A Sensor for the Synchronous Combined Measurement of Both Linear and Angular Displacement Based on an Alternating Electric Field

The use of multiple sensors for multidimensional measurements can introduce issues such as Abbe errors and installation difficulties. To address this, we introduce a cylindrical sensor that performs concurrent measurements of both linear and angular displacement. The sensor consists of two parts: a moving ruler and a fixed ruler. When the moving ruler moves linearly or rotates relative to the fixed one, the sensor can realize the simultaneous measurement of linear and angular displacement of the relative movement by calculating the inductive signal output from the moving ruler. By establishing a column surface displacement measurement model, this study characterized the interrelationship between the phases of axial and circumferential electrical signals and actual displacement information, providing theoretical support for the design of a novel sensor structure. The feasibility of this measurement principle was validated through a simulation of the sensor model. A physical cylindrical sensor prototype was then manufactured using flexible printed circuit board (PCB) technology, and a testing platform was built on which to perform linear and rotational movement synchronization experiments. The experimental results showed that this novel sensor exhibited a linear displacement measurement error of $34.8~\mu $ m over a distance of 100 mm, and an angular displacement measurement error of 68 within an angle range of 0°–360°. These results verified the accuracy of our earlier theoretical analysis and emulation.