Kinematic Couplings

1. Kinematic Couplings Gus Hansen Phil Wayman Sunny Ng

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

3. 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 • It can be separated and rejoined at will • 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.

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

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

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

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

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

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

10. Methods of Coupling Found at http://pergatory.mit.edu/kinematiccouplings/html/design_process/define.html

11. Kinematic Coupling History:(from “Optimal Design Techniques for Kinematic Couplings”, L.C. Hale, A.H. Slocum) • James Clerk Maxwell (1876, 3-vee) • Lord Kelvin (“Kelvin Clamp”) • Professor Robert Willis (~1849) Other Advantages: • Economical • No wear in period • Contaminates

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

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

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

15. Inputs • Coupling Force • Displacement • Thermal • Disturbances • Vibration • Temperature fluctuation

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

17. Error/Source Analysis • Kinematic/Geometry/Materials • 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

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

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

20. Improvements → Desire Output • Spreadsheet – instantaneous results • Assembly techniques & calibration • Refine procedures w/ minor alignment adjust • Symmetric torque pattern • Apply stepped preload (25%–50%–75%–100%) • Lubricate the fasteners and the contact surfaces • Solid Lubricant • MoS2, PTFE • Polyamide, Polyethylene • Graphite • Sprayable • Water Dilute-able • Non-combustible • Low in Solvents

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

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

23. Critical Design Issues • Material Selection • Geometry Specification

24. Critical Design Issues Material Selection Steel vs. Ceramics • Cycle count considerations • Fracture toughness considerations • Repeatability considerations Adapted from “Design of three-groove kinematic couplings”, Slocum, Alexander

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

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

27. 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

28. Types of CKC’s Tangential Flexure, 3 Pl • 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. (Hale 1999)

29. Sphere in Cone Contact • Can we approximate the line contact of a sphere in a cone as contact between 2 parallel cylinders? D2 • If so, can we use the following contact stress from Rourke? • Max s = 0.798*[p/(KDCE)]1/2 • Where CE = (1-n2)/E1 – (1-n2)/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 PN P D1= Line of contact (L) Conical Seat Needs further validation, but contact area is larger than ball in V or on Flat

30. 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)

31. Types of CKC’s • V-Groove Beam Flexures (Culpepper, Slocum)

32. 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)

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

34. 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)

35. CKC Repeatability Comparison • Different sources show CKC repeatabilities between 5 and .25 mm (Culpepper, Slocum) CKC repeatability falls between pinned joints and elastic averaging.

36. CKC Summary • CKC’s are a compromise between elastic averaged and kinematic connections • Load capability • Similar to elastic averaging • 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

37. 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.

38. Bibliography • A. C. Weber, Precision Passive Alignment of Wafers, Master’s Thesis, Massachusetts Institute of Technology, February 2002. http://pergatory.mit.edu/kinematiccouplings/documents/Theses/weber_thesis/Precision passive alignment of wafers.pdf • M. L. Culpepper, Design and Application of Compliant Quasi-Kinematic Couplings, Master’s Thesis, Massachusetts Institute of Technology, February 2000. http://pergatory.mit.edu/kinematiccouplings/documents/Theses/culpepper_thesis/quasi_kinematic_couplings.pdf • M. L. Culpepper, A. H. Slocum, Kinematic Couplings for Precision Fixturing and Assembly, Lecture notes. http://pergatory.mit.edu/kinematiccouplings/documents/Presentations/kinematic_couplings_for_precision • M. L. Culpepper, K. M. Varadaranjan, Active Compliant Fixtures for Nanomanufacturing, December 2004. http://pergatory.mit.edu/kinematiccouplings/documents/Papers/Active_Compliant_Fixtures_for_Nanomanufacturing.pdf • L. C. Hale, Principles and Techniques for Designing Precision Machines, Ph. D. Thesis, Massachusetts Institute of Technology, February 1999. http://www.llnl.gov/tid/lof/documents/pdf/235415.pdf • M. L. Culpepper, Design of Quasi-kinematic Couplings, Precision Engineering, December 2002. http://psdam.mit.edu/2_76/Reading/QKC%20Theory.pdf • Carr-Lane Manufacturing Company on-line catalog, http://www.carrlane.com/Catalog/index.cfm/27025071F0B221118070C1C512D020609090C0015482013180B041D1E173C3B2853524459 • 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.

39. Bibliography • A.H.Slocum, Design of three-groove kinematic couplings, found in “Precision Engineering”, April 1992 Vol 14 No 2 http://pergatory.mit.edu/kinematiccouplings/documents/Papers/three_ball_and_groove_couplings/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 1988. http://pergatory.mit.edu/kinematiccouplings/documents/ • L. C. Hale, A. H. Slocum, Optimal Design Techniques for kinematic Couplings, “Precision Engineering” 2001 http://pergatory.mit.edu/kinematiccouplings/documents/Papers/three_ball_and_groove_couplings/Optimal_design_techniques_for_kcs.pdf

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