05 flexures sullivan sp09

Precision Machine Design ME 250

Flexures

(Adapted from ME 324 course material , Dan DeBra, Stanford University)

Mark Sullivan February 12, 2009

Precision Machine Design Flexures

Sullivan Feb 12, 2009

Acknowledgements Text and figures in these lecture notes are taken from the

following sources: Slocum, A. H., FUNdaMENTALs of Design, MIT, 2008. Blanding, D., Exact Constraint: Machine Design Using Kinematic

Principles, ASME Press, New York, 1999. DeBra, D. ME 119 Lecture Notes on Flexures, Stanford University,

1987. Jones, R. V., Anti-distortion Mountings for Instruments and

Apparatus, J. of Sci. Instr., vol. 38, October 1961, pp. 408-409. Jones, R. V., Some Uses of Elasticity in Instrument Design, J. of

Sci. Instr., vol. 39, 1962, pp. 193-203. Hale, L. C., Principles and Techniques for Designing Precision

Machines, UCRL-LR-133066, Lawrence Livermore National Laboratory, 1999. (http://www.llnl.gov/tid/lof/documents/pdf/235415.pdf)

Smith, S. T., Flexures, Gordon and Breach Science Publishers, 2000.

Trease, B., Flexures Overview, ME 599 Lecture Notes, University of Michigan, 2004.



Introduction Flexures

Chart from FUNdaMENTALs of Design, Slocum



Flexure History

Chart from ASPE Flexure Course Notes, Culpepper



Flexures The Good Simple, inexpensive Smooth, continuous motion No friction No backlash No wear No noise No lubrication required Can be fabricated from single, monolithic material

Compatible with planar manufacturing Milling, EDM, water jet, chemical milling, photolithography (MEMS)

Fewer parts No assembly required Mechanical leverage easily implemented Failure mechanisms well understood (yield, fatigue)

Repeatable Sub-micron accuracy Increased life



Flexures The Bad & The Ugly Small range (short travel distance) Low load capacity Proper design often requires high stiffness in direction of

motion Simple flexures have parasitic motion in unwanted directions

Parasitic error Low stiffness for out-of-plane motions Force-displacement characteristics require good knowledge of:

Elastic modulus (E) Geometry / dimensions

Sensitive to (accidental) overload Plastic deformation (misalignment) Buckling



Engineering Knowledge Required Material Properties

Load-deflection characteristics Hookes Law

Geometry Load-deflection relationships for different shapes

Element deformation, e.g., beam bending

Constraints Understand how to constrain / guide motion

Constraints / kinematics Stiffness matrices Reciprocity

Text from ASPE Flexure Course Notes, Culpepper



Blade Flexure

Figure from Limitations of Flexures, McCarthy



Conceptual Basis for Flexure Design

Kinematic Design A rigid body has 6 DOF with respect to a reference frame (or

another rigid body) With exactly 6 constraints suitably arranged, no relative motion. If more than 6 constraints are applied to the body, it is

overconstrained and can be strained if its support base strains If less than 6 constraints are applied, movement is made possible

(e.g., bearings): 1 rotation free - spindle, rotary bearing 1 translation free - carriage on ways



Constraints and Strain Attenuation

A constraint is (relatively) stiff along its line of constraint Can substitute suitable arranged flexible elements to provide

functionally equivalent constraint Ex. Your stick models

Strain attenuation is important Frictional forces from contacts can transmit unwanted strain


Sullivan Feb 12, 2009 From Hale, 1999

Is this mount over-constrained?

Kinematic and Semi-Kinematic Constraint



Basic Building Blocks of Flexures

Rod Which DOF are Stiff

Which are Flexible?

Bellows Which DOF are Stiff

Which are Flexible?

x z

y

x z

y Rx

Rz Ry

Rx

Rz Ry



Basic Building Blocks of Flexures (2)

Sheets or plates Which DOF are Stiff

Which are Flexible?

bh determines strength L influences buckling strength

Ex. of combining sheet flexures to reduce constraints.

Ex. of combining sheet flexures to increase constraints.

x z

y h

b

L

Rz Rx Ry



Blade Flexures Rigid constraint in its own plane (x, y, & z) Three degrees of freedom: z, x, & y.



Parallel-Blade Flexure



Cross-Blade Flexure



Commercial Flexures

http://www.c-flex.com/home.html



Design Guidelines for Flexures

Chart from FUNdaMENTALs of Design, Slocum



Rowlands Ruling Engine

Henry Augustus Rowland III [1848-1901] - American physicist



Anti-Distortion Mountings

Jones, 1961



Other Flexures

Jones, 1962



Other Flexures, cont.

Jones, 1962

Why have 2 sets of cantilevered blade flexures?

(At least 2 reasons)



Series and Parallel Connections of Springs

Rule 1: The equivalent compliance of springs connected in series is the sum of their individual compliances.

Rule 2: The equivalent stiffness of springs connected in parallel is the sum of their individual stiffnesses.

cseries



Series and Parallel Connections of Springs (2)

Corollary: When springs are connected in series, add stiffnesses like resistors in parallel. When springs are connected in parallel, add stiffnesses like resistors in series.

k1 k2 k3



Parallel Springs (Flexures)




Series Flexures




Parallel & Series Flexures




Hexapod




1 DOF Flexure Example

Chart from Limitations of Flexures, McCarthy



1 DOF Flexure

Photo from Danaher Motion http://www.DanaherPrecision.com



2 DOF Flexure

Photo from Danaher Motion http://www.DanaherPrecision.com



Evolution of the Translational Flexure

Figure from Flexures Overview, Trease



Flexure Used for Simple Lever Motion Amplifier

Figure from PI Piezo University (http://physikinstrumente.com)



Parallelogram Flexure with Motion Amplification




Zero-arcuate-error Flexure System




Example: PI Piezo Stages




PI Piezo x-y Stage




PI Piezo Stage w/Position Sensors


Link to PI



Macro Flexure Systems




Macro Flexure Systems (2)




Macro Kinematic Mechanism




Micro Flexures




Carbon Nanotube (CNT) Flexures


05 flexures sullivan sp09

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