Kinematic Model and Performance Research of Zero Stiffness Cross Reed Flexible Hinge_Hinge Knowledge

The flexible mechanism is a groundbreaking concept in the field of mechanics, as it utilizes the elastic deformation of materials to transmit motion, force, or energy. This mechanism has gained popularity in various industries, including precision positioning, MEMS processing, and aerospace, due to its numerous advantages such as zero friction, seamless operation, easy maintenance, high resolution, and integrated processing capabilities.

However, the traditional rigid mechanisms still dominate the market due to certain limitations of the flexible mechanism. One of these limitations is the positive stiffness that occurs in the functional direction during the action of the mechanism. This positive stiffness requires a larger driving force and strict requirements on the driver, which ultimately reduces the energy transfer efficiency. These shortcomings have hindered the wider application of the flexible mechanism.

To overcome the adverse effects of positive stiffness, many scholars have introduced the concept of zero stiffness into the flexible mechanism. By cleverly using negative stiffness to offset positive stiffness, a mechanism with zero stiffness can be achieved. Such a system, also known as a flexible static balance mechanism, can achieve a static equilibrium state at any point in the range of motion. This type of mechanism offers several advantages, including excellent force transmission performance, the ability to operate with smaller driving forces, and high energy transmission efficiency. Consequently, the research focus in the field of flexible static balance mechanisms has mainly been on flexible micro-clamps.

Among the various components of flexible mechanisms, flexible hinges have received significant attention due to their exceptional characteristics. The relative travel of generalized cross-reed flexible hinges is relatively short, making them highly valuable for a wide range of applications. Consequently, the zero-stiffness flexible hinge based on this design has become the preferred choice for constructing complex flexible static balance mechanisms, making its research highly significant.

To achieve zero stiffness characteristics in flexible hinges, it is necessary to offset the torsional positive stiffness with rotational negative stiffness. In this regard, a rotational negative stiffness model has been developed. The model involves using a leaf spring composed of two overlapping reeds, one fixed and the other free. When the deformation of the opening end is relatively small compared to the length of the reed, the spring exhibits good linearity and can be analyzed as a zero-length spring.

The analysis of the rotational negative stiffness model considers the torques exerted by the two springs on a specific point in the system. Based on the triangular sine law, the torques can be expressed mathematically. By combining these torques, the total torque exerted on the point can be determined. This analysis reveals that when the angle of rotation is less than 90 degrees, the springs exert a torque in the same direction as the rotation angle, thereby creating rotational negative stiffness.

To establish an accurate zero-stiffness flexible hinge model, it is crucial to analyze the mechanical properties of the generalized cross-reed flexible hinge. This analysis considers various factors such as the influence of radial force and pure torsional load on the hinge's torsional stiffness. By understanding these factors, the dimensionless torsional stiffness of the hinges can be calculated. The conceptual model of the zero-stiffness flexible hinge can then be obtained by replacing the revolving pair and balance springs in the rotational negative stiffness model. This conceptual model is symmetrical, allowing for the analysis of counterclockwise rotation of the moving platform.

To verify the accuracy of the theoretical model, finite element analysis using Ansys software is conducted. The analysis involves simulating and analyzing the moment-rotation angle characteristics of the zero-stiffness flexible hinge. The results are then compared to the theoretical calculations. The simulation is performed on hinges with different parameters, and the stiffness of the balance spring is gradually adjusted until the hinge's stiffness is reduced to zero. By comparing the simulation results and theoretical calculations, it is confirmed that the theoretical model accurately represents the behavior of the zero-stiffness flexible hinge.

Furthermore, the feasibility of using leaf springs as balance springs in zero-stiffness flexible hinges is explored. A finite element model is established for this purpose, and the simulation results are compared to those obtained using the Combine14 element. The results once again validate the accuracy and reliability of the theoretical model.

In conclusion, the use of rotational negative stiffness to offset positive stiffness in flexible hinges allows for the creation of zero-stiffness flexible hinge systems. These systems offer numerous advantages, including reduced driving torque, improved force transmission performance, and increased energy utilization efficiency. Two different balance methods, namely double balance springs and single balance springs, are analyzed, and their static equilibrium conditions are determined. The theoretical results are then verified through finite element analysis. The study confirms that the double balance spring method is suitable for scenarios where the radial force does not affect the hinge's stiffness, while the single balance spring model has a wider range of applications. However, the latter model's axial space compactness is somewhat compromised, necessitating comprehensive consideration during structural design. Overall, the research on zero-stiffness flexible hinges and their applications holds significant importance in advancing the field of flexible mechanisms.