[PPT] - Controlling DESIGN PRINCIPLE: To achieve a highly precise and PowerPoint Presentation

SLIDE 1

Controlling Degrees of Freedom

DESIGN OF PRECISION MACHINES

Controlling Degrees of Freedom

Excessive constraints/ Over-constrained

Smooth action in x-direction is difficult to achieve unless the parts have been perfectly machined and assembled so that interference among the redundant constraints does not interfere.

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Controlling Degrees of Freedom

From a kinematic viewpoint, excessive constraints must be avoided to produce a rationally designed guide. DESIGN PRINCIPLE: To achieve a highly precise and smooth action which requires minimal force to operate, avoid excessive constraints. (The principle of kinematic design) Kinematic design thus means employing

ptimum constraints when designing a machine.

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Controlling Degrees of Freedom

Eliminating excessive constraints

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SLIDE 2

Controlling Degrees of Freedom

Four column press

Constrained DOFs = 8 x 4 DOFs = 32 DOFs Much of the machining effort is intended to prevent positional over constraint being manifested in the design.

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Controlling Degrees of Freedom

Alternative concept

With preload Thermal centre Without preload

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Controlling Degrees of Freedom

Table top and table legs

Bending moments transferred to table top Kinematic mount of table top on table structure

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Controlling Degrees of Freedom

Exact constrained design For a high level of predictable behaviour and a minimum number of accurate dimensions, exact constrained design is a necessary condition.

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SLIDE 3

Controlling Degrees of Freedom

Elements to constrain degrees of freedom

Symbol for ONE translation Symbol for ONE rotation

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Controlling Degrees of Freedom

Constraining one translation by contact

A sphere against a flat surface F

Constrained DOF

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Controlling Degrees of Freedom

Contact stress and stiffness with ball support

F

Constrained DOF

N/m 10 3 . 4 stiffness contact N/m 10 1360 : ball Steel

3 1 3 1 6 2 6 3 1 2 max ,

F r d dF r F

Hz

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Controlling Degrees of Freedom

Contact stress and stiffness with ball support

F

Constrained DOF

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SLIDE 4

Controlling Degrees of Freedom

Damaging steel balls is very easy!

g 20 mm

! N/mm 3000

2

Hz
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Controlling Degrees of Freedom

Poor position accuracy in z-direction due to spherical contact area

2

1 ) cos( 2 r

r_h

z : error

z

ion approximat

2 2

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Controlling Degrees of Freedom

Poor position accuracy in z-direction due to spherical contact area

2

r

r_h

z 2 1 ) cos( ) cos( r) (r_h r) r_h ( z : error

z

ion approximat

2 2

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Controlling Degrees of Freedom

Constraining ONE translation

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SLIDE 5

Controlling Degrees of Freedom

Constraining ONE translation

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Controlling Degrees of Freedom

Only one location and direction:

no high bending compliance
no torsion

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Controlling Degrees of Freedom

Demo – Folded sheet flexure

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Controlling Degrees of Freedom

The principle of the “Folded Sheet Flexure”

1 3 3

5 6 3

A

G b a EI b a u F c

z z z

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SLIDE 6

Controlling Degrees of Freedom

Constraining ONE rotation

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Controlling Degrees of Freedom

Constraining ONE rotation

torsionally stiff body torsionally stiff body torsionall

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Controlling Degrees of Freedom

Constraining ONE rotation

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Controlling Degrees of Freedom

Constraining ONE rotation

Be careful with intermediate elements!

buckling
resonances
fatigue

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SLIDE 7

Controlling Degrees of Freedom

Constraining ONE rotation

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Controlling Degrees of Freedom

Constraining TWO translations

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Controlling Degrees of Freedom

Constraining TWO translations

More robust embodiment!!!

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Controlling Degrees of Freedom

Constraining one translation and one rotation

about the same axis…. about perpendicular axes...

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SLIDE 8

Controlling Degrees of Freedom

Constraining two translations and one rotation in one plane

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Controlling Degrees of Freedom

Constraining two rotations

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Controlling Degrees of Freedom

Constraining three translations

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Controlling Degrees of Freedom

Constraining three translations

Example: elastic ball joint with coinciding poles

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SLIDE 9

Controlling Degrees of Freedom

Constraining three DOFs

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Controlling Degrees of Freedom

Constraining three DOFs using folded sheet flexures

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Controlling Degrees of Freedom

Constraining three DOFs using folded sheet flexures

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Controlling Degrees of Freedom

Constraining three rotations

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SLIDE 10

Controlling Degrees of Freedom

Constraining two translations and two rotations

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Controlling Degrees of Freedom

Two degrees of freedom (translations) in one plane

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Controlling Degrees of Freedom

Free one DOF: translation

Correct parallel guiding

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Controlling Degrees of Freedom

Free one DOF: rotation

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SLIDE 11

Controlling Degrees of Freedom

Free one DOF: rotation

Example: cross spring pivot

centre line leaf spring

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Controlling Degrees of Freedom

Constraining 6 DOF: kinematic mount

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Controlling Degrees of Freedom

Constraining 6 DOFs with 2 sheet flexures?

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Controlling Degrees of Freedom

Constraining 6 DOFs with 2 sheet flexures?

translation is over-constrained, rotation free rotation free

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SLIDE 12

Controlling Degrees of Freedom

Examples of controlling DOFs

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Controlling Degrees of Freedom

Ball joint with intermediate body

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Controlling Degrees of Freedom

Ball joint with intermediate body

Play-free mounting of the ball hinge cup

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Controlling Degrees of Freedom

Ball hinge based on “wire flexures”

Friction release is uncontrolled Flexure ball hinge lacks hysteresis

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SLIDE 13

Controlling Degrees of Freedom

Linking shafts which are not aligned precisely

Transferring ONE DOF: a rotation

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Controlling Degrees of Freedom

Linking shafts which are not aligned precisely

Transferring ONE DOF: a rotation

Coupling with single thin bar

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Controlling Degrees of Freedom

Linking shafts which are not aligned precisely

Transferring ONE DOF: a rotation

Angular precision dependent

n alignment errors:

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Controlling Degrees of Freedom

Flexible coupling with 3 thin bars

(universal joint)

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SLIDE 14

Controlling Degrees of Freedom

Flexible coupling with 2 times 3 thin bars

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Controlling Degrees of Freedom

Torsionally stiff coupling based on elastic elements equivalent to “Oldham coupling”

Courtesy Huco

in

ut
ut

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Controlling Degrees of Freedom

Detailed design “Koster-coupling”

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Controlling Degrees of Freedom

Torsionally stiff coupling based on folded sheet flexures

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SLIDE 15

Controlling Degrees of Freedom

Transmitter of information on one angle Version suitable for high rotational velocities

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Controlling Degrees of Freedom

Constraining axial displacement without using material at the centre line

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Controlling Degrees of Freedom

Point of support should be in neutral plane of membrane

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Controlling Degrees of Freedom

Self-centering driver

Compare to a splined-shaft...

shafts remain centered in relation to another
every point of contact has equal load

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SLIDE 16

Concept of Thermal Centre (TC)

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Controlling Degrees of Freedom

The Concept of Thermal Centre (TC)

Using symmetry to position the thermal centre in the object centre

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Controlling Degrees of Freedom

The body is free to expand without affecting the centre position

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Controlling Degrees of Freedom

Constraining a centre line

Instant centre of rotation does not coincide with the thermal centre

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SLIDE 17

Controlling Degrees of Freedom

Constraining a centre line with folded sheet flexures

Advantages:

no rotation
stiffer

Lower axial stiffness

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Example: Thermal centre laser-welding head

Controlling Degrees of Freedom

Three balls in V-grooves: kinematic support

Use radially stiff bodies to minimise virtual play

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Controlling Degrees of Freedom

V-groove coupling designed to avoid expansion induced hysteresis Cross-section A-A Cross-section B-B

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SLIDE 18

Controlling Degrees of Freedom

V-groove coupling designed to avoid expansion induced hysteresis: alternative embodiment

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Controlling Degrees of Freedom

Kinematic connection (not dismountable)

Elastic version (not dismountable)

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Controlling Degrees of Freedom

Nest of Springs

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Controlling Degrees of Freedom

The stiffness of a slanted truss

2

cos '

c

c

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SLIDE 19

Controlling Degrees of Freedom

The stiffness of a slanted truss

r

r rad

c c c

2

2

cos sin

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Controlling Degrees of Freedom

Radial stiffness of a nest of springs

n times cr (ct = 0)

r

r rad

c n c n c

2

cos sin 2

2 2

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Controlling Degrees of Freedom

Example of a nest of springs: ball bearing

ball v

c n c 2

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Controlling Degrees of Freedom

Introducing an object into a nest of springs

Perfect nest of springs Perfect cylinder in a perfect nest of springs Non-round cylinder in a perfect nest of springs. The point that coincides with M is the centre of gravity MC

f the cylinder circumference

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SLIDE 20

Controlling Degrees of Freedom

Radial stiffness of a nest of springs

n times cr and ct

t r r

c n c n c

2

2

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Controlling Degrees of Freedom

Nest of springs in a glass holder of an old fashioned oil lamp

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Controlling Degrees of Freedom

Lens mount based on a nest-of-springs-suspension

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Controlling Degrees of Freedom

In conclusion:

Why “Exactly Constrained” Designs?

Minimum number of accurate tolerances
No “transfer” of deformations
Predictable thermal behavior
Predictable force paths

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SLIDE 21

Fine manipulation and adjustment

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y

x e e a u u u 1 1 1

3 2 1

x

y

e e a

1

u

2

u

3

u

In-plane fine manipulation with adjustment procedure

3

2 1

2 1 2 1 2 1 2 1 2 2 1 u u u e e e a e a y x

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y

x e u u u 1 1 1

3 2 1

e

1

u

2

u

x

y

3

u

In-plane fine manipulation with limited adjustment procedure

3

2 1

1 1 1 1 u u u e e y x

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x

y

2

u

1

u

3

u

r

y

x r u u u 1 1

3 2 1

b a l l

l

l l

In-plane fine manipulation with independent adjustments (1/2)

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SLIDE 22

x

y

2

u

1

u

3

u

r

y

x r u u u 1 1

3 2 1

l l l l

l

In-plane fine manipulation with independent adjustments (2/2)

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y

x a a a u u u 1 2 3 2 1 2 3 2 1

3 2 1

x

y

1

u

2

u

3

u

120º 120º a

In-plane fine manipulation for maximum stiffness

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Accuracy of an operation: closeness of the agreement between the actual value resulting from an operation and a target value of the

quantity. Accuracy is a qualitative description.

Uncertainty of an operation: parameter, associated with the result

f an operation that characterizes the dispersion of the values that

could reasonably be attributed to the quantity. Resolution: smallest difference between indications of displaying device that can be meaningfully distinguished. Repeatability (of results of operations): closeness of the agreement between the results of successive operations of the same quantity carried out under the same conditions. Reproducibility: closeness of the agreement between the results of

perations of the same quantity carried out under changed

conditions.

P. Schellekens et al., Design for Precision: Current Status and Trends, CIRP 1998

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Adjusting 6 DOFs (1/2)

Adjustment sequence: 1) position x,y,z 2) angles ,,

x y

z
u1

u2 u3 u4 u5 u6 r r r

z

y x r r r u u u u u u 1 1 1 1 1 1

6 5 4 3 2 1 DESIGN OF PRECISION MACHINES

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SLIDE 23

Adjusting 6 DOFs (2/2)

3 orthogonal 2 DOF adjustments

z

y x r r r u u u u u u 1 1 1

6 5 4 3 2 1

y

x
z
u2

u5 r

P

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y

x
z
u1

u2 u4 u5 u6 2r 2r 2r

z

y x r r r r r r u u u u u u 1 1 1 1 1 1

6 5 4 3 2 1

P E,A,l u3

Equal stiffness in all directions

l EA c 2

2

2 r l EA k

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6-DOF Stewart platform using piezo motors

6-DOF motion mechanism is based on elastic hinges
Accuracy sub-micron
High stiffness due to parallel actuator design

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