A Novel FBG-based Tri-Axis Tip Force Sensor: Design, Modeling, and Application

This article presents the design, modeling, and application of a miniature tri-axis tip force sensor with fiber Bragg grating (FBG) for cardiac ablation. A compliant mechanism (CM) composed of thin-walled beams is designed to convert the distal forces applied at the tip of the sensor to the variations of the wavelengths of the FBGs. The CM design reserves the middle channel for an optical fiber used in laser ablation (LA). The differential principle is utilized to eliminate the impact of the environmental temperature on orthogonal forces (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{f}_x},\ {{f}_y}$</tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{f}_z}$</tex-math></inline-formula>). The uniqueness condition for the measurement of forces and temperature is established. To enable rapid iteration of sensor design, an accurate and efficient reduced-order global transfer matrix method is proposed to develop the unified statics/dynamics model of the sensor. Static calibration experiments reveal resolutions of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$11.6{\rm{\ mN}}$</tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4.7{\rm{\ mN}}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$6.2{\rm{\ mN}}$</tex-math></inline-formula> for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ - x$</tex-math></inline-formula>, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ - y$</tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ - z$</tex-math></inline-formula> axes, respectively. The force ranges are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0--2\mathrm{N}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ - 1\sim 1\mathrm{N}$</tex-math></inline-formula> for axial and flexural directions. Modal test shows the 1<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> natural frequency of 1071.6 Hz. Linearity, repeatability, and hysteresis errors are below <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5.3{\rm{\% FS}}$</tex-math></inline-formula>. A novel application involving LA with the designed sensor on an ex vivo tissue from a pig heart was conducted to help understand the thermomechanical interaction between the laser and the tissue.