The speed of an electromechanical scanner is limited by its first resonance frequency. To maximize scan speed, input signals are required that contain negligible frequency components near, or above the first resonance frequency. Such signals are usually obtained by low-pass filtering the desired scan trajectory. However, this introduces curvature and ripple into linear (constant velocity) scan regions. In this work, input signals are designed with guaranteed linear regions and minimal harmonic components above a chosen frequency. The proposed scanning trajectories are proven by simulation and experiment to induce less vibration than existing techniques.