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In this work, a cylindrical lead-free rotary-linear ultrasonic motor was attached to piezoelectric plates of MnO₂-doped (Ba_0.97Ca_0.03)(Ti_0.96Sn_0.005Hf_0.035)O₃ ceramics using the first bending vibration to pull a thread output shaft of the interior of a stator. The effect of the proposed ceramics’ d₃₃ and Q_m values are the key factors for ultrasonic motors. Therefore, MnO₂-doped (Ba_0.97Ca_0.03)(Ti_0.96Sn_0.005Hf_0.035)O₃ lead-free piezoelectric ceramics with high values of d₃₃ = 230 pC/N, Q_m = 340.8 and a good temperature stability of their dielectric and piezoelectric properties are suitable for application to linear piezoelectric motors. The structure of the linear piezoelectric motor was simulated and fabricated by Finite Element Analysis. The characteristics of linear piezoelectric motors were also studied. The output characteristics of the lead-free piezoelectric motor were a left-pull velocity = 3.21 mm/s, a right-pull velocity = 3.39 mm/s, an up-pull velocity = 2.56 mm/s and a force >2 N at 39.09 kHz for an input voltage of approximately 200 V_p-p (peak to peak). These results are comparable to those for a lead-based piezoelectric motor that uses PZT-4 ceramics. The proposed lead-free piezoelectric motors were successfully fabricated and used to pull a 0.5 mL commercial insulin syringe.