•Force
Desire Outputs•Desired Location
Improvement
Actual Outputs•Actual Location
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
Kinematic Coupling Design ProcessKinematic Coupling Design ProcessDisplacementDisturbance
ForceDisturbance
Inputs•Displacement
•Force
Desire Outputs•Desired Location
Improvement
Actual Outputs•Actual Location
Actual OutputActual OutputAlignment error with
galaxy NGC383 must be less than
2 micron!!!!
Made byLockheed Martin SSC
Ooo…..Challenging…
.NOT!!!!
Critical Design IssuesCritical Design Issues
Material SelectionMaterial Selection
Geometry SpecificationGeometry Specification
Critical Design IssuesCritical Design Issues
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
Critical Design IssuesCritical Design Issues
Material SelectionMaterial SelectionSteel vs. Silicon CarbideSteel vs. Silicon Carbide
From “Kinematic Couplings for Precision Fixturing-Part 1:Formulation of design parameters”, Slocum, Alexander
Critical Design IssuesCritical Design Issues
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
Types of CKC’sTypes of CKC’s
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)
Types of CKC’sTypes of CKC’s
V-Groove Beam FlexuresV-Groove Beam Flexures
(Culpepper, Slocum)
Types of CKC’sTypes of CKC’s
Axial Spring Ball PlungerAxial Spring Ball Plunger• Balls mating with V-grooves through
spring force locate and clock coupling. This has the following advantages:
• Location and clocking geometry same as kinematic 3 ball & V groove (6 contact points)
• 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)
Types of CKC’sTypes of CKC’s
Axial Spring Ball PlungerAxial Spring Ball Plunger
Cheaper version, with less accuracy…?
High accuracy, at reasonable cost?(Culpepper, Slocum)
Types of CKC’sTypes of CKC’s
Actively Controlled CKC’sActively Controlled CKC’s• Balls mate in V-grooves whose
spacing can be actively controlled. This has the following advantages:
• Location and clocking geometry same as kinematic 3 ball & V groove (6 contact points)
• 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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