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  • Precision Machine Design ME 250

    Flexures

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

    Mark Sullivan February 12, 2009

  • Page 2

    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.

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    Precision Machine Design Flexures

    Sullivan Feb 12, 2009

    Introduction Flexures

    Chart from FUNdaMENTALs of Design, Slocum

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    Precision Machine Design Flexures

    Sullivan Feb 12, 2009

    Flexure History

    Chart from ASPE Flexure Course Notes, Culpepper

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    Precision Machine Design Flexures

    Sullivan Feb 12, 2009

    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

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    Precision Machine Design Flexures

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    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

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    Precision Machine Design Flexures

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    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

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    Precision Machine Design Flexures

    Sullivan Feb 12, 2009

    Blade Flexure

    Figure from Limitations of Flexures, McCarthy

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    Precision Machine Design Flexures

    Sullivan Feb 12, 2009

    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

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    Precision Machine Design Flexures

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    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

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    Precision Machine Design Flexures

    Sullivan Feb 12, 2009 From Hale, 1999

    Is this mount over-constrained?

    Kinematic and Semi-Kinematic Constraint

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    Precision Machine Design Flexures

    Sullivan Feb 12, 2009

    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

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    Precision Machine Design Flexures

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    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

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    Precision Machine Design Flexures

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

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    Precision Machine Design Flexures

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    Parallel-Blade Flexure

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    Precision Machine Design Flexures

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    Cross-Blade Flexure

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    Precision Machine Design Flexures

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    Commercial Flexures

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

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    Precision Machine Design Flexures

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    Design Guidelines for Flexures

    Chart from FUNdaMENTALs of Design, Slocum

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    Precision Machine Design Flexures

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    Rowlands Ruling Engine

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

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    Precision Machine Design Flexures

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    Anti-Distortion Mountings

    Jones, 1961

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    Precision Machine Design Flexures

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    Other Flexures

    Jones, 1962

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    Precision Machine Design Flexures

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    Other Flexures, cont.

    Jones, 1962

    Why have 2 sets of cantilevered blade flexures?

    (At least 2 reasons)

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    Precision Machine Design Flexures

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    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

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    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

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    Precision Machine Design Flexures

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    Parallel Springs (Flexures)

    Chart from ASPE Flexure Course Notes, Culpepper

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    Precision Machine Design Flexures

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    Series Flexures

    Chart from ASPE Flexure Course Notes, Culpepper

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    Precision Machine Design Flexures

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    Parallel & Series Flexures

    Chart from ASPE Flexure Course Notes, Culpepper

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    Precision Machine Design Flexures

    Sullivan Feb 12, 2009

    Hexapod

    Chart from ASPE Flexure Course Notes, Culpepper

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    Precision Machine Design Flexures

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    1 DOF Flexure Example

    Chart from Limitations of Flexures, McCarthy

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    Precision Machine Design Flexures

    Sullivan Feb 12, 2009

    1 DOF Flexure

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

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    Precision Machine Design Flexures

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    2 DOF Flexure

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

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    Precision Machine Design Flexures

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    Evolution of the Translational Flexure

    Figure from Flexures Overview, Trease

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    Precision Machine Design Flexures

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    Flexure Used for Simple Lever Motion Amplifier

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

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    Precision Machine Design Flexures

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    Parallelogram Flexure with Motion Amplification

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

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    Precision Machine Design Flexures

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    Zero-arcuate-error Flexure System

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

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    Precision Machine Design Flexures

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    Example: PI Piezo Stages

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

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    Precision Machine Design Flexures

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    PI Piezo x-y Stage

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

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    Precision Machine Design Flexures

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    PI Piezo Stage w/Position Sensors

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

    Link to PI

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    Precision Machine Design Flexures

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    Macro Flexure Systems

    Chart from ASPE Flexure Course Notes, Culpepper

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    Precision Machine Design Flexures

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    Macro Flexure Systems (2)

    Chart from ASPE Flexure Course Notes, Culpepper

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    Precision Machine Design Flexures

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    Macro Kinematic Mechanism

    Chart from ASPE Flexure Course Notes, Culpepper

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    Precision Machine Design Flexures

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    Micro Flexures

    Chart from ASPE Flexure Course Notes, Culpepper

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    Precision Machine Design Flexures

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    Carbon Nanotube (CNT) Flexures

    Chart from ASPE Flexure Course Notes, Culpepper