Multi-Point Tendon Vibration

• Multi-point tendon vibration is a technique that applies controlled vibrations at discrete tendon sites to induce neuromechanical responses and precise distributed sensing.
• Advanced fiber-optic and multimodal sensing architectures capture high resolution spatial and temporal vibration profiles for improved signal disambiguation.
• This approach is pivotal in applications like VR haptics, surgical robotics, and biomechanical monitoring by mitigating nonlinearities and enhancing control fidelity.

Multi-point tendon vibration refers to the application, measurement, or exploitation of vibrational phenomena at multiple discrete sites along tendons—either biological (for neuromechanical and perceptual research) or artificial (in robotic and sensing systems). Research in this domain spans fields including biomechanics, virtual reality haptics, minimally invasive surgical robotics, and fiber-optic sensor engineering. Multi-point tendon vibration systems are utilized to achieve fine-grained sensing, induce and control kinesthetic illusions, mitigate nonlinearities in tendon-driven mechanisms, and monitor distributed mechanical events with high spatial and temporal resolution.

1. Principles of Multi-Point Tendon Vibration

Multi-point tendon vibration exploits the physical and physiological properties of tendons to either induce specific neuromechanical responses or obtain distributed sensing data. In biological contexts, mechanical vibration applied to multiple tendon sites simultaneously elicits responses in muscle spindle afferents and Golgi tendon organs, leading to altered proprioception—such as illusions of movement or the modulation of perceived limb heaviness (Ushiyama et al., 20 Oct 2025, Hirao et al., 2022). In artificial systems, vibrational energy is injected or detected at multiple locations along tendons or tendon-like structures to sense distributed mechanical inputs, mitigate hysteresis, or enable precise control (Chatterjee et al., 2021, Park et al., 4 Mar 2025, Monteiro et al., 26 Sep 2025).

2. Fiber-Optic Sensing Architectures for Multi-Point Vibration

Photonic and fiber-optic sensing frameworks constitute a foundational technology for multi-point tendon vibration measurement:

• Concatenated Modal Interferometers: Systems deploy multiple modal interferometers along a single optical fiber using photonic crystal fiber (PCF) sections, with each interferometer acting as an independent probe. Mechanical strain from tendon vibration alters the effective length (L) of the PCF section, leading to shifts in the optical interference pattern. The response of the $j$th interferometer is characterized as

$$I_j = I_{cr} + I_{cl} + 2\sqrt{I_{cr} I_{cl}} \cos(\phi)$$

where $\phi = \frac{2 \pi L (n_{cr} - n_{cl})}{\lambda}$ and $I_{cr}, I_{cl}$ are the core and cladding mode spectral intensities, respectively. Vibrational fields $X = X_0 \sin(\omega t + \varphi)$ induce periodic interference peak shifts, enabling simultaneous monitoring of amplitude, frequency, phase, and vibration sequence at each sensor point. The global sensitivity is additive: $S_{total} = \sum_{j=1}^N S_j$ (Chatterjee et al., 2021).

• Multimodal Speckle-polarization Fiber Sensing: Advanced approaches combine speckle analysis in multimode fibers (MMFs) with polarization interrogation in single-mode fibers. Local perturbations induce unique speckle field changes, mathematically described by $$I(r,t) = |E(r,t)|^2 = |\sum_{j=1}^N a_j(t) \psi_j(r) e^{i\phi_j(t)}|^2$$, and allow centimeter-scale localization of vibration sources. High-bandwidth polarization sensing completes the temporal response up to at least 40 kHz, enabling reconstruction of complex, distributed vibration profiles (Monteiro et al., 26 Sep 2025).
• Implementation and Signal Disambiguation: The superposition of signals from multiple interferometers or modes requires sophisticated spectral analysis (wavelet transforms, FFTs) and, in some cases, inversion of sensitivity matrices using techniques such as Moore-Penrose pseudo-inverses. Photonic sensing platforms offer high spatial resolution, environmental robustness, and immunity to electromagnetic interference.

3. Neuromechanical and Perceptual Effects of Multi-Point Tendon Vibration

Applying mechanical vibration at multiple sites along human tendons induces a range of perceptual and neuromotor phenomena, largely mediated by muscle spindle and Golgi tendon organ afferents:

• Kinesthetic Illusions and Weight Perception: Vibrating the flexors of the wrist, elbow, and upper arm (typically at 70-80 Hz, with amplitudes 5 g–70 m/s²) induces illusions of arm extension or resistance, systematically increasing perceived heaviness during lifting tasks. The psychophysical point of subjective equality (PSE) shifts by up to 42% (from 304 g to 427 g in a 300-g reference task), with statistical significance (Cohen's d = 2.05, p < 0.001). Posterior (extensor) stimulation trends toward decreasing heaviness but is not statistically robust (Ushiyama et al., 20 Oct 2025).
• Pseudo-Haptics in Virtual Reality: Simultaneous multi-tendon stimulation acts as "noise" on haptic cues, raising the detection threshold for discrepancies between visual and physical motion—by approximately 13%—and thereby extending the dynamic range of pseudo-haptic effects. Notably, vibration-induced weight cues are equivalent to a visual gain of 0.64, allowing the effective simulation of multiple discrete virtual weight levels in VR tasks. Just Noticeable Difference (JND) in weight discrimination remains essentially unaltered with vibration (0.19–0.20), maintaining perceptual resolution (Hirao et al., 2022).

Table: Summary of Perceptual Modulation via Multi-Point Tendon Vibration

Effect	Modulation (Magnitude)	Statistically Significant?
Perceived Heaviness (Flexors)	Increase (PSE shift +42% for 300g reference)	Yes
Perceived Heaviness (Extensors)	Decrease (PSE −11%)	No
Detection Threshold in VR	Increase (+13%)	Yes
Weight Discrimination (JND)	No degradation (0.19–0.20)	-

4. Mitigation of Hysteresis in Tendon-Driven Mechanisms via Vibration

Tendon-sheath mechanisms (TSMs), ubiquitous in minimally invasive surgery (MIS) and robotics, are subject to complex hysteresis due to friction, backlash, and elasticity. Multi-point (or distributed) vibration along the tendon trajectory has been shown to mitigate these nonlinearities:

• Vibration-Assisted Compensation: Longitudinal vibration is generated via an eccentric crank-slider mechanism, imparting a displacement $x \approx l + r\cos(\theta)$ (eccentricity $r=0.2$ mm). Experimental studies across 0–100 Hz revealed up to 23.41% reduction in RMSE for position tracking (from 2.2345 mm to 1.7113 mm) and an 85.2% reduction in MAE when combined with a Temporal Convolutional Network (TCN) model for compensation (from 1.334 mm to 0.1969 mm). Dead zones and phase lag are diminished, enabling more accurate, robust, and efficient control strategies (Park et al., 4 Mar 2025).
• Integration with Neural Compensation Models: TCNs trained on data with applied vibration learn the (linearized) system dynamics more efficiently, reducing the parameter count needed for high-accuracy compensation and exhibiting improved validation MSE (0.091 with vibration vs. 0.1596 without for the smallest model).

These findings confirm that, for tendon-based actuation in precision systems, controlled vibration applied at multiple points can directly enhance model tractability and practical performance.

5. Control and Calibration of Vibration Effects

The magnitude of both mechanical and perceptual effects induced by multi-point tendon vibration can be systematically controlled by varying the amplitude, frequency, and spatial configuration of stimulation:

• Amplitude and Saturation: Detailed psychophysical studies demonstrate a non-linear relationship between vibration amplitude (10–70 m/s²) and perceived heaviness, with at least three levels of detectable modulation in the 350–450 g range for a 300 g reference. Saturation or decrease in effect is observed at the highest amplitudes, potentially implicating reflex phenomena or vibrotactile interference (Ushiyama et al., 20 Oct 2025).
• Individual Variability: Anatomical and perceptual sensitivity necessitate calibration for optimal and reproducible results, especially in VR and haptic device applications (Hirao et al., 2022).
• Localization and Bandwidth: Fiber-optic sensing approaches achieve centimeter-scale spatial localization and bandwidths up to 40 kHz, leveraging the orthogonal strengths of speckle and polarization modalities (Monteiro et al., 26 Sep 2025).

6. Applications and Implications

Multi-point tendon vibration techniques span diverse application domains:

• Medical Sensing: High-resolution, multi-point vibration detection enables real-time diagnostics and localization of tendon pathologies, non-invasive monitoring during rehabilitation, and the development of advanced biomechanical assessment platforms (Chatterjee et al., 2021).
• Haptic Interaction and Virtual Reality: Programmable vibration at several tendon sites allows rendering of virtual object heaviness, force, and resistance effects without bulky mechanical actuators. This approach augments the dynamic range and granularity of pseudo-haptic feedback for training, simulation, entertainment, and telepresence (Hirao et al., 2022, Ushiyama et al., 20 Oct 2025).
• Robotics and Surgical Systems: In tendon-driven robots, vibration-assisted hysteresis mitigation enhances control fidelity, streamlines neural/hybrid compensation models, and boosts reliability in critical applications such as MIS (Park et al., 4 Mar 2025).
• Structural and Biomechanical Monitoring: Fiber-optic multi-point vibration sensing architectures permit distributed monitoring of mechanical events in extended structures (e.g., pipelines, bridges), as well as real-time tracking of tendon or muscle vibrations in biological tissues (Monteiro et al., 26 Sep 2025).

7. Mechanistic and Theoretical Considerations

The biophysical and perceptual consequences of multi-point tendon vibration are attributed primarily to the activation patterns of muscle spindles and the sensorimotor mismatch framework. Vibration-induced spindle afferent activity scales with frequency and amplitude, leading to perceptual illusions (movement or heaviness) when incongruent with descending motor commands. Mathematical models (e.g., MLE-based sensory integration, force perception functions $$P_{force} \propto f(\text{efferent signals}, \text{afferent activity})$$) provide theoretical frameworks for understanding and quantifying these effects (Ushiyama et al., 20 Oct 2025, Hirao et al., 2022). In engineered systems, the conversion of vibrational signals into spectral or spatial signatures via optical or electronic transduction underlies advances in distributed mechanical and biomedical sensing.

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Multi-point tendon vibration, as investigated across sensing, haptics, robotics, and biomechanics, is characterized by its utility for high-resolution distributed measurement, controlled modulation of kinesthetic perception, mitigation of actuation nonlinearities, and as a foundation for advanced sensing architectures. The field continues to benefit from the convergence of photonic technologies, robust signal processing, and psychophysical calibration methodologies.