Miniaturized Six-Degree-of-Freedom Force/Moment Transducers for Instrumented Teeth

Tooth movement in orthodontic therapy is achieved by application of forces and moments to individual teeth. For lack of properly sized force/moment transducers (FMTs), the measurement of the applied force and moment vectors has remained a challenge. This paper reports on two six-degree-of-freedom FMTs termed Designs A and B, which were developed for this purpose. Their measurement principle makes use of the fact that external loads acting on them cause mechanical stress distributions, which are mapped using piezoresistive microsensors integrated in CMOS sensor chips. In Design A, two metal pins sandwich a single sensor chip, whereas in the newer Design B two CMOS chips are mounted in a back-to-back configuration between two pins. With a diameter of 4.5 mm and length of 16.4 mm, Design B is slightly larger than Design A, but still comparable with a tooth root. The two designs were calibrated and tested by applying forces and moments in the clinically relevant ranges of ±3 N and ±30 Nmm. The design changes from Designs A to B improve the smallest singular value of the sensitivity matrix by a factor of 10. The resolution achieved by Design B is 21 mN, 39 mN, and 100 mN for the three force components and <inline-formula> <tex-math notation="LaTeX">${24\times {10^{-3}}}{~\text {Nmm}}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">${33\times {10^{-3}}}{~\text {Nmm}}$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">${4\times {10^{-3}}}{~\text {Nmm}}$ </tex-math></inline-formula> for the three moment components. In comparison with Design A, these values represent improvements by factors of 2.3 to 4.5.