Loadcells
Measuring displacement of a point or surface, rather than measuring the deformation of a flexure, offers many possibilities for compact, low-cost load cells. This page gathers some resources on this topic and presents work towards a simple six degree-of-freedom (DOF) loadcell based on these ideas.
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

Honeywell Hall Effect Handbook
as5013-test/ contains pcb source files for a board to evaluate 3d tracking using the AS5013 (nominally an 8-bit 2-axis device). This IC contains an array of 5 hall effect elements for measuring


To characterize the use of the AS5013 as a three-dimensional tracking device, we use a 5 axis stage (2 axes motorized, 3 manual) built around two Thorlabs PT1M micrometer stages. After setting a magnet height and orientation, we can sample the 5 hall elements over a two dimensional array of magnet displacements. Executing this for a handful of magnet heights should let us fit functions for X, Y, and Z in terms of the 5 hall readings.
6 DOF Concept
A concept for a 6 degree of freedom magnetic load cell is shown below. It uses a pair of flexures (aluminum or titanium plates on top and bottom) to set relative stiffnesses of Fx, Fy, Fz, Tx, Ty, Tz. A central rod carries a disk with four small neodymium magnets which moves when loads are applied. Four AS5013 hall array ICs are positioned just below the rest positions of the magnets on a single PCB. M3 standoffs and screws hold the entire stack together.

Features of a "good" 6 DOF flexure:
- Ability to tune relative stiffnesses (e.g. Fx/Fz, Tx/Tz, etc.)
- Minimal cross talk (e.g. Fx doesn't induce a displacement in y or a twist, etc.)
- Fits into a reasonably small bounding volume.
Fusion 360 lets us quickly test loading cases for flexure designs. Below are simulations of a force and a moment applied to the loadcell.