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The advance of minimally invasive interventional surgeries has accelerated the iterative upgrading of continuum surgical robots. High compatibility with robotic applications and high precision are key features of sensors for robot navigation. In this paper, a spun multi-core fibre (SMCF) 3D shape sensor for continuum surgical robots is proposed. The sensor is fabricated by ultraviolet (UV) light inscribing fibre Bragg gratings (FBGs) in the SMCF, showing good spectra characteristics. Shape reconstruction is realized by the Frenet–Serret (F–S) frame and sensing characteristics such as twisting, strain and temperature are systematically analyzed. Especially, the twisting characteristics of SMCF and MCF are compared and the feasibility of self-torsional compensation of SMCF is demonstrated. In addition, shape measurement experiments with three known shapes are performed. The mean relative error (MRE) for each shape is 0.49%, 1.90% and 5.13%, respectively. These results show that the proposed sensor can accurately measure 3D shapes with temperature and twisting compensation, enabling its application prospects in the online shape feedback of continuum surgical robots. [ABSTRACT FROM AUTHOR]