Kinematic Couplings Gus Hansen Phil Wayman Sunny Ng

Agenda Coupling Definition Methods of Coupling Kinematic Coupling Design Critical Design Issues Compliant Kinematic Couplings Conclusion

What is a “Coupling” For the purposes of this discussion, a “coupling” is a device with the following characteristics: A coupling connects two parts or assemblies A coupling connects two parts or assemblies It can be separated and rejoined at will It can be separated and rejoined at will The resulting connection will have some level of stiffness. The resulting connection will have some level of stiffness. The specific locating features of the connection will result in some level of accuracy and repeatability. The specific locating features of the connection will result in some level of accuracy and repeatability.

Methods of Coupling Pin/Hole Method Elastic Averaging Method Quasi-Kinematic Method Planar-Kinematic Method Kinematic Method

Pinned Joints Advantages A seal between the coupling components A seal between the coupling componentsDisadvantages Jamming & Wedging = high assembly/mfg cost Jamming & Wedging = high assembly/mfg cost “Slop” = component relative location not uniquely defined. “Slop” = component relative location not uniquely defined. Repeatability ↑ Tolerance↑ Repeatability ↑ Tolerance↑

Elastic Averaging Advantage: Capability of withstanding high loads Capability of withstanding high loads Large amount of contact area allow for a stiff joint design. Large amount of contact area allow for a stiff joint design. Better repeatability than pin joint Better repeatability than pin jointDisadvantage: Grossly over constrained Grossly over constrained Susceptible to surface finish & contaminants Susceptible to surface finish & contaminants Repeatability requires an extended period of “wear-in” Repeatability requires an extended period of “wear-in”

Quasi-Kinematic Coupling Advantage = Disadvantage Near kinematic Near kinematic Improve load capacity over K.C. Improve load capacity over K.C. Not as over constraint as Elastic Averaging Not as over constraint as Elastic Averaging Less sensitive in placements of their locating features = mfg. cost lower Less sensitive in placements of their locating features = mfg. cost lower

Planar Kinematic Coupling Extension to QKC Mixed nature of coupling Mixed nature of coupling Large contact surface with line or point to constraint degrees of freedom Large contact surface with line or point to constraint degrees of freedom High stiffness and load capacity High stiffness and load capacity Good repeatability Good repeatability

Kinematic Coupling Advantage Low cost Sub-micron repeatability Low cost Sub-micron repeatability Less sensitive to contamination Less sensitive to contaminationDisadvantages High stress concentration High stress concentration Does not allow for sealing joints Does not allow for sealing joints

Methods of Coupling Coupling Type Contact Type Repeatability Stiffness/Load Capacity Industrially Ideal Basic Pin Joint SurfacePoor (~5  m) HighFair Elastic Averaging SurfaceFair (~1  m) HighGood Planar Kinematic MixedGoodHighGood Quasi- Kinematic LineGood (~0.5  m) Medium to High Good KinematicPointExcellent (~0.01  m) Varies (Usually Low) Poor Found at

Kinematic Coupling History: (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: Economical Economical No wear in period No wear in period Contaminates Contaminates

Geometry Coupling System Others Material Kinematics Kinematic Coupling Design Process DisturbanceRequirements Inputs Displacement Force Desire Outputs Desired Location Improvement Actual Outputs Actual Location

Geometry Coupling System Others Material Kinematics Kinematic Coupling Design Process Displacement Disturbance Requirements Inputs Displacement Force Desire Outputs Desired Location Improvement Actual Outputs Actual Location

Requirements Identify the various parameter for the coupling system Accuracy Accuracy Repeatability Repeatability Interchangeability Interchangeability Understanding constrain & bounds of these parameter Place priority on requirements – helps identify critical path to a successful solution

Inputs Coupling Force DisplacementThermalDisturbances Vibration Vibration Temperature fluctuation Temperature fluctuation

Geometry Coupling System Others Material Kinematics Kinematic Coupling Design Process Displacement Disturbance Force Disturbance Inputs Displacement Force Desire Outputs Desired Location Improvement Actual Outputs Actual Location

Error/Source Analysis Kinematic/Geometry/Materials Example: Three-Groove K.C. Example: Three-Groove K.C. Balls diameters, groove radii Coordinate location of balls Contact force direction Preload force magnitude and direction External load magnitude and direction Young’s modulus & Poisson’s Ratio of materials

Error/Source Analysis Stress and deflection at contact pts. Force and momentum equilibrium Six error motion terms

Geometry Coupling System Others Material Kinematics Kinematic Coupling Design Process Displacement Disturbance Force Disturbance Inputs Displacement Force Desire Outputs Desired Location Improvement Actual Outputs Actual Location

Improvements → Desire Output Spreadsheet – instantaneous results Assembly techniques & calibration Refine procedures w/ minor alignment adjust Refine procedures w/ minor alignment adjust Symmetric torque pattern Symmetric torque pattern Apply stepped preload (25%–50%–75%–100%) Apply stepped preload (25%–50%–75%–100%) Lubricate the fasteners and the contact surfaces Solid Lubricant MoS 2, PTFE MoS 2, PTFE Polyamide, Polyethylene Polyamide, Polyethylene Graphite GraphiteSprayable Water Dilute-able Water Dilute-able Non-combustible Non-combustible Low in Solvents Low in Solvents

Geometry Coupling System Others Material Kinematics Kinematic Coupling Design Process Displacement Disturbance Force Disturbance Inputs Displacement Force Desire Outputs Desired Location Improvement Actual Outputs Actual Location

Actual Output Alignment error with galaxy NGC383 must be less than 2 micron!!!! Made by Lockheed Martin SSC Ooo….. Challenging…. NOT!!!!

Critical Design Issues Material Selection Geometry Specification

Critical Design Issues Material Selection Steel vs. Ceramics Cycle count considerations Fracture toughness considerations Repeatability considerations SteelSiliconNitride Repeatability Initial Worn In Ball & Groove 0.1  m 10  m GrooveBall 50 nm 0.1  m Ball & Groove < 0.1  m Adapted from “Design of three-groove kinematic couplings”, Slocum, Alexander

Critical Design Issues Material Selection Steel vs. Silicon Carbide From “Kinematic Couplings for Precision Fixturing-Part 1:Formulation of design parameters”, Slocum, Alexander

Critical Design Issues Geometry Specification Ball-Mounting Methods Ball-Mounting Methods Grind flat  Annular grooves Grind/machine a shaped seat Hemisphere Hemisphere Cone Cone Tetrahedron Tetrahedron Symmetry Symmetry Reduces manufacturing costs Simplifies design Allows coupling for rotary joints

Combining Kinematic & Elastic Compliant Kinematic Couplings (CKC’s) combine features of Elastic Averaging Couplings and Pure Kinematic Couplings The merger of concepts combines strengths from both, with some compromises

Types of CKC’s Flexural 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 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/(K D C E )] 1/2 Where C E = (1- 2 )/E 1 – (1- 2 )/E 2 D 2 = ball diameter K D = D 2 for D 1 = = cross section of cone p = load per unit length of contact = P N /L. Hale (1999) has posed this as a possible method, without above stress formula D2D2 Line of contact (L) P PNPN Needs further validation, but contact area is larger than ball in V or on Flat D1=D1= Conical Seat

Types of CKC’s V-Groove Beam Flexures (“Kineflex” TM ) 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’s V-Groove Beam Flexures (Culpepper, Slocum)

Types of CKC’s Axial 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’s Axial Spring Ball Plunger Cheaper version, with less accuracy…? High accuracy, at reasonable cost? (Culpepper, Slocum)

Types of CKC’s Actively 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 Comparison CKC repeatability falls between pinned joints and elastic averaging. Different sources show CKC repeatabilities between 5 and.25  m (Culpepper, Slocum)

CKC Summary CKC’s are a compromise between elastic averaged and kinematic connections Load capability Load capability Similar to elastic averaging Moderate accuracy and repeatability Moderate accuracy and repeatability Accuracy similar to pinned elastic averaged connections Lower cost of kinematic connections CKC’s features are useful for applications requiring moderate repeatability of elastic averaged connections, at lower cost

Conclusions Pinned & Elastic Averaging methods can result in couplings with high load capacity, but limited repeatability and accuracy, and higher cost. Kinematic coupling methods can result in couplings with extremely high accuracy, but with limited load capability, at potentially lower cost. Quasi-kinematic and Compliant Kinematic methods can result in couplings with cost, load capability and accuracy between the extremes of elastic averaging and kinematic methods.

Bibliography A. C. Weber, Precision Passive Alignment of Wafers, Master’s Thesis, Massachusetts Institute of Technology, February passive alignment of wafers.pdf passive alignment of wafers.pdf passive alignment of wafers.pdf M. L. Culpepper, Design and Application of Compliant Quasi-Kinematic Couplings, Master’s Thesis, Massachusetts Institute of Technology, February atic_couplings.pdf atic_couplings.pdf atic_couplings.pdf M. L. Culpepper, A. H. Slocum, Kinematic Couplings for Precision Fixturing and Assembly, Lecture notes. _precision _precision _precision M. L. Culpepper, K. M. Varadaranjan, Active Compliant Fixtures for Nanomanufacturing, December _Nanomanufacturing.pdf _Nanomanufacturing.pdf _Nanomanufacturing.pdf L. C. Hale, Principles and Techniques for Designing Precision Machines, Ph. D. Thesis, Massachusetts Institute of Technology, February M. L. Culpepper, Design of Quasi-kinematic Couplings, Precision Engineering, December Carr-Lane Manufacturing Company on-line catalog, B041D1E173C3B B041D1E173C3B B041D1E173C3B M. L. Culpepper, A. H. Slocum, F. Z. Shaikh, Compliant Quasi-Kinematic Couplings for Use in Manufacturing and Assembly W. C. Youg, Rourke’s Formulas for Stress and Strain, McGraw Hill Book Company, 1989.

Bibliography A.H.Slocum, Design of three-groove kinematic couplings, found in “Precision Engineering”, April 1992 Vol 14 No 2 gs/Design_of_Three-groove_kinematic_couplings.pdf gs/Design_of_Three-groove_kinematic_couplings.pdf A. H. Slocum, Kinematic Couplings for Precision Fixturing – Part 1: Formulation of design parameters, Massachusetts Institute of Technology, April L. C. Hale, A. H. Slocum, Optimal Design Techniques for kinematic Couplings, “Precision Engineering” gs/Optimal_design_techniques_for_kcs.pdf gs/Optimal_design_techniques_for_kcs.pdf

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