2. Concept and Design
2.2. Maintaining Internal Tension
2.3. Displacement Change Measurement
3.1. Basic Model
3.3. Advanced Model
3.3.1. Gap between Parts
3.3.2. Shape of the Cross Section
3.4. Sensor Gain
3.5. Axial Force Robustness
3.6. Axial Rotation Robustness
4. Characteristics of the Proposed Bend Sensor
- Low costThe proposed sensor is made of low-cost materials and can be manufactured easily without specialized fabrication techniques. The sensor can be assembled with off-the-shelf parts within 15 min.
- High degrees of freedom for the sensor’s dimensionsThe dimensions of the sensor are determined by the diameter and length of the helical coil. Thus the size of the sensor can be easily and finely adjusted because there is a wide range of choices for the diameter of the extension spring, and the spring can be cut to the desired size.
- Intuitive and easy to useThe principle of the proposed sensor is the mechanical conversion of information about bending to information about displacement of the sensing wire. Thus the measurand of the proposed sensor is the displacement of the sensing wire. Because there are various options for the displacement transducer, the user can select one based on their preferences. No complex signal processing or specialized data acquisition device is required because the measurement from the displacement transducer is proportional to the bend angle of the sensor.
- No directionalityThis sensor can detect bending in any direction because the helical coil’s shape and properties are symmetrical along the axial line. And because the sensing wire is placed in the center of the helical coil, the axial displacement of the sensing wire changes with bending in any direction along the helical coil.
- Measures the accumulated bend angleThis sensor cannot detect the direction of bending or the specific location where bending occurs because it only measures one-degree-of-freedom information, that is, central displacement changes of the coil. However, it can detect the accumulated bend angle along the sensor, as depicted in Figure 4, because any local bending along the helical coil causes a central displacement change along the sheath.
- Large sensing rangeThe sensor’s physical sensing range is restricted only by the maximum bend curvature of the helical coil that does not cause permanent strain on the sheath. Widely used extension springs made of spring steel or stainless steel have high elasticity and can enable large curvature of the sensor.
- Theoretical performanceThe theoretical performance of the sensor depends on the design parameters and performance of the sensor that is used to measure the displacement change of the sensing wire. The Hall-effect sensor provides high performance for both a linear and a rotary configuration. An incremental Hall-effect encoder with 8192 counts per resolution can provide 0.2° resolution for a bend sensor consisting of a 3-mm outer diameter helical coil and a 6-mm diameter spool. A potentiometer is an economical option that provides sufficient performance.
- Bend stiffnessThe bend stiffness of the sensor is determined by the stiffness of the helical coil and the tension of the sensing wire. A large spring constant and a large-diameter coil lead to high bend stiffness of the sensor because energy is required to elongate the spring coil, as shown in Figure 6. Also, greater tension in the sensing wire and a larger helical coil diameter contribute to the restoring force from the sensing wire, which increases the bend stiffness. Bend stiffness increases as the sensor bends if a spring is used to provide tension on the sensing wire. Because bend stiffness can be modeled as a function of design parameters, a bend stiffness profile can be adjusted by changing the radius of the spool and the constant of the linear spring. An actuator can be used as a tensioning device to provide more degrees of freedom for the stiffness profile or to allow variable sensor stiffness.
- Environmental robustnessThe absence of electronic components on the bending part ensures good robustness to environmental conditions. Stainless steel, Teflon, and aramid, which are used in the helical coil, liner, and sensing wires, respectively, have high chemical resistance and thermal resistance (the melting point of Teflon and aramid is 327 °C and 500 °C, respectively). Because the sensor is mechanically operated, it is immune to electromagnetic interference and moisture, allowing it to be used even when submerged in boiling water or high-temperature oil.
5. Prototype Development
6.1. Quasi-Static Experiment
6.2. Static Large Deflection Experiment
Conflicts of Interest
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|Property||Proposed Sensor||Flex Sensor||Optical Fiber-Based Sensor|
|Length||Unlimited 1||Fixed||Unlimited 1|
|Measurand||Position||Electrical resistance||Light 2|
|Module size 3||Medium||Compact||Large|
|Fabrication||Simple||Off the shelf||Complicated|
|Stiffness 5||Adjustable||Fixed||Depends on fiber|
|Helical coil||Extension spring: Φ3.0 mm × Φ2.0 mm × 500 mm||$1|
|Lining||Outer Teflon tube: Φ1.38 mm × Φ1.88 mm;|
Inner Teflon tube: Φ1.40 mm × Φ0.90 mm
|Wire||Braided Dyneema wire: Φ0.45 mm||$0.1|
|Structure||3D printed with VeroWhitePlus™ (Objet Connex; Stratasys Ltd., Eden Prairie, MN, USA)||$1|
|Spring||Miniature extension spring||$0.3|
|Displacement sensor||Hall-effect sensor: RMB20IC13BC10 (RLS; 8192 pulses per turn, ±0.5° accuracy, 0.18° hysteresis, onboard RC filter with 720 Hz cut-off frequency for sine and cosine signal of magnetic flux); Magnet: Φ4 mm × 4 mm||$50|
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