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

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 i...

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Bibliographic Details
Published in:Symmetry (Basel) Vol. 15; no. 2; p. 562
Main Authors: Zheng, Chao, Zou, Luming, Zheng, Zhi, Xue, Xin
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.02.2023
Subjects:
Algorithms
Analysis
Damping
Degrees of freedom
Efficiency
Extreme environments
Impact resistance
Iterative algorithms
Iterative methods
Jacobi matrix method
Jacobian matrix
Kinematics
Mathematical models
Mechanical devices
Newton-Raphson method
Quaternions
Rubber
Sensors
Singularities
Springs (elastic)
Stiffness
Vibration
Vibration analysis
Vibration control
Vibration isolators
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary: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.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym15020562