Mechanics of Designing Precision Machines

9/17/2002Precision Engineering Research Group, MIT

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Mechanics of (passionately) Designing (fun)Precision Machines

Prof. Alexander H. SlocumMacVicar Faculty Teaching Fellow

Department of Mechanical EngineeringMassachusetts Institute of Technology

77 Massachusetts Avenue, Room 3-445Cambridge, MA 02139

617.253.0012 617-258-6427 (fax) [email protected]://pergatory.mit.edu


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Thought Processes "Personal self-satisfaction is the death of the scientist. Collective self-

satisfaction is the the death of research. It is restlessness, anxiety, dissatisfaction, agony of the mind that nourish science" Jacques-Lucien Monod

To help generate and create ideas, thought processes can be used as catalysts Systematic Variation

Consider all possibilities Persistent Questioning

Continually ask Who?, What?, Why?, Where, How? Reversal: Forward Steps

Start with an idea, and vary it in as many ways as possible to create different ideas, until each gets to the end goal

Also called the method of divergent thought Reversal: Backwards Steps

Start with the end goal and work backwards along as many paths as possible till you get to the beginning

Natures Way How would nature solve the problem?

Exact Constraints What are the minimum requirements


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Thought Processes: Reversal

Being able to rapidly switch between the methods of Forward Steps and Backward Steps is an invaluable skill

Example: Given length equalities indicated by the colored pointy end cylinders, prove that the yellow cylinder is the perpendicular bisector of the purple and red cylinders?

Never be afraid to add your own sketching to a problem that is given you The thin red and blue lines and vertex labels were added!

If you do not rapidly see how to move forward, try going backwards!

As given:A

B

C

DE

F

After user inflicted clarifying features:


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Working with Industry to Create Precision Machines

Moore Tool PAMT for Defense Logistics Agency Moore Tool 5-axis Contour MillMoore Nanotech 150 Aspheric GrinderWeldon 1632 Gold Cylindrical GrinderCoorsTek all-ceramic grinderNCMS Cluster SpindleOMAX JetMachining CentersElk Rapids 5 axis cutter grinderNCMS HydroBushing and HydroSpindleAnorad/Dover MiniMillTeradyne K-Dock System, Manipulator & Apollo Sorter


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How Does Good Design Happen?

Good design has mechanical, electrical, and software components Being able to determine how a design will work before it is built is the premise of modern

industry Deterministic design is the key:

62.5 grams of prevention is worth a kilogram of cure! Good mechanics, makes it easier on the mechanics! Random Results are the Result of Random ProceduresRandom Results are the Result of Random Procedures

Geoffe Portes


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How Does Good Design Happen?

Good design is based on philosophy, experience, and analysis Philosophy is how we create our brains bio neural nets to give deep insight into problems

It is the hardest thing to teach and learn, and contributes to the idea that design is a black art

Experience depends on learning how things have been done (e.g., take-apart & how things work) and doing it, again and again and again

Human learning begins with touching Analysis is taught widely, and established web-based teaching methods exist

Students need philosophy and experience to help them learn how to use analysis and what level of analysis is appropriate


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FUNdaMENTAL Principlesof Mechanical Design

Patterns Occams Razor: KISS & MISS Saint-Venants Principle Golden Rectangle Abbes Principle Maxwells Reciprocity Self-Principles Stability Superposition Parallel Axis Theorem

Accuracy, Repeatability, Resolution Sensitive Directions Reference Features Structural Loop Free Body Diagram Centers of Action Exact Constraint Design Elastic Averaging Dimensional Analysis Leading and Bleeding edges

Imagine the feeling you get when you engage in an activity in which you RULE! When you MASTER the FUNdaMENTALs of design, you get the same feeling, continuously!

Robot World will help students master the FUNdaMENTALs! Philosophy, theory, practice! AND the issues in cost/performance tradeoffs

How fundamentals can be used to identify disruptive technologies


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Patterns: StrategiesConceptsModulesComponents Deterministic Design leaves

LOTS of room for the wild free creative spirit, and LOTS of room for experimentation and play

Deterministic Design is a catalyst to funnel creativity into a successful design

It is OK to iterate A goal is to never have to

backtrack A good engineer,

however, knows when its time to let go

1 2 3 4 5 6 7

41 2 3 4 5 6 7

61 2 3 4 5

5

1 2 3 4 5 6

3

1 2

2

1 2 3

1

1 2 3 4

2

1 22

1 2 31


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Occams Razor: KISS & MISS William of Occam (or Ockham) (1284-1347) was an English philosopher and

theologian Ockham stressed the Aristotelian principle that entities must not be multiplied beyond what

is necessary Ockham wrote fervently against the papacy in a series of treatises on papal power and

civil sovereignty. The medieval rule of parsimony, or principle of economy, frequently used by Ockham came to be known as Ockham's razor. The rule, which said that plurality should not be assumed without necessity (or, in modern English, keep it simple, stupid), was used to eliminate many pseudo-explanatory entities (http://wotug.ukc.ac.uk/parallel/www/occam/occam-bio.html)

A problem should be stated in its basic and simplest terms The simplest theory that fits the facts of a problem is the one that should be selected Limit Analysis is an invaluable way to identify and check simplicity

Use fundamental principles as catalysts to help you Keep It Super Simple Make It Super Simple Because Silicon is cheaper than cast iron(Don Blomquist)


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Saint-Venants Principle Saint-Venants Principle

Saint-Venant did extensive research in the theory of elasticity, and many times he relied on the assumption that local effects of loading do not affect global strains

e.g., bending strains at the root of a cantilever are not influenced by the local deformations of a point load applied to the end of a cantilever

The engineering application of his general observations are profound for the development of conceptual ideas and initial layouts of designs:

To NOT be affected by local deformations of a force, be several characteristic dimensions away

On the city bus, how many seats away from the smelly old drunk do you want to be?

To have control of an object, apply constraints over several characteristic dimensions

These are just initial layout guidelines, and designs must be optimized using closed-form or finite element analysis

Barr de Saint-Venant1797-1886

Wheel

Shaft

Sliding bearing in structure

!!Non Optimal!! Wheel

Shaft

Sliding bearing in structure

!!Optimal!!


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The Golden Rectangle The proportions of the Golden Rectangle are a natural starting point for preliminary sizing of

structures and elements Golden Rectangle: A rectangle where when a square is cut from the rectangle, the remaining rectangle

has the same proportions as the original rectangle Watch Donald in Mathmagic Land!

Example: Bearings: The greater the ratio of the longitudinal to latitudinal (length to width) spacing:

The smoother the motion will be and the less the chance of walking (yaw error) First try to design the system so the ratio of the longitudinal to latitudinal spacing of bearing

elements is about 2:1 For the space conscious, the bearing elements can lie on the perimeter of a golden rectangle

(ratio about 1.618:1) The minimum length to width ratio is 1:1 to minimize yaw error

1.618:1 1:1

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

5 4.6 4.2 3.8 3.4 3 2.6 2.2 1.8 1.4 1 0.6 0.2

width/height

roll

ang

le (

deg

)

a


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Abbes Principle

In the late 1800s, Dr. Ernst Abbe (1840-1905) and Dr. Carl Zeiss (1816-1888) worked together to create one of the worlds foremost precision optics companies: Carl Zeiss, GmbH (http://www.zeiss.com/us/about/history.shtml)

The Abbe Principle (Abbe errors) resulted from observations about measurement errors in the manufacture of microscopes:

If errors in parallax are to be avoided, the measuring system must be placed coaxially with the axis along which the displacement is to be measured on the workpiece

Strictly speaking, the term Abbe error only applies to measurement errors

When an angular error is amplified by a distance, to create an error in a machines position, for example, the strict definition of the error is a sine or cosine error

From www.zeiss.com

eL

L(1-cos(e)) Le2/2

Lsin(e)

L


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Abbes Principle: Locating Components Geometric: Angular errors are amplified by the distance from the source

Measure near the source, and move the bearings and actuator near the work!

Thermal: Temperatures are harder to measure further from the source Measure near the source!

Thinking of Abbe errors, and the system FRs is a powerful catalyst to help develop DPs, where location of motion axes is depicted schematically

Example: Stick figures with arrows indicating motions are a powerful simple means of depicting strategy or concepts


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Abbes Principle: Cascading Errors A small angular deflection in one part of a machine quickly grows as

subsequent layers of machine are stacked upon it A component that tips on top of a component that tips If you give a mouse a cookie..

Error budgeting keeps tracks of errors in cascaded components Designs must consider not only linear deflections, but angular deflections and their

resulting sine errors

Motion of a column as it moves and deflects the axis upon which it rides

R

Tool

WorkError


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Maxwells Reciprocity

Maxwells theory of Reciprocity Let A and B be any two points of an elastic system. Let the displacement of B in

any direction U due to a force P acting in any direction V at A be u; and the displacement of A in the direction V due to a force Q acting in the direction U at Bbe v. Then Pv = Qu (from Roark and Young Formulas for Stress and Strain)

The principle of reciprocity can be extended in philosophical terms to have a profound effect on measurement and development of concepts

Reversal Critical Thinking

James Clerk Maxwell 1831-1879


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Reciprocity: Reversal A method that is used to take out repeatable measuring instrument errors from

the measurement See ANSI standards for axis of rotation, straightness and machine tool metrology

for excellent tutorials on applying reciprocity to measurement!

One of the principal methods by which advances in accuracy of mechanical components have been continually made

There are many application variations for measurement and manufacturing Two bearings rails ground side-by-side can be installed end-to-end A carriage whose bearings are spaced one rail segment apart will not pitch or roll

dCMM(x) dpart (x) before reversal

after reversal

Zprobe before reversal(x) = dCMM(x) - dpart(x)

Zprobe after reversal(x) = dCMM (x) + dpart(x)

dpart(x) = -Zprobe before reversal(x) + Zprobe after reversal(x)

2

CMM repeatability

Part before reversal

Part after reversal


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Kinematic Couplings for Precision Fixturing James Clerk Maxwell (1831-1879) likes three grooves

Symmetry good for manufacture, dynamic stability Easy to obtain very high load capacity

William Thomson (later Lord Kelvin) (1824 - 1907) likes ball-groove-tetrahedron

More intuitive, and more easily applied to non-planar designs

X

YZ

Planar Vertical


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Repeatability Measurements

-0.20

-0.10

0.00

0.10

0 5 10 15 20 25 30 35 40 45 50

erro

r [

mm ]

-0.10

0.00

0.10

0 5 10 15 20 25 30 35 40 45 50

erro

r [

mm

]

Coupling

Measurement system

Canoe-Ball Kinematic Elementfor high Load Capacity and Repeatability

Canoe Ball

Modular microscope for Univ. of Illinois


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Kinematic Couplings: Three-Groove Design Guidelines

Keep Hertz contact pressure below 75% of tensile yield Material fails in shear below the surface Contact area center should ideally not be closer than one diameter from edge Materials must be non-galling and non-fretting Preload to keep coupling from tipping Split Groove coupling spreads one of the grooves to give appearance of a 4 point

mount, and thus provide somewhat greater unpreloaded tipping resistance

Align grooves with coupling triangle angle bisectorsBall 1

Ball 2 Ball 3

Angle bisector between sides 23 and 31

Plane containing the contact force vectors

Coupling triangleCoupling centroid


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Kinematic Couplings: Load Capacity of Contacts 25 mm diameter stainless steel half-sphere on 25 mm diameter cylinders

Fmax = 111 N Vertical deflection = 3.2 mm Contact ellipse major diameter = 0.425 mm , minor diameter = 0.269 mm

25 mm diameter stainless steel half-sphere in a Vee Fmax = 229 N Vertical deflection = 4.7 mm Contact ellipse major diameter = 0.488 mm , minor diameter = 0.488 mm

25 mm contact diameter x 125 mm radius crowned cone in a Vee Fmax = 1106 N Vertical deflection = 11 mm Contact ellipse major diameter = 2.695 mm , minor diameter = 0.603 mm

250 mm diameter stainless steel half-sphere in a Vee Fmax = 16160 N Vertical deflection = 47 mm Contact ellipse major diameter = 4.878 mm , minor diameter = 4.878 mm

Above based on maximum contact pressure of 1.3 GPa, and E=193 GPa

Heinrich Hertz 1857-1894


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Quasi-Kinematic Couplings for Ford Engine AssemblyProf. Marty Culpeppers Ph.D. thesis

QKC Attributes and Characteristics: Partial surfaces of Revolution ->

Short Line Contact Weakly Over-constrained Sub-micron Repeatability Sealing Contact High Stiffness without dowel pinsVery low cost

Groove Seat

Side Reliefs

Spherical Protrusion

dinitial d = 0dfinal

PROCESS: Mating force/displacement applied

Ball & groove comply

Brinell out surface finish

Elastic recovery restores gap


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Engine Assembly Performance

Bedplate

2nd Block Fixture

JL Cap Probe

JR Cap Probe

1st Block Fixture

Bedplate Fixture

CMM Head

Axial Cap Probe

Axial

Sensitive

QKC Error in Sensitive Direction

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 1 2 3 4 5 6 7 8

Trial #

dc, m

icro

ns

JL

JR

QKC Error in Axial Direction

-2.0

-1.5-1.0-0.50.0

0.51.01.5

2.0

0 1 2 3 4 5 6 7 8

Trial #

da,

mic

rons

Max x Dislacement

9

(Range/2)|AVG = 0.65 mm (Range/2) = 1.35 mm

CL


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MAGNABOTS: Hosptial Automation?!

Ceiling based trackless system: Zero footprint, high degree of flexibility in motion Ceiling of thin metal sheets: Can be bent into any shape; easily

expandable and scalable Graduate Students: Shorya Awtar and John Hart


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MAGNABOTS: Development Phase I

Proof-of-concept Demonstration at CIMIT, Oct 1701:

Steel ceiling installed in CIMIT Simulation Center Operating Room: Overhead horizontal sections for traversing across

the OR Vertical wall-side section for payload docking

Open-loop radio-controlled vehicles: Three vehicles: simple pendulum and triangle-

pendulum designs Detachable payload carriers Two magnetic driving wheels Passive delrin wheels for guidance along vertical

wall section


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0 50 100 150 200 250 300-1.5

- 1

-0.5

0

0 .5

1

1 .5

position [mm]

pitc

h er

ror

[arc

sec

] at 1

0 m

m/s

raw accuracy:2.44raw repeat:0.5

FRDPARRC Sheet Topic: Precision Low Cost Linear Motion Stage

Functional Requirement (Event) Preload air bearings for minimal cost

Design Parameter (description of idea) Preload air bearings using magnetic attractive force of motor, so air bearings need only ride on two surfaces instead of having to wrap around a beam; thus many precision tolerances to establish bearing gap can be eliminated

Sketch:

Analysis (physics in words) The magnet attraction force is 5x greater than the motor force, so it can be positioned at an angle such that even preload is applied to all the bearings. As long as the magnet attraction net vertical and horizontal force are proportional to the bearing areas and is applied through the effective centers of the bearings, they will be evenly loaded without any applied moments.

Analysis

References: Vee & Flat bearings used on many common machine tools where gravityprovides preload. NEAT uses two magnet tracks, one horizontal and one vertical, to provide horizontal and vertical preload force. Patent search revealed no other relevant art.

Risks: The magnet pitch may cause the carriage to pitch as the motors iron core windings pass over the magnets

Countermeasures: Add steel out of phase with motor core position, or if the error is repeatable, map it and compensate for it in other axes

tan

arctan

V V

H H

V

H

F AF A

AA

q

q

= =

=

sin

cosV magnets

H magnets

F FF F

q

q

=

=

Motor coreCarriage

Bearing rail

Air bearing pad

Magnet track

Linear Motor Magnet Preloaded Bearings

Assume we want even preload pressure per padMotor preload angle 26.57Motor attraction force, Fm 4000Motor width (mm), L 130Motor thickness 47Space for motor thickness 65Supply pressure, Ps (Pa, atm) 600000bearing efficiency, m 0.35preload proportion of total load capacity, f 0.5vertical/horizontal load capacity, vh 2X direction pads' total area (mm^2), Ax 21994Y direction pads total area, (mm^2) Ay 43989


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Linear Motor Magnet Preloaded Bearings Primary research challenges

Carriage pitch caused by magnets is acceptable for modest precision or wafer transport systems

Two-axis proof-of-concept grinding machine designed and built (in 2 months) at Overbeck Machine Tool Corp.

Side L Blocks

Top Blocks Top Plate

Replicating Fixturing Removal Fixturing

Top Jack Screws

Side Jack Screws

0 50 100 150 200 250 300-1.5

-1

-0.5

0

0.5

1

1.5

position [mm]

pitc

h er

ror

[arc

sec

] at

10

mm

/s

raw accuracy:2.44raw repeat:0.5


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Low-Cost Actuator/Bearing Structures Can preload of a nut on a screw be done in three-dimensions instead of just

one Can threaded-rods, the cheapest machine elements, can be made a precision

bearing and actuator?1-14 Greased Threaded Rods

Adjustable Preload Nuts Additional Flexures


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Low-Cost Actuator/Bearing Structures Preliminary tests were very encouraging!

FlexuresFixed Brass NutPreload

dy

dx

dy

dx

.0012.019.009.02

.007.010.006.02

.00065

.001

Prototype Results

.02

.02

FR (Full Scale)

.004.010Accuracy

.021.014Repeatability

Prototype Error Budget

Full Scale Error Budget


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Next: Personal Fabricators

How can we create low cost precision technologies to bring manufacturing to under-developed regions

Rolled threaded rod with preloaded nuts.

Bits to atoms on a large scale..?


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MEMS: Wafer Alignment Alexis Webers SM thesis was to see how repeatable are legos (several microns) and can we

learn from them and other work on kinematic couplings to create a new means to precisely stack up wafers:

4-inch double-sided polished (100) wafers were used and the convex features and cantilever flexures are fabricated through a backside KOH etch.

The individual flexures are released through a front-side DRIE. The concave features are bulk micro-machined through a KOH etch. 3 mm feature size

reference alignment marks were patterned initially using a custom mask. Chrome masks made from emulsion transparencies were used to create the alignment

features. Testing of the passive alignment features was done on an Electronic Vision Group TBM8

wafer alignment inspection system, and wafer-to-wafer alignment on the order of 1 micron was achieved, and repeatability was in the submicron range

This alignment technique is not (YET!) compatible with anodic bonding due to the rough surface finish left by the KOH etch. It can however be used for eutectic bonding, among other bonding methods.


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MEMS

Flexures have been used for centuries as a means to create extremely high accuracy small range of motion instrument stages

Prof. Sridhar Kota at UMI has an entire laboratory devoted to the design of compliant mechanisms

From staples to windshield washer blades to sophisticated MEMs devices He has created field-search algorithms to find optimum flexural linkage

designs to meet user defined FRs constraints http://www.engin.umich.edu/labs/csdl/index.htm

Much of the work in MicroElectroMechanical Systems (MEMS) is based on the use of tiny silicon flexures


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MEMS: Relays Jin Qius Ph.D. thesis has led to a bistable double-beam flexure

It is bistable without any initial preload

In trying to help us make it better, Prof. Michael Brenner (formally of MIT)developed an entirely new way of looking at optimization problems

When design engineers and applied mathematicians get together to play, its a productive day!


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Force Displacement Curve For The Switch

Force Ratio is 2:1.


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The Optimization: Changing Beam Shape Improves PerformanceB

ette

r F

orce

Rat

io


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Optimized Switch

Force Ratio is 1:1 !


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Shape of Optimized Beam


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Nanogate The Nanogate is a device that precisely meters the flow of tiny amounts of fluid.

Precise control of the flow restriction is accomplished by deflecting a highly polished cantilevered plate.

The opening is adjustable on a sub-nanometer scale, limited by the roughness of the polished plates.

The Nanogate can be fabricated on a macro-, meso- or micro- (MEMs) scale. This research grew out of understanding of flow metering garnered from years of hydrostatic

bearing research

This research was funded by an NSF award, number 9900792, and James White is a recipient of a a Hertz Fellowship

Possible fuel injector application?


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Nanogate Operation

The outer diameter of the gate plate 620 is forced down

The annular thin wall structure 630 acts like a torsion spring pivot

The gate plate surface 641 lifts up creating a gap 777

Fluid can then flow from source 670a to sink 670b

601a

601b

665620

650640641

667

668

622

670b 670a681a

682a

681b682b

630

667

668

100

d

F F

601a

601b

665620650

641

667

668

622

670b 670a681a

682a

Fig. 7

681b682b

630

777

D

682c

682e

682d

640100


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Molecular Sensing and Filtration Using the NanogateThe Nanogate is micro-mechanical device that can accurately and repeatably control a nanometer sized gap. Precise control of the gate opening is accomplished by deflecting a cantilevered plate that is anchored by an annular torsion spring. The opening is adjustable on a sub-nanometer scale using a piezoelectric actuator. The ability to control flow channels at nanometer length scales may enable sensing and filtration of large molecules such as proteins and DNA.

Graduate students James White and Hong Ma are building instrumentation around the Nanogate to precisely measure the gate opening and to image the flow of molecules in these constrained conditions. The actuation is achieved by a Nu Focus Picomotoractuator while the displacement sensing will be implemented using a Zygo single point optical probe interferometer.Figure 2: Schematic of the Nanogate Instrumentation


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Nanogate Molecular Sieve?

Flowrate of large molecules is nonlinearly dependent on the gap size, and modulation frequency, for very small gaps

How does the mobility of a protein depend on the size and surface properties of the channel?

Can proteins be mechanically filtered based on size? What dynamic effects would play a role?

Can adsorption be controlled?

Can we accomplish small gap chromatography?

Proteins


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0.5-dimensional probe Interact with a few molecules at a

time Low throughput Elastic forces ~ molecular

attraction

Molecules are constrained in a 2.5-dimensional space.

Interact with many molecules Higher throughput Elastic forces >> molecular

attraction

AFM and the Nanogate


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Nanogate Instrumentation

Planned fluid connections Instrument schematic First version - Super Invar flexure, piezoelectric motor, Michaelson interferometer for displacement measurement.


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Results: 2nm Resolution!Displacement due to 2 steps

80

85

90

95

100

105

0 0.02 0.04 0.06 0.08 0.1 0.12

time (s)

disp

lace

men

t (nm

)

raw dataAveraged


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Results: Opening and Closing the Gate

Mechanical Characteristics

0

20

40

60

80

100

120

140

0 5 10 15 20 2 5 30

Picomotor Steps

Dis

pla

cem

ent

(nm

)

Going up (gateclosing)

Going Down(Gate Opening)

Conclusion: Very good relative repeatability


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Conclusions

The fundamental principles of design can be applied at all scales Deterministic design is most important!

What we do on a large scale, often provides insight on the small scale There is no shortage of engineering challenges at ALL scales

Documents

Mechanics of Designing Precision Machines