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Vibration-assisted machining, known as hybrid processing technology, offers several benefits over conventional machining methods. However, developing mechanical structure designs to generate a non-resonant frequency source remains challenging. The objective of this study is to propose a novel design for an XY flexure positioner by combining the pseudo-rigid-body model with the Lagrange technique, finite element analysis and Crayfish optimization algorithm. Firstly, the mechanism was designed by combining a hybrid amplifier and parallel driving mechanism integrated with right circular hinges to increase the natural frequency and precision for potential application to VAM CNC milling. Then, the analytical model was established by the pseudo-rigid-body and Lagrange method. Next, the theoretical result was verified by finite element analysis. The first natural frequency results of theory and FEM methods were found at 990.74 Hz and 1058.5 Hz, respectively. The error between the two methods was 6.4%, demonstrating a reliable modeling approach. Based on the analytical equations, the Crayfish optimization algorithm was utilized for optimizing the main design variables of the mechanism. Next, the prototype was fabricated. The results showed that the experimental and simulated frequencies were 1127.62 Hz and 1216.6 Hz, with an error between the two methods of 7.31%. Finally, the workpiece was installed on the prototype and a real vibration-assisted CNC milling process was carried out in the frequency range [700 Hz, 1000 Hz]. The best surface roughness of the specimen was achieved at a frequency of 900 Hz with a Ra of 0.287 µm. This demonstrates that the proposed XY mechanism is an effective structure for generating a non-resonant frequency source for vibration-assisted machining. [ABSTRACT FROM AUTHOR]

We introduce a comprehensive analysis of several approaches used in stock price forecasting, including statistical, machine learning, and deep learning models. The advantages and limitations of these models are discussed to provide an insight into stock price forecasting. Traditional statistical methods, such as the autoregressive integrated moving average and its variants, are recognized for their efficiency, but they also have some limitations in addressing non-linear problems and providing long-term forecasts. Machine learning approaches, including algorithms such as artificial neural networks and random forests, are praised for their ability to grasp non-linear information without depending on stochastic data or economic theory. Moreover, deep learning approaches, such as convolutional neural networks and recurrent neural networks, can deal with complex patterns in stock prices. Additionally, this study further investigates hybrid models, combining various approaches to explore their strengths and counterbalance individual weaknesses, thereby enhancing predictive accuracy. By presenting a detailed review of various studies and methods, this study illuminates the direction of stock price forecasting and highlights potential approaches for further studies refining the stock price forecasting models. [ABSTRACT FROM AUTHOR]