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Kinematic Couplings

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Title: 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/kinematiccouplin
gs/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
Kinematic Coupling Design Process
Disturbance
Requirements
  • Inputs
  • Displacement
  • Force
  • Desire Outputs
  • Desired Location
  • Actual Outputs
  • Actual Location

Improvement
13
Kinematic Coupling Design Process
Displacement Disturbance
Requirements
  • Inputs
  • Displacement
  • Force
  • 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
Displacement Disturbance
Force Disturbance
  • Inputs
  • Displacement
  • Force

Kinematics
Geometry
Material
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
  • Youngs modulus Poissons Ratio of materials

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

19
Kinematic Coupling Design Process
Displacement Disturbance
Force Disturbance
  • Inputs
  • Displacement
  • Force
  • 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 (255075100)
  • Lubricate the fasteners and the contact surfaces
  • Solid Lubricant
  • MoS2, PTFE
  • Polyamide, Polyethylene
  • Graphite
  • Sprayable
  • Water Dilute-able
  • Non-combustible
  • Low in Solvents

21
Kinematic Coupling Design Process
Displacement Disturbance
Force Disturbance
  • Inputs
  • Displacement
  • Force
  • 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 1Formulation 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 (CKCs) combine
    features of Elastic Averaging Couplings and Pure
    Kinematic Couplings
  • The merger of concepts combines strengths from
    both, with some compromises

28
Types of CKCs
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 contactload 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 0.798p/(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 CKCs
  • V-Groove Beam Flexures (KineflexTM)
  • 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
    groovesthis removes an over-constraint if
    spacing between the plates or clamping are
    desired attributes.

(Culpepper, Slocum)
31
Types of CKCs
  • V-Groove Beam Flexures

(Culpepper, Slocum)
32
Types of CKCs
  • 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
    groovesthis removes an over-constraint if
    spacing between the plates or clamping are
    desired attributes.

(Culpepper, Slocum)
33
Types of CKCs
  • Axial Spring Ball Plunger

(Culpepper, Slocum)
Cheaper version, with less accuracy?
High accuracy, at reasonable cost?
34
Types of CKCs
  • Actively Controlled CKCs
  • 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
  • CKCs 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

CKCs 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, Masters Thesis, Massachusetts Institute
    of Technology, February 2002. http//pergatory.mit
    .edu/kinematiccouplings/documents/Theses/weber_the
    sis/Precision passive alignment of wafers.pdf
  • M. L. Culpepper, Design and Application of
    Compliant Quasi-Kinematic Couplings, Masters
    Thesis, Massachusetts Institute of Technology,
    February 2000. http//pergatory.mit.edu/kinematicc
    ouplings/documents/Theses/culpepper_thesis/quasi_k
    inematic_couplings.pdf
  • M. L. Culpepper, A. H. Slocum, Kinematic
    Couplings for Precision Fixturing and Assembly,
    Lecture notes. http//pergatory.mit.edu/kinematic
    couplings/documents/Presentations/kinematic_coupli
    ngs_for_precision
  • M. L. Culpepper, K. M. Varadaranjan, Active
    Compliant Fixtures for Nanomanufacturing,
    December 2004. http//pergatory.mit.edu/kinematicc
    ouplings/documents/Papers/Active_Compliant_Fixture
    s_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/2
    35415.pdf
  • M. L. Culpepper, Design of Quasi-kinematic
    Couplings, Precision Engineering, December 2002.
    http//psdam.mit.edu/2_76/Reading/QKC20Theory.pdf
  • Carr-Lane Manufacturing Company on-line catalog,
    http//www.carrlane.com/Catalog/index.cfm/27025071
    F0B221118070C1C512D020609090C0015482013180B041D1E1
    73C3B2853524459
  • M. L. Culpepper, A. H. Slocum, F. Z. Shaikh,
    Compliant Quasi-Kinematic Couplings for Use in
    Manufacturing and Assembly
  • W. C. Youg, Rourkes 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/docum
    ents/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/k
    inematiccouplings/documents/
  • L. C. Hale, A. H. Slocum, Optimal Design
    Techniques for kinematic Couplings, Precision
    Engineering 2001
  • http//pergatory.mit.edu/kinematiccouplings/docum
    ents/Papers/three_ball_and_groove_couplings/Optima
    l_design_techniques_for_kcs.pdf

40
Appendix
41
Appendix
42
Appendix
43
Appendix
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