Maltese-cross force sensors
Size a multi-axis force sensor
before you cut metal.
This calculator dimensions the flexures of a Maltese-cross force sensor, predicts the strain each gage will read on every axis, and finds the geometry that hits your target output. The model is shear-corrected beam theory, cross-checked against finite-element results and against measured bridge output on a built prototype.
- 6channels
- Fx Fy Fz Mx My Mz
- 7parameters
- a through g, in millimetres
- 500µε
- typical design target
- < 3% error
- vs FE at the gage on Fz, Mx and Mz; Fx within 9%
Plan view · draft-optimised geometry
mm
- Strain gages
- Elastic beams
- Boundary beams · platform
What the tool does
Three problems, one model.
A Maltese-cross sensor is a compromise between sensitivity and stiffness, resolved across seven dimensions at once. Change the beam length and every channel moves. These tools let you work the compromise deliberately instead of by iteration.
Forward analysis
Enter the seven flexure dimensions and the gage position. Get micro-strain on all six channels, the strain profile along the beam, per-channel sensitivity, and the root-stress safety factor.
- Six-channel gage output
- Strain profile along the flexure
- Root stress and overload margin
Dimension optimizer
Set a target output — or individual goals per channel — put bounds on each dimension, and let a deterministic multistart search return the geometry that lands closest while staying inside the size envelope.
- Target or goal-attainment modes
- Lockable bounds per dimension
- Envelope-constrained search
FEA cross-check
The beam model is only worth what it agrees with. Compare the predicted strain path against finite-element results case by case, with the error at the gage and the mesh convergence delta shown alongside.
- Path comparison per load case
- Error at the gage position
- Mesh convergence delta
Anatomy
Seven dimensions decide everything.
A square platform is suspended by four elastic beams arranged in a cross. Each beam ends in a thin boundary beam that spans tangentially and anchors into the outer frame — that compliant end is what lets the cross deflect predictably instead of behaving like a plate. Gages sit on the top surface of the elastic beams, at a position you choose.
Every part shares one top plane, machined from below, so the whole sensor comes off a single setup and the gages bond to a continuous surface.
| Key | Parameter | Draft optimum |
|---|---|---|
| a | Width of elastic beam (in-plane) | 8.3 mm |
| b | Height of elastic beam (vertical) | 4.2 mm |
| c | Length of elastic beam | 17.5 mm |
| d | Width of boundary beam (along beam axis) | 1 mm |
| e | Length of boundary beam (tangential span) | 40 mm |
| f | Height of boundary beam | 9.8 mm |
| g | Width of central square platform | 21.8 mm |
| x | Gage position from the platform edge | 6 mm |
The overall footprint is constrained by 2c + 2d + g, which the tools track against a size limit you set — 62 mm by default.
Method
Verified, then published.
Shear-corrected beam theory
The flexures are short and deep, where ordinary bending theory under-predicts deflection. The model carries the shear term and the compliance of the boundary beam, so the end condition is part of the answer rather than an assumption.
Checked against finite elements
Quadratic-element models of the full sensor are solved for each load case and the strain path along the beam is extracted. Agreement is judged over the middle half of the beam, away from the root fillet where a stress concentration lifts the FE result.
Checked against hardware
The draft prototype's bridge output was measured at roughly 491 µε under rated load. The model predicts 493 µε for the same geometry — inside half a percent.
Computed server-side
The model itself runs on our servers. This page sends dimensions and loads, and renders what comes back. Nothing about the formulation is shipped to your browser.
Start from the draft optimum, or from your own envelope.
Both tools open pre-filled with a verified working design. Change what you need to change — the safety panel and the envelope gauge will tell you when you have gone too far.