Optimal Design of Hexapod Mechanism Parameters for Large Stroke Flexible Hinge_Hinge Knowledge_Talls

Abstract:

The performance of a large-stroke flexible hinge Hexapod mechanism relies heavily on the performance of the flexible hinge. A larger stroke in the flexible hinge results in lower off-axis stiffness, thereby reducing the overall static stability, stiffness, and accuracy of the mechanism. This paper discusses the inverse kinematics solution of the Hexapod mechanism, including the expansion and contraction length of each branch chain and the rotation angle of each hinge. Based on this, the parameters of the Hexapod mechanism with a large-stroke fully flexible hinge are optimized to minimize the stroke requirements of each hinge while meeting the motion space requirements of the moving platform.

Optical systems are extensively used in various ultra-precision engineering fields such as optical microscopes, semiconductor production, and space exploration. In order to ensure the accuracy of the optical path, precise positioning systems are required for optical components. The positioning accuracy requirements of sub-mirror splicing of large-aperture space telescopes, such as the Space Spherical Optical Telescope (SPOT), are extremely high. Traditional parallel robots with kinematic pairs, such as ball joints and universal joints, are used for precise positioning of optical components. However, these mechanisms can cause loss of precision. To overcome this, a new type of parallel robot with flexible hinges as kinematic pairs has been developed. Flexible hinges offer advantages such as a simple structure, no friction, and high precision, enabling highly precise and accurate systems. However, traditional fully flexible parallel robots have limited working space, mostly in cubic micron level. To achieve a larger stroke, two-stage kinematic mechanisms are often used, which increases system complexity and cost. To address this, researchers have developed flexible parallel robots with large strokes. This paper focuses on the parameter optimization design of a large-stroke flexible hinge Hexapod mechanism for precise positioning of optical components.

Kinematics Inverse Solution:

A pseudo-rigid body model of the flexible hinge Hexapod mechanism is established, and the flexible hinge is assumed to be a spherical joint with rotational stiffness. The inverse kinematics solution involves determining the expansion and contraction length of each branch chain and the rotation angle of each hinge. The rotation matrix of each branch chain is calculated, and the rotation angles of the flexible hinges are obtained. With the known rotation matrices, the overall rotation matrix of each branch chain is calculated. The rotation angles of each joint relative to the initial position can then be determined. The joint motion amounts or angles can be obtained by subtracting the initial positions or attitudes from the obtained values.

Hexapod Parameter Optimization:

The optimization design of Hexapod mechanism parameters aims to minimize the maximum deformation of the flexible hinges while meeting the workspace requirements. The design parameters include the radius of the circles connecting the fixed and moving platforms, the height between the fixed and moving platforms, and the angles. The optimization process involves finding the maximum rotation angle and movement of the flexible hinges for different platform parameter combinations. The weight-sum of these maximum values is calculated, and the platform parameters that result in the smallest weight-sum are considered optimal. The design parameters can be classified into three categories based on the weights assigned to the