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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. [ABSTRACT FROM AUTHOR]

Abstract We discuss existence of factorizations with linear factors for (left) polynomials over certain associative real involutive algebras, most notably over Clifford algebras. Because of their relevance to kinematics and mechanism science, we put particular emphasis on factorization results for quaternion, dual quaternion and split quaternion polynomials. A general algorithm ensures existence of a factorization for generic polynomials over division rings but we also consider factorizations for non-division rings. We explain the current state of the art, present some new results and provide examples and counter examples. [ABSTRACT FROM AUTHOR]

Rigid motion computation or estimation is a cornerstone in numerous fields. Attitude computation can be achieved by integrating the angular velocity measured by gyroscopes, the accuracy of which is crucially important for the dead-reckoning inertial navigation. The state-of-the-art attitude algorithms have unexceptionally relied on the simplified differential equation of the rotation vector to obtain the attitude. This paper proposes a functional iteration technique with the Rodrigues vector (named the RodFIter method) to analytically reconstruct the attitude from gyroscope measurements. The RodFIter method is provably exact in reconstructing the incremental attitude as long as the angular velocity is exact. Notably, the Rodrigues vector is analytically obtained and can be used to update the attitude over the considered time interval. The proposed method gives birth to an ultimate attitude algorithm scheme that can be naturally extended to the general rigid motion computation. It is extensively evaluated under the attitude coning motion and compares favorably in accuracy with the mainstream attitude algorithms. This paper is believed having eliminated the long-standing theoretical barrier in exact motion integration from inertial measurements. [ABSTRACT FROM AUTHOR]