Sensing shape and motion with bistable switches that digitize material strain caused by flexure


(US Patent # 5563458. Apparatus and Method For Sensing Surface Flexure - expired)

The domes/indentations are forced to buckle and snap toward the outside of a curvature when the material around them is bent, not by pressure. Overlapping bistable domes form structures that share the flexural forces that switch individual domes.

A prototype sensor confirms that a row if overlapping bistable domes (OBDs) made into switches can simultaneously tell a computer where, how much, and in which direction it is bent (ie. up/down), regardless of its position in space.

When fully developed a low cost paper thin electromechanical material can be used like a skin to digitize the shape and motion of the surface parallel to it. It will enable almost any flexible surface to be used as a shape sensor.

Predictability of dome behavior may make this simple digitizing technology particularly well suited for artificial intelligence and machine learning. It can expand the ways in which computers interact with the physical world and promises new markets for computer-related technology and products.

It can be used to make robots with a soft touch, shape measuring and recording tools, and car seats that know who's sitting in them.

Clothing-thin sensors made with this technology can improve human/computer interaction and make it easier to monitor human motion for physical rehabilitation, ergonomic studies, virtual reality and sports training.

Its multidimensional capabilities and digital nature are unique among existing contact/tactile bend and shape sensors. No other bend sensor technology offers comparable 2D profiling capabilities. No existing shape sensing technology offers comparable utility, simplicity, and mass-producibility.

NOTE: The bistable dome rows used in these prototypes are individually stamped by hand. Minimum radius, resolution, and accuracy could be increased considerably with modern manufacturing technologies.


  1. Sensor features
  2. How it works: flex actuated overlapping bistable domes and the effects of overlapping.
  3. 2D sensor
  4. 2D sensor prototype
  5. Shape sensor prototype
  6. Shape sensors for robotics, automated manufacturing, air bag deployment, identification, safety, scientific measurement, interactive toys, etc.
  7. Clothing-thin biomechanical measuring and recording devices for ergonomic studies, physical rehabilitation, virtual reality, sports training, etc.
  8. Miscellaneous applications
  9. Automobile seat sensors: occupant classification for safe air bag deployment
  10. Shape and motion sensing for toys, games, and sports
  11. A simple digital bend sensor with 'one-sided' bistable domes
  12. Individual flex-actuated switches for buttons and keyboards
  13. Sensor construction
  14. Other bend and shape sensor technologies
  15. Bistable dome arrays- using bistable domes for controlling springback and creating shape memory in thin high strength materials.
  16. Flex-actuated Bistable Dome Pump- a flexible pump that pumps when bent.



Multi-dimensional capabilities:  a single sensor strip may be used as simple digital bend sensor and a computer could continuously monitor the radii, location, and orientation of multiple concave and convex curvatures (2D) along the length of the same narrow ribbon of sensor material. Multiple 2D profiles (grids, webs, nets, etc.) could provide 3D shape information (see prototype photos).

Measure and monitor changes in: bend, curvature, displacement, indentation, impact, shape, force, motion, fluid motion, pressure, timing, position, weight, etc. Compare profile features and radii for object identification. Multiple profiles can provide rich digital information of surface shape and motion. Indentation characteristics can be managed with a wide range of variables.

Digital: eliminates the need for analog to digital processing- reduces hardware/interface requirements and cost. Changing bend and shape information can be managed more easily. 

Contact: remote sensing and point-of-view considerations not necessary. Offers an alternative where such systems are too expensive or impractical.

Compliments non-contact/remote sensing systems.

Paper thin/flexible/lightweight/portable.

Low cost: simple mass-producible construction, lower processing requirements than analog sensor arrays.

Large surface capabilities.

Resolution, accuracy, and minimum radius limits will be tied largely to ongoing miniaturization efforts in two well-developed and developing industries. A minimum radius under 1/4" may be obtained in early stages.

Predictability: Behavior of simple one-piece bistable dome component is very predictable, ideal for artificial intelligence/machine learning.


Flex actuated bistable domes: The basis for the technology is a very shallow bistable dome with a circular perimeter formed in thin hard materials. Flex-actuated bistable domes are almost flat, a slight indentation, and may have a height not much more than the thickness of the material it is formed in. Dome diameter may be 40 times material thickness (for example).

When the material around an individual dome is bent far enough toward the same side as the dome it will buckle and turn inside out, snapping from the inside of the curvature toward the outside. The increment of flexure necessary to invert a single dome is determined by its structural and material characteristics.

Material hardness is required to minimize or preferably eliminate absorption of flexural forces that switch domes.

A bistable dome can be included in a paper thin flexible circuitry laminate to make it into a contact switch that can be monitored by computer. By being on or off the switch indicates whether it has been bent to one side of flat or the other at its particular location. An individual bistable dome measures a single increment of flexure or bend angle.

Overlapping bistable domes: Overlapping domes are structurally linked and function as individual bistable components of a longer bistable structure that runs along the middle of the dome row. Switching forces that switch individual domes are shared and transferred along the tops of the domes and their intersecting perimeters.

Functionally, the length of this central bistable structure is measured not along the tops of the domes but as a total of the straight distances between the overlapping dome perimeters. To make a 2D sensor the dome row is constructed so that this central structure is slightly longer than its two edges. 

The edges are suspended in the neutral flex axis of the overall sensor construction and wherever the sensor is bent this difference in length creates switching forces proportional to the radius of curvature of the edge.

As long as switching forces are not absorbed in the material the bistable domes are forced to switch from one side of the neutral flex axis to the other to neutralize those forces. Only a certain predictable number and pattern of domes can remain on either side of any 2 dimensional profile that the edge describes.

The patterns can be used to digitize three parameters necessary for profiling complex 2D curvature — orientation, radius, and location.


A basic 2D sensor uses a row of bistable domes with overlapping perimeters formed in a single narrow strip of metal.

Curvature orientation: The 2D prototype sensor is constructed so that when it is flattened approximately every other switch is oriented to the same side. The bistable domes are forced from the inside to the outside of a curvature and the computer can determine whether a curvature is positive or negative/up or down with respect to flat, regardless of the sensor's position in space.

Curvature radius: For any particular section of the sensor the number of switches that are forced to the outside of a curvature is proportional to the magnitude of the local flexural stresses, which are proportional to the radius of curvature. When all of the switches in a particular section of the sensor are on it has reached its minimum measurable radius in that section and on that side of flat. When all of the same switches are off the same section of the sensor has reached its minimum measurable radius in the opposite side of flat.

Curvature location: The location of each switch on the sensor is known by the computer so it can determine where the sensor is being bent.



Two videos demonstrate a low resolution sensor prototype made from a row of 31 overlapping bistable domes (8 inches long) formed in .006 inch thick, 302 type stainless steel (sometimes used for spring mechanisms).

Each dome is wired to an LED which lights up when contact is made in the up position and goes out when in the down position (a few aren’t working). The sensor and contact wires are protected in a longer length of clear vinyl tubing (21 inches long) which also serves to contain the edge of the metal bistable dome row. A much thinner design is possible using standard commercial flexible circuitry.

Video 1 demonstrates the proportionality between the bend radius and the number of bistable domes that are on or off. It also demonstrates the sensor’s ability to indicate which direction from flat the sensor is bent. The switches have a tendency to group but a more uniformly constructed rows with better edge containment show a more even distribution.

Video 2 demonstrates the sensor’s unique 2D capabilities. The bistable domes not only indicate how much, and in which direction from flat the sensor is bent, but where it is bent.

See: Flex-actuated Bistable Dome Pump - a simple pump that pumps when bent, for another description and diagrams. Volume pumped is proportional to flexure.



The simple low resolution sensor prototype shown in pictures at right demonstrate how flex actuated bistable dome sensors can be used to determine a wide range of parameters for measurement and identification, without remote sensing.

Construction: 5 rows of bistable domes are made into switches and suspende/protected between a sandwich of 2 thin polycarbonate strips. The metal rows of overlapping bistable domes are attached to the flexible polycarboate strips only by their edges. The switches are actuated by flexure as the edges of the bistable dome row, not by contact with the domes.

The 5 sensors are attached at each end and kept seperate and parallel to each other. The switch rows are at rest in a convex position with all switches off. As the sensors are bent toward concave, contact is made to light five corresponding rows of LEDs displayed behind the sensor.

When flattened approximately half are on and half are off.



include robotics, automated manufacturing, air bag deployment, identification, safety, scientific measurement, interactive toys, etc.

  • Smart pads, bumpers and wheels for object identification, measurement, location, guidance, avoidance and safety.
  • Robot gripper pads- deflection and indentation of the sensor provides position, force, profile, and slippage information.
  • Shape sensing conveyor belt rollers and accessories could help count, identify, and monitor location of objects, etc.
  • Offers many possibilities for making automation softer, safer and more human interactive.
  • Low cost and large area options.



Existing technologies used for measuring human motion are expensive and have limited capabilities for measuring complex motion. Bistable dome sensor technology will allow the creation of a wide range of low cost sensors for measuring simple as well as complex human motion:

  • For ergonomics studies, physical rehabilitation, electromechanical aids, virtual reality, sports training, and other human/computer interface purposes.
  • For measuring simple bend/angle such as for finger, elbow, knee.
  • For measuring complex motion such as wrist, ankle, shoulder, neck, back.
  • Clothing thin and flexible with little or no interference to normal motion- may be worn comfortably and unobtrusively.
  • Inexpensive and simple enough for personal use- simple motion analysis/recorders.
  • Will simplify and lower the cost of computer analysis.
  • Easily adapted for a wide range of tasks such as for measuring and counting specific motions, angles, repetitions, etc.
  • Versatility - multi-dimensional position-independent capabilities will make positioning and sizing easier.



2D profile measuring tape: Portable wrap around sensor for measuring 2D radii, profile, and contour as well as length. Biological, medical, morphological, anthropological applications. Also for inventory, identification and counting classification, and measurement in industrial and retail applications, perhaps where bar code technology is impractical.

Thin flexible sensor ribbons could be used to monitor fluid motion- surface wave motion as well as subsurface motion and turbulence in fluids and gasses.

Tools for measuring and fitting the human body- for medical, prosthetic, athletic, clothing, shoes, furniture, etc.

Smart carpet for gait analysis, security/alarm, safety, identification- a grid of sensors could be placed between a carpet and carpet padding to provide presence, position, weight, shoe print and gait information. May add accuracy/redundancy to other identification methods.

Smart handles and doorknobs for comparison of palm and relative finger position/size/force imprints- for door entry and equipment, vehicle, and handgun use.

Portable soft shape sensor with position and orientation sensors might save time when used to establish starting points, such as corners, edges, objects in a room, for instance, for building virtual environments and characters, etc.



Seat sensors could help control air bag inflation according to passenger characteristics such as weight, size, shape, and position. Pressure and bend sensor arrays presently being considered cannot provide the 2D or 3D profiling that will be required by tomorrow's 'smart seat'. Bistable dome seat sensors can add unique multidimensional shape information and increase the range of parameters used in passenger classification while simplifying processing requirements.

The use of indentation shape and size information may solve problems that pressure sensors exhibit in rough road conditions. As long as the seat cushion remains in close contact with the passenger, certain shape information will remain the same whether the passenger is bouncing or stable. The same might apply to extreme seat belt tensioning of children.

Other automobile related applications include identification for security, starting, automatic personalized seat adjustment, crash test dummies, vehicle impact studies, and smart tires.



Low cost medium resolution bistable dome sensors can be used to make a wide variety of new electronic toys, games, and athletic training devices, such as:

  • Very low cost virtual reality gloves and other human motion monitoring sensors. 
  • Targets that keep score for games or athletic training analysis. 
  • Bats, balls, punching bags, etc., that tell how fast, hard, where, and how many times they are hit.
  • Squeezable controllers and joy stick handles with programmable button/trigger locations for individualized comfort or preference.
  • Flex sensitive buttons/triggers that respond to changing finger pressure in discrete digital increments.
  • Low cost digital position sensing for advanced game control and interface devices (see low cost 3D position control).



A low cost and easily constructed option for digitally measuring single point bending for certain applications may be the 'one sided' non overlapping flex actuated bistable domes as described in US Patent 5563458. 

One-sided domes collapse when bent to a certain point and stay actuated as long as the material continues to be bent in the same direction past that point. When the flexure is reversed they can return to their original state at the same angle or point of flexure, depending on their design.

A grid of such domes formed in thin flexible metal might start with all switches off and the more it is bent the more switches go on. The starting profile doesn't have to be flat. Actuation timing/sensitivity can be controlled in manufacture.



Flex actuated bistable dome switches that respond indirectly to pressure might be made smaller and thinner than switches that respond directly to pressure. Small groups of such switches could be used to make very simple button sensors that indirectly monitor changing pressure in multiple digital increments. See 'one-sided' bistable domes in Patent 5563458.

Thin one piece flexible circuitry construction may offer advantages for multiple button assembly, perhaps lowering cost while offering greater flexibility in keyboard, joystick and game control design.



The sensor combines two well developed mass production technologies. Sensor resolution, accuracy, and minimum radius limits will be tied largely to ongoing miniaturization efforts in common high tech industries.

Bistable Domes: Formed in hard flexible materials. It is important that switching forces are not absorbed by the material the dome is formed in. Simplicity of the dome structure suggests it is well suited for computer aided design and manufacture. Dome characteristics such as its bistable nature, sensitivity, tactility, actuation range, etc., can be engineered to suit a variety of sensing requirements and applications by manipulating the relative dimensions and material characteristics of the dome and/or the flexible substrate it is attached to.

Flexible Circuitry Construction: The dome layer can be included in a flexible circuitry laminate. The basic sensor design follows standard flexible circuitry mass production design parameters. Flex manufacturers commonly laminate circuitry with thin metals such as stainless steel. Flex circuit construction allows for rapid prototyping and low tooling costs, and short runs are common. This will make product development and customization easier. The flexible circuitry industry is well developed and competitive. See: Shape sensor design example for flexible circuitry.

Finished Form: In its simplest form a single 2D sensor might be a thin flat ribbon that would be protected in plastic, perhaps looking and behaving like a cable/wire tie such that it could only bend within a 2D plane perpendicular to its flat surface. Such a sensor could monitor its own 2D profile (of multiple complex curvatures) and changing profile along that 2D plane.

Design Considerations: A sensor's at rest or starting shape can be flat or contoured. The sensor's flexibility and paper-thin profile offers design versatility for a wide range of applications. It could be attached to or included in many different flexible materials. Sensitivity would depend largely on overall sensor flexibility. 

Individual domes or arrays of individual non-overlapping domes, and to a lesser extent overlapping domes, can be customized in construction to be non-equally bistable so that a larger percentage of domes are active for a particular application. For specialized applications the 'one-sided' bistable domes referred to in the Patent 5563458 (Fig. 7) may be useful. Note: Patent illustrations are simplified and not to scale.

The basic sensor design suggests modular possibilities for many different applications. For applications requiring multiple simultaneous samples or multidimensional measurement, sensor arrays might be constructed with circuitry connections in one piece. Multiple 2D profile sensors can be included in a single construction. Large area possibilities.



Bistable dome sensing technology offers a number of advantages over currently available bend and shape sensors.

Existing angle/bend sensors (fiber optic, strain gauge, mechanical, etc.) can be very accurate but are analog, position dependent, and incapable of actual 2D sensing.

Current contact/tactile shape sensing technologies attempt to provide 2D and 3D information with arrays of independent one dimensional analog angle or force/pressure measurements. They are impractical and inadequate except in specialized applications. Processing requirements, physical limitations, and high cost limit them from many everyday applications that could be satisfied with low-cost, low and medium resolution bistable dome sensor technology.

Until now remote sensing technologies have offered the only real possibilities for multidimensional shape sensing. Bistable dome sensors can complement remote systems or even replace them in applications where high resolution is not of primary importance- particularly where high cost, time, processing requirements, or the necessity of having an external point of view are limiting.



Flex actuated bistable domes can be used to make a very simple pump. The overlapping dome row is enclosed in a flexible housing and displacement is created when it is bent back and forth. Volume pumped is proportional to the change in degree of curvature. Flow is directed by check valves. Its simple design is well suited for small or large scale. A single dome may be used as well.

It can be actuated with a wide range of motions such as wave, wind, animal, the relative motion between mechanized parts, etc.

Applications include renewable energy generation, fluid and air pumping, desalination, and automated lubrication of moving parts.

Detailed description: Flex-actuated Bistable Dome Pump.

See also: US Patent # 6132187- Flex-actuated Bistable Dome Pump (expired).



Contact: bistabledomes at




Fist indentation increasing in same place 

Flat surface registers as approximately half on and half off, depending on pressure and position