Angular displacement sensors are the quiet workhorses of modern engineering. They sit inside CNC machine tools, robotic arms, drones and humanoid robots, feeding back the precise rotational position that keeps motion smooth and machinery accurate. Yet the most widely used technologies—resolvers, capacitive sensors and photoelectric encoders—all share a common weakness: they need external power. In untethered robots and aerial vehicles, that means batteries, and batteries mean weight, bulk and limited operating time. Now a team of researchers writing in Advanced Science has unveiled a sensor that sidesteps this constraint entirely, harvesting its own electricity from the very rotation it measures while achieving arcsecond-level resolution in a package just 50 millimeters across.

The device, called a self-powered angular displacement sensor (SPADS), is built on the triboelectric nanogenerator, or TENG, a technology first introduced by Wang and colleagues that converts mechanical friction into electrical signals through contact electrification. TENG-based sensors have already found roles in energy harvesting, vibration detection and flow monitoring, prized for their simple structure, low cost and broad material adaptability. But when it comes to measuring displacement, TENG sensors have long faced a frustrating trade-off: improving resolution traditionally requires narrower electrodes and denser electrode grids, which in turn weakens the output signal and forces the sensor to grow larger to compensate.

The SPADS breaks this deadlock by borrowing a trick from an entirely different measurement tradition: time-grating technology. Instead of subdividing electrodes ever more finely, the researchers transform the angular position information into the phase of a traveling wave. The sensor consists of a stator and a rotor, both manufactured with standard printed circuit board techniques. Ten dual-sinusoidal copper electrodes, each spanning an 18-degree fan angle, are patterned on the rotor, while the stator carries forty annular fan-shaped electrodes with 8-degree sectors separated by 1-degree gaps. A thin PTFE film covers the stator, serving both as protection and as the high-performance triboelectric material that generates charge during sliding.

As the rotor turns, charge on its copper electrodes attracts opposite charges to the upper surface of the PTFE film, while the stator electrodes compensate through charge flow in the external circuit. The induced potential is proportional to the coupling area between rotor and stator electrodes, and because the rotor electrodes are shaped as sinusoids, the resulting signals vary smoothly as sine waves with rotation angle. Every four stator electrodes are wired together to form one of four output channels, and two non-adjacent channels produce a pair of sinusoidal signals that are spatially orthogonal—offset by exactly 90 degrees of phase.

The clever part comes in the signal processing. The two orthogonal sinusoids are multiplied by a pair of high-frequency reference signals and then summed, producing a traveling wave whose phase encodes the rotor’s angular position. This spatial-to-temporal conversion means that resolution is no longer dictated by electrode width. Instead, it depends on how finely the phase difference between the traveling wave and the reference can be timed. The signals are converted to square waves by comparators and fed into an FPGA with a 50 MHz crystal oscillator, which counts clock pulses between rising edges to determine the phase. With ten pole pairs and a 5 kHz modulation frequency, the theoretical resolution works out to just 5.18 arcseconds—remarkable for a device with no external power supply.

The team validated the design through extensive simulation and laboratory testing. Finite element modeling in COMSOL confirmed the analytical capacitance model, showing how the open-circuit voltage varies sinusoidally with position. The simulations also guided optimization: thinner PTFE films yield stronger output because less charge is trapped within the dielectric, while wider electrodes boost voltage at the cost of resolution. The researchers settled on an 8-degree electrode width as a balance, noting that similar output can be recovered by lengthening the electrodes radially without sacrificing angular precision.

Performance testing with a servo motor and a Keithley 6514 electrometer revealed the sensor’s characteristics across speeds and loads. Open-circuit voltage proved largely independent of rotational speed, since it depends only on the coupling area, while short-circuit current rose with speed—reaching peaks of 0.0042, 0.0089 and 0.0119 microamperes at 10, 20 and 30 rpm respectively. Under a 5-gigohm load, the sensor delivered a peak voltage of 3.64 volts, and output power peaked at roughly 9 nanowatts near 2 gigohms. A 3600-second stability test showed the output voltage remained essentially unchanged throughout, demonstrating robust long-term operation.

Measurement accuracy was assessed over full rotations at various speeds, with the sensor tracking complex motion sequences including reversals, pauses and speed changes. The maximum error stayed within ±716 arcseconds across the entire 360-degree range, with repetitive positioning errors of ±0.352 degrees under uniform motion and ±0.278 degrees under reciprocal motion. The error distribution showed a periodic pattern tied to the cyclic electrode arrangement but no systematic accumulation. The output frequency also tracked rotational speed with a correlation coefficient of 0.9998, confirming the signal’s suitability for precise angle computation.

How does this stack up against the competition? Conventional optical encoders achieve sub-arcsecond to arcsecond resolution but demand external power and occupy moderate to large diameters. Brushless resolvers offer accuracies in the tens to hundreds of arcseconds but require AC excitation and draw more power in larger volumes. Among TENG-based displacement sensors, the comparison is even more striking. The researchers introduce a metric called the resolution conversion rate—the ratio of resolution to electrode width—and the SPADS achieves a value of 1.8×10⁻⁴, orders of magnitude better than previous devices ranging from 0.03 to 1.6. In plain terms, it extracts far more angular precision from a given electrode size than any prior triboelectric sensor.

The implications reach well beyond the laboratory bench. For industrial robotic arms, humanoid robots and UAVs where every gram and every milliwatt counts, a sensor that generates its own signal while resolving rotation to arcseconds could reshape how motion feedback is designed. The SPADS demonstrates that the long-standing tension between resolution and output in triboelectric sensing can be dissolved not by cramming in more electrodes, but by shifting the measurement into the time domain—a conceptual leap that may well define the next generation of self-powered machine perception.

Subject of Research: A self-powered angular displacement sensor based on a triboelectric nanogenerator with time-grating signal processing for high-resolution rotation measurement.

Article Title: A High‐Resolution Self‐Powered Angular Displacement Sensor Based on Triboelectric Nanogenerator With Time‐Grating

Article References: Wang, S., An, D., Liu, S., & Wu, Z. (2026). A High‐Resolution Self‐Powered Angular Displacement Sensor Based on Triboelectric Nanogenerator With Time‐Grating. Advanced Science, 13(56), Article e76634. https://doi.org/10.1002/advs.76634

Image Credits: AI Generated

DOI: 10.1002/advs.76634

Keywords: triboelectric nanogenerator, angular displacement sensor, self-powered sensor, time-grating, robotics, unmanned aerial vehicles, PTFE, FPGA, phase modulation, motion control, encoders, energy harvesting