Flexures

Flexures are a different way to design machinery, a little-understood one. They have many surprising advantages and disadvantages compared to traditional machinery, the kind made of rigid bodies that interact by intermittent and often sliding contact, plus the occasional discrete spring. At present, they are mostly used for bearings and “living hinges”, but they are capable of much more.

Disadvantages of flexures include:

• Typically, movements are very small relative to the size of the machine or device, because most materials have a relatively small elongation at break;
• Continuous rotary motion is impossible and you must settle for reciprocating motion;
• Routing “signals” is difficult in a way that it is not in traditional machinery, as (at least in flexures cut from a sheet) crossing two “signals” over one another is tricky, as if you were laying out a one-sided printed-circuit board;
• very limited design tradition; the 2008 edition of the Machinery’s Handbook contains 3740 pages of information on designing traditional machinery, but not a single mention of flexure design, other than springs.

The advantages of flexures, however, are astonishing:

• Because there is no sliding contact, there is no wear. There may be fatigue, but just as with traditional springs, it is possible to keep fatigue at bay for impressively long times.
• There is no backlash, and thus no tradeoffs between backlash and binding.
• Flexures do not need to be lubricated, because they have no sliding contact.
• There is no static friction; although flexures can be designed to lock in positions of local energy minima, they don’t develop them spontaneously every time they stop moving, the way sliding contact does.
• Very high precision is achievable because of the lack of wear, backlash, and static friction; scanning tunneling microscopes, for example, maneuver their probe tips with a repeatability in the range of 10 picometers.
• In the appropriate materials, dynamic friction can be made arbitrarily low, although this involves tradeoffs against speed, and consequently efficiency can be made arbitrarily high.
• Because of the lack of wear, backlash, and static friction, as well as the resulting high precision, flexures are increasingly favorable at small sizes.
• Flexures can tolerate fairly contaminated environments without losing precision.
• Flexures that can be fabricated by cutting a sheet or plate can be manufactured at extremely low cost, even without mass production. Here in Buenos Aires, laser-cutting shops will cut 3mm MDF to a precision of about 100μm at a cost of about US$50/hour and a cutting speed of about 30mm/s, which is to say about 300 “pixels” per second; this gives you about 20 kilopixels per dollar. Plasma-cut sheet steel is about twice as expensive, but about an order of magnitude better performance by most measures.
• Flexures in hard materials can effectively use piezoelectric actuators, which can act at frequencies up into the megahertz. By contrast, air bearings are limited to frequencies of around 150krpm (16 kHz), two or three orders of magnitude lower, and non-air- bearing sliding-contact machinery is typically limited to no more than 10krpm (1kHz). So flexure machinery can exceed the speed of sliding-contact machinery by two to five orders of magnitude.
• Flexures have no trouble operating in conditions that are very hostile to lubricants, including hard vacuum, cryogenic cold (with appropriate flexure material), and extreme heat (again, with appropriate material).

In the early 1990s, as a rebuttal to concerns that molecular nanotechnology would not provide practical advantages in computation because of high energy consumption, Ralph Merkle outlined the design of a flexure-based reversible computer using “buckling-spring logic”, so flexures are capable of very complex tasks. Given their reliability and speed advantages over sliding-contact machinery, flexures are likely to shine in mechanical computing and automated fabrication applications.

Stuart Smith’s 2000 book on flexures defines them as “a mechanism consisting of a series of rigid bodies connected by compliant elements that is designed to produce a geometrically well-defined motion upon application of a force.” He cites the following as their advantages and disadvantages:

Advantages of flexures

1. They are simple and inexpensive to manufacture and assemble.

2. Unless fatigue cracks develop, the flexures undergo no irreversible deformations and are, therefore, wear-free.

3. Complete mechanisms can be produced from a single monolith.

4. Mechanical leverage is easily implemented.

5. Displacements are smooth and continuous. Even for applications requiring displacements of atomic resolution, flexures have been shown to readily produce predictable and repeatable motions at this level.

6. Failure mechanisms such as fatigue and yield are well understood.

7. They can be designed to be insensitive to thermal variations and mechanical disturbances (vibrations). Symmetric designs can be inherently compensated and balanced.

8. There will be a linear relationship between applied force and displacement for small distortions. For elastic distortions, this linear relationship is independent of manufacturing tolerance. However, the direction of motion will be less well defined as these tolerances are relaxed.

Disadvantages of flexures

1. Accurate prediction of force-displacement characteristics requires accurate knowledge of the elastic modulus and geometry/dimensions. Even tight manufacturing tolerances can produce relatively large uncertainty between predicted and actual performance.

2. At significant stresses there will be some hysteresis in the stress-strain characteristics of most materials.

3. Flexures are restricted in the length of translation for a given size and stiffness.

4. Out of plane stiffness values are relatively low and drive direction stiffness tends to be relatively high in comparison to other bearing systems.

5. They cannot tolerate large loads.

6. Accidental overload can be catastrophic or, at least, significantly reduce fatigue life.

7. At large loads there may be more than one state corresponding to equilibrium, possibly leading to instabilities such as buckling or ‘tin-canning’.