High-Accuracy Cylindrical Capacitive Sensors Designed According to a Posture Error Model for the Combined Measurement of Linear and Angular Displacements

The combined measurement of linear and angular displacements using a single two-dimensional (2D) sensor is of considerable interest in robotics, precision machining, and related fields. However, existing 2D sensors are subject to numerous sources of error and limited measurement ranges that greatly restrict their use in these fields. Moreover, relatively few studies have analyzed these error sources and established posture error models for optimizing sensor designs. The present work addresses these issues by proposing a novel cylindrical capacitive 2D sensor composed of a stator subject to linear displacements in thexdirection and a rotor subject to rotational displacements about thexaxis. First, a mathematical model of sensor measurements is derived, and a corresponding mathematical model of posture error is constructed to analyze the influence of deviations between the stator and rotor on the measurement accuracy. Second, the posture error model is applied to optimize the sensor design by arranging four sets of induction electrodes in offset configurations along the linear and rotational directions, and thereby suppressing both periodic and long-range measurement errors. Furthermore, the validity of the proposed modifications is demonstrated based on the results of numerical electric field calculations. Finally, the obtained results are verified experimentally based on systematic analyses of the measurement performances observed for a prototype sensor. The prototype sensor achieves a linear displacement measurement accuracy of 17.3 μm within a 0–100 mm range and an angular displacement accuracy of 58.3″ over a 0–360° range. Accordingly, the posture error model reported herein provides critical guidance for the design, structural optimization, and error compensation of cylindrical capacitive 2D sensors.