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A novel piezoelectric actuator using a two-stage flexure hinge structure is proposed in this paper, which is used in a compact and high-precision electromechanical field. The two-stage flexure hinge structure is used to provide horizontal thrust and vertical clamping force to the driving feet, which solves the problems of unstable clamping force and insufficient load capacity in traditional stick-slip piezoelectric actuators. Firstly, the main structure of the driver and the working process under the triangular wave excitation voltage are briefly introduced. Secondly, after many simulation tests, the structure of the actuator is optimized and the stability of the structure in providing clamping force is verified. Finally, through the research of the operating performance, when the amplitude is 150 V and the frequency is 3.25 kHz as the excitation source, the maximum speed can reach 338 mm/s and can bear about 3 kg load. It can be seen from the analysis that the two-stage flexure hinge structure can improve the displacement trajectory.

The multidimensional motion ultrasonic motor with a single spherical stator is studied in this paper. It has the characteristics of miniaturization and can be used in precision motion applications. By bonding six identical pieces of piezoelectric ceramic onto the stator and applying the voltage signal of high frequency, the deformation of the inverse piezoelectric effect is used to excite the stator yaw vibration mode. The orthogonal superposition of the modes of the spherical stator on the driving foot produces elliptical trajectory around X, Y, and Z directions by different excitation methods. According to the yaw vibration mode of the spherical stator, 12 driving feet are designed to drive the rotation of the spherical rotor. The structure and mechanical characteristics of the motor are simulated by using simulation software, and the transient response of the stator driving foot was obtained, which proved its feasibility. Finally, the output performance of the motor in actual operation is given through experiments, which provides a new reference scheme in the field of precise multi-degree-of-freedom motion. At a voltage of 100 V and a frequency of 26.7 kHz, the prototype has a no-load speed of 73, 70, and 114 rpm around X, Y, and Z axes, respectively.

Let µ be a positive Borel measure on the interval [0, 1). The Hankel matrixa n z n is an analytic function in D, the Hilbert operator is defined byThe Derivative-Hilbert operator is defined asIn this paper, we determine the range of the Hilbert operator and Derivative-Hilbert operator acting on H ∞ .

Let µ be a positive Borel measure on the interval [0, 1). For γ > 0, the Hankel matrix H µ,γ = (µ n,k ) n,k≥0 with entries µ n,k = µ n+k , where µ n+k = ∞ 0 t n+k dµ(t). formally induces the operatoron the space of all analytic functions f (z) = ∞ k=0 a k z k in the unit disc D. Following ideas from [5] and [7], in this paper, for 0 ≤ α < 2, 2 ≤ β < 4, γ ≥ 1, We characterize the measure µ for which H µ,γ is bounded(resp.,compact)from D α into D β .