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Page 8 of 15 Zhong et al. Soft Sci. 2025, 5, 3 https://dx.doi.org/10.20517/ss.2024.52

from 0° to 30° and then returning to 0°. We recorded the signal response throughout this process to ensure
the accuracy and reliability of the data. Figure 3C shows the testing results at a time range of 10,000 s. The
insets offer detailed views of the signal within the initial, intermediate, and concluding ten cycles. As can be
seen, both the red and blue light signals exhibit stability and maintain near-synchrony. The root-mean-
square errors (RMSEs) calculated for the red and blue lights during the initial ten cycles and the concluding
ten cycles demonstrate values of 1.26% (red light) and 1.37% (blue light), respectively.

The resolution of the proposed sensor underwent further testing. The sensor was securely affixed to the
bending mechanism (with a rotation radius of 15 mm) using adhesive tape [Supplementary Figure 4]. The
operation of the stepper motor was controlled by pulse signals generated by a microcontroller, with each
pulse causing the motor to rotate by 0.5°. The step angles of the stepper motor were set by varying the
frequency of these pulse signals. The stepper motor induced incremental rotations at step angles of 10°, 5°,
and 2.5°, respectively, and the stepwise signals of the corresponding sensor were observed. Consequently,
the sensor’s limit resolution can reach up to 2.5°, as shown in Figure 3D. The negligible deviation observed
between the measured angle and the established ground truth confirms the high precision of the proposed
sensor.

To validate the accuracy of the bending angle without calibration, the DCLS sensor underwent bending
around rotation axes with radii of 10, 12, 15, and 18 mm, respectively. The bending radius of the sensor is
the same as the rotating shaft radius of the test apparatus. The sensor underwent a 90° rotation by the test
apparatus. As depicted in Figure 3E, the DCLS sensor demonstrates consistent and reliable angle
measurements even when adapting to varying bending radii. To verify the universal application of the
DCLS sensor in different joints without calibration, a comparative experiment of three types of bending
sensors was conducted, including a non-stretchable sensor, a stretchable sensor, and the DCLS sensor
[Supplementary Movies 1 and 2]. The study evaluated their performance in measuring the bending angles
of wrist, elbow, and knee joints by employing distinct joint protective equipment tailored to each sensor
type (detailed information can be found in Supplementary Texts 4 and 5). Participants were instructed to
wear the equipment and bend their joints from a neutral state to a bending state of 30°. With only a single
calibration, the traditional non-stretchable bending sensor exhibited measurement errors of 5.2%, 22.8%,
and 43.3% for the wrist, elbow, and knee joints, respectively [Supplementary Figure 5A]. Meanwhile, the
stretchable bending sensor demonstrated measurement errors of 1.3%, 33.3%, and 183.3%, respectively
[Supplementary Figure 5B]. In contrast, the DCLS sensor recorded errors of less than 2% when measuring
the bending angles of the three distinct joints [Supplementary Figure 5C], demonstrating its superior
calibration-free characteristics and adaptability across diverse joint configurations. A comparison of the
experimental results of the three sensors can be found in Supplementary Figure 5D and Supplementary
Table 1. Moreover, Supplementary Table 2 also provides a comparison of the performance between
conventional optical waveguide-based bending sensors and DCLS sensor. More details can be found in
Supplementary Figures 6-8.

Finally, additional tests were conducted to evaluate the sensitivity of the DCLS sensor to impact and
temperature, and its tolerance to mechanical stress. The DCLS sensor was mounted on a fixed basement
and subjected to strikes of 40, 80, and 120 kPa via strike rod. The signal response of the sensor was observed
to fall within the range of [0.0, 0.05]. Furthermore, the signal response under impact was compared among
the proposed sensor and traditional flexible bending sensors [Supplementary Text 5, Supplementary Figure
9]. To further examine the pressure limit of the sensor, the sensor was mounted beneath a standard force
sensor (DY-920, DAYSENSOR, China), and pressure was applied starting from 0 to 1,000 kPa. The
experimental findings have ascertained that the withstand pressure level of the DCLS sensor, within its