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The VIVACE device, which utilizes flow-induced vibration for harvesting ocean current energy, has been a research hotspot in the field of renewable energy. In this study, the flow-induced vibration characteristics and energy conversion efficiency of a D-section prism were investigated using the k-ω SST turbulence model and Newmark-β method. The vibration amplitude, frequency, equilibrium position offset, and energy conversion efficiency of the two-degree-of-freedom cylinder were systematically analyzed at seven angles of attack between 0 and 180 degrees. The Reynolds number ranged from 368 to 14,742, corresponding to equivalent speeds of 2 to 20. The results indicate that the angle of attack has a significant influence on the flow-induced vibration response of the D-section prism. As the angle of attack changes, the vibration amplitude of the cylinder continuously increases, and the cylinder sequentially enters the vortex-induced vibration, vortex-induced vibration-galloping, and fully galloping branches. The change in the angle of attack disrupts the symmetry of the cylinder’s vibration in the streamwise direction, leading to a shift in the equilibrium position of the cylinder’s vibration. When the angle of attack is 0°, the energy conversion efficiency of the column reaches a maximum of 11.75%. Additionally, at high Reynolds numbers, the vibration of the cylinder is not self-limiting, making it more advantageous for energy conversion devices compared to cylinders with circular cross-sections.

Piezoelectric accurate actuation plays an important role in industrial applications. The intrinsic frequency of previous actuators is invariable. However, variable frequency can approach the range near the low-intrinsic-frequency and realize a high actuation capability. The frequency-variable linear and rotary motion (FVLRM) principle is proposed for rotor-blade-based two-degree-of-freedom driving. Inertial force is generated by frequency-variable piezoelectric oscillators (FVPO), the base frequency and vibration modes of which are adjustable by the changeable mass and position of the mass block. The variable-frequency principle of FVPO and the FVLRM are recognized and verified by the simulations and experiments, respectively. The experiments show that the FVLRM prototype moves the fastest when the mass block is placed at the farthest position and the prototype is at the second-order intrinsic frequencies of 42 Hz and 43 Hz, achieving a linear motion of 3.52 mm/s and a rotary motion of 286.9 mrad/s. The actuator adopts a lower operating frequency of less than 60 Hz and has the function of adjusting the natural frequency. It can achieve linear and rotational motion with a larger working stroke with 140 mm linear movement and 360° rotation.

In recent years, vortex-induced vibration (VIV) has been widely employed to collect small-scale wind energy as a renewable energy source for microelectronics and wireless sensors. In this paper, a two-degree-of-freedom (2DOF) VIV-based piezoelectric energy harvester (VIVPEH) was designed, and its aerodynamic characteristics were thoroughly investigated. First, based on the traditional model theory and combined with the knowledge of vibration dynamics, the governing equations of the 2DOF VIVPEH were established. The dynamic responses, including the displacement and voltage output, were numerically simulated. Compared with the traditional 1DOF VIVPEH, the 2DOF VIVPEH proposed in this paper produced two lock-in regions for broadband wind energy harvesting. Furthermore, it was unveiled that the first- and second-order resonances were induced in the first and lock-in regions, respectively. Subsequently, a parametric study was conducted to investigate the influences of the circuit and mechanical parameters on the energy harvesting performance of the 2DOF VIVPEH. It was found that when the 2DOF VIVPEH was induced to vibrate in different lock-in regions, its optimal resistance became different. Moreover, by varying the masses and stiffnesses of the primary and secondary DOFs, we could adjust the lock-in regions in terms of their bandwidths, locations, and amplitudes, which provides a possibility for further customization and optimization.

To overcome high periodic maintenance requirements, difficult replacement, and large application limitations of wireless sensor nodes powered by chemical batteries during the vibration control process of stiffened plates, a two-degree-of-freedom diagonal beam piezoelectric vibration energy harvester was proposed. Multidimensional energy harvesting and broadband work are integrated into one structure through the combined action of oblique angle, mass blocks, and piezoelectric beam. The mechanical model of the beam is established for theoretical analysis; the output characteristics of the structure are analyzed by finite element simulation; a piezoelectric energy harvesting experimental bench is built. The results show that: The structure has a wider harvesting band, multi-order resonant frequency, multi-dimensional energy harvesting, and higher output voltage and power than the traditional cantilever structures. The output performance of the specimens with 45° oblique angle, 5 g:5 g mass ratio, and 0.2 mm thickness of piezoelectric substrate is good in the frequency band of 10~40 Hz. When the excitation frequency is 28 Hz, the output voltage of the sextuple array structure reaches 19.20 V and the output power reaches 7.37 mW. The field experiments show that the harvester array can meet the requirements of providing auxiliary energy for wireless sensor nodes in the process of active vibration control of stiffened plates.

Symmetries play very important in the dynamics of robot systems. The relevant control of robot arm motion with fault diagnosis including the optimized fuzzy algorithm based on the error rate adjustment P, I, D value (Fuzzy PID algorithm) model relies on symmetry principles. A robot is a kind of mechanical device that can program and perform certain operations and mobile tasks under automatic control. The manipulator is a very complex multi-input multi-output non-linear system and the main actuator of the robot. This paper focuses on the design of a control algorithm for a two-degree-of-freedom (2-DOF) manipulator. First, the mathematical model of a 2-DOF articulated manipulator is established, that is, the functional relationship between the input driving force vector and the output rotation angle vector of a 2-DOF manipulator. Then, a set of trajectory planning algorithms are designed by using gradient model control, which can calculate the trajectory of the end-effector of a 2-DOF manipulator according to the user’s task requirements. The experimental results verify the effectiveness of the proposed algorithm.

This study aims to present a new two-degree-of-freedom (DOF) linear resonant actuator (LRA) and its motion control method without a position sensor. The design method of 2-DOF LRA which resonates with only detent force without a mechanical spring is proposed. Since the information of displacement and direction is required to control 2-DOF LRA, a sensor or an estimator is needed. Therefore, we proposed a position estimator and a motion controller for 2-DOF LRA. This paper proved that reciprocating motion, elliptical motion, and scrolling motion can be controlled without a position sensor. Finite element analysis (FEA) and dynamic simulation results validated the proposed method as well.

In the displacement measurement of the wafer stage in lithography machines, signal quality is affected by the relative angular position between the encoder head and the grating. In this study, a two-degree-of-freedom fiber-coupled heterodyne grating interferometer with large operating range of rotation is presented. Fibers without fiber couplers are utilized to receive the interference beams for high-contrast signals under the circumstances of large angular displacement and ZEMAX ray tracing software simulation and experimental validation have been carried out. Meanwhile, a reference beam generated inside the encoder head is adopted to suppress the thermal drift of the interferometer. Experimental results prove that the proposed grating interferometer could realize sub-nanometer displacement measurement stability in both in-plane and out-of-plane directions, which is 0.246 nm and 0.465 nm of 3σ value respectively within 30 s.

A two-degree-of-freedom direct-drive induction motor (2DoFDDIM), whose solid rotor is coated with a copper layer, is capable of linear, rotary, and helical motions and has widespread applications. For solid-rotor motors, the calculation and analysis of rotor total eddy current loss (TECL) are crucial in studying the factors causing such a loss and possible loss reduction methods. In this study, a new nonlinear analytical method considering the saturation of the rotor core is proposed to solve the fundamental magnetic field. The new method divides the time period into segments. The magnetic field distribution at any time is obtained using Maxwell equations. The eddy current losses in the copper layer and rotor core caused by the fundamental magnetic field are calculated. The surface eddy current losses in the copper layer and rotor core caused by harmonics are calculated using a 2D analytical method. TECL is determined by the sum of eddy current and surface eddy current losses. Coefficients are utilized to consider eddy, saturation, and end-region effects when calculating the rotor core TECL. The new method is verified using 3D FEM, and the results show the proposed method has higher accuracy than the original method. The errors of the rotor core and copper layer TECLs are less than 6 % and 7.3 % , respectively.