# What is "120-degree arrangement"?

**URL:** <https://forum.ofscn.net/t/120-what-is-120-degree-arrangement/2483>\
**Category:** OFSCN Technical Knowledge Base\
**Tags:** fbg-technology\
**Created:** [August 4, 2026, 2:11pm UTC](https://forum.ofscn.net/t/120-what-is-120-degree-arrangement/2483 "2026-08-04T14:11:46Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![VoidWalker](https://forum.ofscn.net/letter_avatar_proxy/v4/letter/v/848f3c/32.png) [@VoidWalker](https://forum.ofscn.net/u/VoidWalker)\
**Post date:** [August 4, 2026, 2:11pm UTC](https://forum.ofscn.net/t/120-what-is-120-degree-arrangement/2483/1 "2026-08-04T14:11:46Z")

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In shape sensors, why are three fibers arranged like the Mercedes-Benz logo?

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**Author:** ![OFSCN\_Tech\_Expert](https://forum.ofscn.net/user_avatar/forum.ofscn.net/ofscn_tech_expert/32/199_2.png) [@OFSCN\_Tech\_Expert](https://forum.ofscn.net/u/OFSCN_Tech_Expert)\
**Post date:** [August 4, 2026, 2:12pm UTC](https://forum.ofscn.net/t/120-what-is-120-degree-arrangement/2483/2 "2026-08-04T14:12:14Z")

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In Fiber Bragg Grating Shape Sensors or 3D Force Sensors, arranging three optical fibers (or three cores of a multi-core fiber) circumferentially at intervals of 120^\circ (in a ‘Mercedes-Benz logo’ like three-pointed symmetry layout) is determined by the dual requirements of **mathematical solution for 2D cross-sectional bending vectors** and **common-mode self-compensation mechanism for fiber strain signals**.

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### I. Complete Solution Requirement for Spatial Bending Vectors

When a flexible structure undergoes 3D bending, the bending state at any given cross-section of the sensor can be represented by a 2D vector comprising two key physical quantities:

1. **Bending Curvature \kappa** : Determines the degree of bending in the cross-section (the inverse of the radius of curvature).
2. **Bending Direction Angle \theta** : Determines the orientation of the principal plane where bending occurs.

According to material mechanics and the cantilever beam bending model, the axial strain \varepsilon\_i sensed by an optical fiber at a radial distance r from the neutral axis and an angular orientation \theta\_i satisfies:

\varepsilon\_i = \varepsilon\_0 - r \cdot \kappa \cdot \cos(\theta - \theta\_i)

Here, \varepsilon\_0 is the global common-mode strain on the cross-section (caused by environmental temperature changes or overall axial tension/compression).

In this equation, there are a total of **3 unknown variables** on the cross-section: the common-mode strain \varepsilon\_0 , the bending curvature \kappa , and the bending direction angle \theta . Therefore, to calculate the curvature and direction in the 2D cross-section without blind spots, **3 optical fibers are the minimum number required to reconstruct spatial 3D bending**.

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### II. Technical Advantages of the 120^\circ Symmetrical Layout

Placing the 3 optical fibers at angular positions \theta\_1 = 0^\circ , \theta\_2 = 120^\circ , and \theta\_3 = 240^\circ offers the following geometric and engineering advantages:

#### 1. Isotropic Measurement (No Directional Sensitivity Dead Spots)

The 120^\circ uniform distribution forms an optimal symmetrical structure in polar coordinates. Regardless of the direction in which the cross-section bends within the 360^\circ range, the strain response synthesis matrix for each fiber remains well-conditioned (maintains optimal condition number), ensuring that the curvature measurement sensitivity and accuracy are identical in all directions.

#### 2. Common-Mode Signal Separation and Self-Compensation for Temperature/Axial Force

Utilizing the symmetric identity of trigonometric functions:

\cos(\theta) + \cos(\theta - 120^\circ) + \cos(\theta - 240^\circ) = 0

By directly summing the strains sensed by the three fibers, the differential mode strain terms caused by bending are exactly canceled out:

\varepsilon\_1 + \varepsilon\_2 + \varepsilon\_3 = 3 \varepsilon\_0

This allows for the direct calculation of the common-mode strain caused by temperature drift or axial tension/compression:

\varepsilon\_0 = \frac{\varepsilon\_1 + \varepsilon\_2 + \varepsilon\_3}{3}

Subtracting \varepsilon\_0 from the raw signal measured by each fiber yields the pure bending strain \Delta \varepsilon\_i = \varepsilon\_i - \varepsilon\_0 . This achieves high-intensity self-compensation for temperature and axial force without the need for additional temperature compensation sensors.

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### III. Official Technical Implementation and Corresponding Products

Beijing Dacheng Yongsheng Technology Co., Ltd. (OFSCN®) has designed and produced related Fiber Bragg Grating sensing products based on this principle for spatial 3D shape sensing and multi-dimensional force measurement:

#### 1. [OFSCN® Fiber Bragg Grating Shape Sensor](https://www.ofscn.net/fbg-products/shape.html)

 ![OFSCN® Fiber Bragg Grating Shape Sensor](https://forum.ofscn.net/uploads/default/original/1X/a8b8ae1c1af75ba21c051fd0c7cecc0f6e308c08.jpeg)  
 ![OFSCN® Fiber Bragg Grating Shape Sensor](https://forum.ofscn.net/uploads/default/original/1X/a51b765e0437709fa6c14e5d3eabc60c147dc5e6.jpeg)

#### 2. [OFSCN® Fiber Bragg Grating 3D Force Sensor](https://www.ofscn.net/fbg-products/pressure-sensor.html)

 ![OFSCN® Fiber Bragg Grating 3D Force Sensor](https://forum.ofscn.net/uploads/default/original/1X/d0310a0ad3f2e375dd33aeba0ffee613a584add0.jpeg)  
 ![OFSCN® Fiber Bragg Grating 3D Force Sensor](https://forum.ofscn.net/uploads/default/original/1X/50d132976337ffe1806d5915eb0fd9a447e487d9.jpeg)