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
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Appendix
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Appendix
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Appendix