Kinematics Modeling and Singularity Analysis of a 6-DOF All-Metal Vibration Isolator Based on Dual Quaternions

Abstract

Driven by the need for impact resistance and vibration reduction for mechanical devices in extreme environments, an all-metal vibration isolator with 6-degree-of-freedom (6-DOF) motion that is horizontally symmetrical was developed. Its stiffness and damping ability are provided by oblique springs in symmetrical arrangement and a metal–rubber elasto-porous damper. The spring is symmetrically distributed in the center axis of the support load surface. It is necessary to investigate the kinematics and the singularity before conducting multi-body dynamics analysis of the vibration isolator. Based on the theory of dual quaternions, the forward kinematics equations of the isolator were successively derived for theoretical kinematics modeling. In addition, an enhanced Broyden numerical iterative algorithm was developed and applied to the numerical solution of the forward kinematics equations of the vibration isolator. Compared with the traditional rotation-matrix method and Newton–Raphson method, the computational efficiency of the enhanced Broyden numerical iterative algorithm was increased by 680% and 290%, respectively. This was due to the enhanced algorithm without the calculations of any inverse matrix and forward kinematics equations. Finally, according to the forward kinematics Jacobian matrix, the position-singularity trajectory at a given orientation and the orientation-singularity space at a given position are calculated, which provides a basis for the algorithm of the 6-DOF vibration isolator to avoid singular positions and orientations.

Experimental Investigation of the Three-Point Bending Property of a Sandwich Panel with a Metal Rubber Core

“…The diameter of the spiral coil, when maintained within a range of 5 to 15 times the diameter of the metal wire, ensures that the metal wire inside the metal rubber products forms a stable interlocking and biting state. Accordingly, the diameter of the spiral coil wound in this work was 3 mm [4]. The spiral coil underwent equal pitch stretching after winding, which ensured the pitch after stretching was approximately equal to the diameter of the spiral coil, effectively improving the uniformity of the quality of the blank.…”

“…Metal rubber products inherit the inherent properties of metal wire and exhibit elasticity and damping properties similar to rubber-like polymer materials. They enhance reliability and environmental adaptability and have been successfully applied in various fields, such as aerospace and biomedicine [3][4][5].…”