Series representations for the rectification of a superhelix

Lim, Sungyeop; Han, Sangmin

doi:10.1016/j.apm.2017.12.011

Cited by 2 publications

(5 citation statements)

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“…Note that (7) has no τ in it, meaning that the local surface strain on the bending cylinder is independent of the torsion of the central curve, the rate of change of the bending direction of the cylinder. This is fairly counter-intuitive to us, because we know that the arc length of a superhelix largely depends on τ, as proven in our previous works [13,14]. This also means that we cannot determine τ directly from the surface strains during the actual process of shape sensing of a cylinder, though we can of course obtain τ indirectly from its relation with ω and ψ.…”

Section: Determining the Local Deformation Factors From The Local Str...mentioning

confidence: 90%

“…In order to alleviate this problem of α-dependence, it may be worthwhile to re-adopt the formula for the arc length of a superhelix from our previous works [13,14]. In our preliminary tests, where we modeled the changed length of the strainsensing interval as the arc length of a segment of a superhelix, it was observed that the influence of α on the accuracy was dramatically reduced.…”

Section: Discussionmentioning

confidence: 99%

“…During this process, the fiber segments are assumed to take the form of segments of superhelices, as shown in figure 2. In our previous works [13,14], we derived the equation of a superhelix, as…”

Section: Determining the Local Deformation Factors From The Local Str...mentioning

confidence: 99%

“…Suppose smid is the array of parameter s at the midpoints of the segments, and psi is the array of ψ values of the segments. Then, we can obtain the array of dψ ds at the midpoints as dpsids = ppval(fnder(spline(smid, psi),1),smid), and we can finally determine τ by substituting these dψ ds values in (14).…”

Section: Determining the Local Deformation Factors From The Local Str...mentioning

confidence: 99%

“…In our previous works [13,14], we suggested a curve known as a superhelix to model the geodesics on the curved surface of a bent and twisted cylinder. A superhelix is a 3D space curve that is helically coiled around a helix, which can represent the geodesics on the surface of a cylinder subjected to 3D bending, and hence can be used as a deformation geometry model for the shape sensing of a cylinder.…”

Section: Introductionmentioning

confidence: 99%

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Shape estimation of a bent and twisted cylinder using strain from a sensor array in triple helices

Lim

Han

2018

Meas. Sci. Technol.

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This study proposes the use of strain sensors in a triple-helix configuration to measure the bending and twist deformation in a cylinder. Arranging the strain sensors on the cylinder in a triple-helix structure allows us to measure the twist and bending deformation simultaneously. The method consists of two steps: first to determine the local deformation factors from the surface strains, and second to reconstruct the overall deflected shape of the cylinder from the local deformation factors. We derived an exact analytical formula for the surface strain on a bent and twisted cylinder according to the deformation variables based on our original superhelix model, in which we regard the deformed cylinder segment as a helical coil and the sensors bound upon it as segments of superhelices. The local deflection rates are iteratively computed by the Newton-Raphson method using the surface strain formula. We incorporate the local deflection rates into the helical extension method, which is an exact solution to the Frenet-Serret formulas, to reconstruct the overall deflected shape of the cylinder. From the simulations, the proposed method was shown to determine the overall deformation state of a cylindrical body with remarkable precision. The position errors decreased rapidly with shorter spatial intervals of strain sensing and lower rates of the helical periodicity of the sensor arrays, showing a strong trend of convergence. Moreover, the pin-pointedness of the strain sensing was found to be one of the most crucial factors when attempting to ensure high accuracy of the shape estimation results. This study demonstrates a potential for general applicability to various fields, especially for the shape sensing of multicore optical fibers.

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Section: Determining the Local Deformation Factors From The Local Str...mentioning

confidence: 90%

Section: Discussionmentioning

confidence: 99%

Section: Determining the Local Deformation Factors From The Local Str...mentioning

confidence: 99%

Section: Determining the Local Deformation Factors From The Local Str...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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