Loadcells
Force measurement is almost always done by measuring the strain of a structure. Most commonly, this is done using a strain gauge, which is bonded to a surface of a structural member. With good bonds, the strain seen by the member is also seen by the strain gauge and a change is resistance is measured. This approach has long been favored because it produces measurable results while allowing the strained member to remain as stiff as possible (and hence, not interfere with the operation of the measured device).
We can also measure strain of a member by measuring the displacement of a point or surface, rather than measuring the material strain directly. This can be advantageous because it eliminates uncertainty from the bond between the member and a strain gauge. These bonds can exhibit hysteresis, can be temperature dependent, and can be a point of failure of the device. If we measure the displacement of a point or surface using a non-contact method, we can circumvent many of these disadvantages.
Non-contact position measurements have historically not had high enough resolution for load cell applications, but have been used commonly for applications that can tolerate larger displacements. For instance, joystick inputs for machines are often sensed using a non-contact magnetic field measurement (c.f. US5831596A). Similarly, many automotive applications (gas pedals, shifter positions, etc.) that sense large displacements are turning to non-contact measurement for the robustness it offers.
Advances in high sensitivity measurement has made it possible to use non-contact measurement for the small displacements required by force sensing applications. For instance, capacitive sensing is used in high resolution digital calipers and has found use in load cells (US10582023). We breifly describe a prototype 3 axis capacitive load cell in a section below. One downside to these techniques is that relatively large overlapping areas are required for a low noise measurement. In many compact load cell applications (particularly for measuring many degrees of freedom), realizing these geometries can be challenging.
Capacitive
One way to determine the proximity of two surfaces is by measuring the capacitance between them. This page documents experiments with a 3 DOF Capacitive load cell using a single printed circuit board.
It is based on a discrete electrostatics solver (shown below), and also documented on the page above.
Magnetic
Another position measurement uses the magnetic field instead of the electric field. These devices consist of one or more magnetic field generating devices and one or more magnetic field sensing devices, usually arranged in pairs on opposing sides of a flexure. The magnetic field generating devices are arrangements of permanent magnets or electrically driven coils. The magnetic field sensing devices are usually spatial arrays of sensor elements, the measurements of which can be combined differentially to nullify external fields or unintentional displacements. The sensing devices are usually positioned at the region of greatest rate of change of magnetic field strength with respect to the degrees of freedom of the flexure.
Magnetic sensing technologies
Among magnetic field sensing technologies, Hall effect sensors are the most ubiquitous. Integrated circuits with arrays of hall effect sensors are available at extremely low cost in very dense packages. Using differential pairs of these elements, non-contact rotary and linear encoders can be made. A great resource for designing such magnetic devices is the Honeywell Hall Effect Handbook. Austrian Microsystems makes a variety of these devices for sensing position or rotation of a magnet.
For more sensitive, low field devices magnetoresistive sensing elements are often used. David Pappas of NIST compares noise floors of these technologies, noting Hall effect sensors register around 300,000 pT/\sqrt{Hz}, while magnetoresistive show roughly 200 pT/\sqrt{Hz}. Honeywell sells a variety of very sensitive magnetoresistive magnetometers, and NVE Corporation sells sensors based on giant magnetoresistance for very low field measurement. Despite these favorable properties, sensors with these technologies are usually more expensive and less dense than those using the Hall effect.
A similar description holds for fluxgate technology, which can achieve the lowest noise of room temperature magnetic field sensing (10 pT/\sqrt{Hz}), according to Pappas. The sensors achieving this specification are often of cubic centimeter volume, and cost thousands of dollars (c.f. Barrington). Some have been miniaturized, like Texas Instruments' DRV425, but this sensor only reports 1500 pT/\sqrt{Hz}.
Giant magnetoinductance sensors are based on changes in skin depth of a signal due to magnetic field, and show low-noise, low-cost sensing (c.f. https://www.scirp.org/journal/PaperInformation.aspx?PaperID=36471). Interesting prototypes have been built, but nothing is commercially available.
Finally, magneto-electric sensors are a nascent technology with exciting prospects (100 pT/\sqrt{Hz} according to Pappas). In these sensors, a magnetostrictive material (usually a metglas) is combined with a piezoelectric material (usually lead zirconate titonate) into stacked layers. The magnetic field produces strain in the stack, and the piezoelectric materials produce a corresponding voltage that can be read. There is a great Nature Materials paper demonstrating that a common SMD 1206 ceramic capacitor can be used as a 1 cent magnetic field sensor based on this physical phenomenon. Again, this technology is promising, but not yet commercially available.