# Flexures¶

Displacement limits are around 10% of the compliant mechanism size.

## Precision and Accuracy¶

Beware of yielding and thus it’s important to avoid going higher than 20% of the yield strength to remain very stable.

Indeed even below the yield strength, microyields are happenning.

To be precise, it’s important to have precise actuation. Imprecise actuation results is imprecise motion output.

### Assembly¶

Assembly create game. To avoid slip, try to design and fabricate the piece in a single piece. Off course it’s not always possible.

The important principle is in that case to keep areas of deformation should be kept away from joint interfaces. The objective is to spread the stresses and strains to avoid microslips and heterogenous behavior..

Also when you have surfaces assembled with bolts, the grounded part is stressed onto the assembled part in a cone the same is true for the assembled part around the bolt.

Because these stresses create strains, they create microslips and limit precision. A good practice to balance that is to make the two cones overlap.

### Sensitivity¶

The calibration of flexures is critical because they depend highly of dimensional and material property errors or other.

Another problem can be time variable errors because the material can creep and relax its strength.

Small dimensional errors can lead to a gigantic change once compounded. For example, if the dimensions of a beam are 5% precise, its total stiffness will vary by 70 percent !

### Thermal variations¶

Temperature can make flexures move but you can modify the design to counter the displacements by exploiting symetry.

Again, we accept the reality of the thermal displacements but we balance it a bit like judo !

### Vibrations¶

Vibrations are always happenning.

Generally speaking, the gain is 1 at low frequency but at some point it increases very fast when we get to the natural frequency and then goes to zero when we go higher than the natural frequency.

In reality, all objects have an infinite number of natural frequencies that combine.

For each natural frequency, there is an associated mode shape.

Mode shapes are defined as the directions in which exchange of potential-kinetic energy is the most favorable at a given frequency.

How to mitigate the vibrations ?

We can increase the natural frequency !

The natural frequency is Wn = sqrt(k/m)

With k being the stiffness and m the mass

so we decrease the mass and increase the stiffness and we mitigate the vibrations effect.

An important safety principle is to avoid aligning with the mode shapes directions with the sensitive directions of the system.

Another solution is damping. Cheap damping is passive, using viscosity. The expensive solution is to use active damping with closed loop control, using sensors and motors .

The other solution is input shaping. That means characterizing the system and changing the input to change.

### Materials¶

Avoid materials susceptible to creep and stress relaxation.

• Do not use polymers
• Avoid high temperatures (for metals, max 1/3 of the melting temperature)

To select the material, choose the high yield strength, and the low Young’s modulus.

To fight thermal temperature, choose a high thermal distributivity and a low thermal expansion ratio.

To fight vibrations, we want a high stiffness and a low mass, so we want the lowest k/m possible so a low Young’s modulus over density.

The best material overall through these criteria is plutonium, but for safety and cost reason, off course we choose other ones.

Overall, aluminium, titanium are excellent and steel is also a good choice.

## Fabrication¶

It depends highly on the material you are using.

### Electric Discharge Machining (EDM)¶

Vaporizing the surface with electrics arks and passively removes all bumps.

Positives

• Kerf is very low (0.1mm for wire)
• Accuracy (5 micron)
• Surface finish( sub-micron)
• No direct contact between tool and work piece : very interesting for delicate features
• 3D features (with die)

Negatives

• Slow (mm/minute)
• Expensive
• Large power consumption
• Limited to conductive materials

### Water jet¶

Positives

• Rapid (cm/min)
• Many materials (including brittle, heat sensitive, non conducting materials)
• Comparatively low-cost

Negatives

• Kerf > 1mm
• Draft angle (taper)
• Accuracy (125 microns) Thickness limitations

### Laser Cutting¶

Positives

• Rapid (cm/min)
• Accuracy (25 microns)
• Kerf 25mm

Negatives

• Limited materials (depending on the absorbtion spectrum of the material and the laser frequency) : No highly reflective materials or thermally conductive materials
• Draft angle (taper)
• Thickness limitations
• Thermal effects (HAZ): Creeping

### Laser Cutting¶

Positives

• Nearly any materials (limited for brittle material)
• Nearly any shapes
• Flexible

Negatives

• High force (No delicate features)
• Surface damages
• Work hardening
• Fixturing : needs to be clamped somewhere.

### Lithography and etching¶

Chemically, optically and electrically (plasma) remove material. Very useful for microfabrication

Creating a mask and select the surface to etch and which to protect and keep.

Positives

• 2.5 D topologies/ shapes
• Monolithic
• Micron-level features

Negatives

• Slow (microns/minutes)
• not flexible (mask not alterable)
• Poor dimensional control
• Scallop

### 3D printing¶

Positives

• Flexible
• Multiple materials
• Different materials can be seamlessly blend into other materials

Negatives * Slow-ish * Expensive for some materials * Often times support material must be used and removed * Resolution for large print is relatively poor * Microstructure has inferior properties to bulk material * Often times the material is porous * Material available is limited.

Last update: March 26, 2021