Planar Six-Axis Force and Torque Sensors
Yu-Jen Wang, Li-Chi Wu, Jian-Dong Ke, Tien‐Fu Lu
Abstract
A novel planar six-axis force and torque (F/T) sensor is proposed, inspired by a 3-RRR compliant mechanism, and having three limbs, each of which has three revolute joints. This design innovatively employs strain gauges on the top and bottom surfaces only, which reduces not only the number of required fabrication processes but also the labor costs associated with attaching strain gauges onto positions that are difficult to access. In this study, the stiffness of the planar F/T sensor associated with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${F}_{x}$ </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">${F}_{y}$ </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">${T}_{z}$ </tex-math></inline-formula> are formulated using inverse kinematics and coordinate transformation methods. For <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}_{x}$ </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">${T}_{y}$ </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 equivalent cantilever beam method is adopted to derive the relationships between loads and strains. Moreover, optimization is performed to determine the optimal design parameters of the F/T sensor. The calibration error using the cubic transformation matrix is 0.29% in the measurement range <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${F}_{x}= {F}_{y}= {F}_{z}= \pm 100$ </tex-math></inline-formula> N, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}_{z} = \pm 10$ </tex-math></inline-formula> Nm, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${T}_{x}= {T}_{y}= \pm 6$ </tex-math></inline-formula> Nm.