Space curve fitting method based on fiber-optic curvature gages

A novel fiber-optic curvature gage, which can measure curvature directly, has been developed in recent years. In order to measure the bending and torsional deformation of space curve shape, an array of looped fiber-optic curvature gages are arranged on two symmetrical surfaces of a flexible layer to form a gage layer system. A calibration method of the gage layer system is proposed. Based on the bending curvature and twist values of space curve structure provided by gage layer system, a moving coordinate system is established by curve tangent and curvature vectors through a differential geometry method. The osculating plane is determined by twist angle in the moving coordinate system. The calculation of curve bending and analysis of the moving coordinate system transformation can be carried out in osculating plane. Then, the space curve is divided into many easily analyzed plane curves. Recursive algorithm is used to obtain the position information of space curve points and the space curve fitting can be realized. The correlative formulas are deduced and the algorithm is validated by a simulation example.

► We propose a fiber curvature gage layer system, which can measure curvature and twist.
► We give a calibration method of fiber curvature gage layer.
► Space curve fitting method is introduced based on curvature and twist values.
► Correlative formulas are deduced and the algorithm is validated by an example.
► The number of curvature and twist values affect accuracy of space curve fitting.