# Research on Decoupling Measurement Technology for 2-DOF Angular Signals Based on Spherical Capacitive Sensors

## TL;DR

This paper introduces a new method using spherical capacitive sensors to accurately measure two-degree-of-freedom angles in precision motion mechanisms.

## Contribution

The paper proposes an improved decoupling model and a novel real-time circuit for measuring 2-DOF angles with high precision and reduced calibration complexity.

## Key findings

- The proposed method achieves an angle measurement resolution of 0.001°.
- It significantly reduces system calibration complexity and suppresses random errors from device parameter dispersion.

## Abstract

As a core functional component of multi-degree-of-freedom precision motion mechanisms, spherical hinges are widely used in high-end equipment fields such as industrial robots, vehicle engineering, and intelligent manufacturing. Their dynamic performance directly determines the motion accuracy and the level of intelligent control of the equipment. The high-precision real-time measurement of two-degree-of-freedom (2-DOF) angles is a key prerequisite for achieving precise closed-loop control of spherical hinges. However, due to the strong coupling characteristics between the 2-DOF angle signals, it is difficult to directly and accurately measure the angular motion parameters of spherical hinges, which has become a core technical bottleneck restricting the improvement in their application efficiency. To address this challenge, this paper presents an improved study of the previously proposed spherical differential quadrature capacitance sensor for measuring the 2-DOF angle signals of spherical hinges. Firstly, the 2-DOF angle signal decoupling model is reconstructed and optimized. Secondly, a real-time decoupling circuit architecture for phase-shift detection with single-frequency signal excitation is innovatively proposed. This solution effectively addresses the incomplete decoupling of 2-DOF angle signals in previous studies, as well as the problems of considerable measurement noise, low resolution, and high calibration difficulty caused by random amplitude and phase errors in the excitation signals. Through the construction of an experimental platform for verification tests, the results show that the proposed scheme can significantly suppress the random errors caused by the parameter dispersion of the device, achieve an angle measurement resolution of 0.001°, and simultaneously considerably reduce the complexity of system calibration, laying a key technical foundation for the engineering application of spherical hinges in the fields of precision measurement and high-performance control.