Search Results (4)

The forward kinematics of the Stewart platform is crucial for precise control and reliable operation in six-degree-of-freedom motion. However, there are some shortcomings in practical applications, such as calculation precision, computational efficiency, the capacity to resolve singular Jacobian matrix and real-time predictive performance. To overcome those deficiencies, this work proposes a hybrid strategy for forward kinematics in the Stewart platform based on dual quaternion neural network and ARMA time series prediction. This method initially employs a dual-quaternion-based back-propagation neural network (DQ-BPNN). The DQ-BPNN is partitioned into real and dual parts, composed of parameters such as driving-rod lengths, maximum and minimum lengths, to extract more features. In DQ-BPNN, a residual network (ResNet) is employed, endowing DQ-BPNN with the capacity to capture deeper-level system characteristics and enabling DQ-BPNN to achieve a better fitting effect. Furthermore, the combined modified multi-step-size factor Newton downhill method and the Newton–Raphson method (C-MSFND-NR) are employed. This combination not only enhances computational efficiency and ensures global convergence, but also endows the method with the capability to resolve a singular matrix. Finally, a traversal method is adopted to determine the order of the autoregressive moving average (ARMA) model according to the Bayesian information criterion (BIC). This approach efficiently balances computational efficiency and fitting accuracy during real-time motion. The simulations and experiments demonstrate that, compared with BPNN, the R² value in DQ-BPNN increases by 0.1%. Meanwhile, the MAE, MAPE, RMSE, and MSE values in DQ-BPNN decrease by 8.89%, 21.85%, 6.90%, and 3.3%, respectively. Compared with five Newtonian methods, the average computing time of C-MSFND-NR decreases by 59.82%, 83.81%, 15.09%, 79.82%, and 78.77%. Compared with the linear method, the prediction accuracy of the ARMA method increases by 14.63%, 14.63%, 14.63%, 14.46%, 16.67%, and 13.41%, respectively. Full article

The determination of maximum singularity-free space is critical to structural design and motion control strategy in the Stewart platform. Nevertheless, in practical applications, there exist several limitations such as computational efficiency, calculation precision, and the reliability of computational results. To overcome those shortcomings, this work proposes an efficient and high-precision method for computing the maximum singularity-free space within the Stewart platform. Firstly, apply K-Means clustering to group the variables, including the range, mean, and standard deviation of driving rod lengths, and the clustering centroids and extreme rod lengths collectively form a set of scenarios to avoid large-scale searching. An additional sorting methodology with a specific parameter is proposed for sorting the aforementioned scenarios in descending order and detecting singular-prone cases. Secondly, compute the initial solution for maximum singularity-free length without gimbal lock through an analytical solution formula, enabling reduction in the search scope. Thirdly, introduce a novel scaling factor to resolve the problem of dimensional inconsistency between rotation and translation within the Jacobian matrix using dual quaternions, and determine the singularity based on the determinant of the newly proposed Jacobian matrix. Finally, employ a CNN-LSTM-Attention model for a secondary verification procedure, specifically targeting the challenge of singularities encountered when solving the forward kinematics of the Stewart platform using zero-position values. The experiments demonstrate that the accelerated discretization method for maximum singularity-free joint space and workspace is applicable to devices with diverse geometric configurations. For two practical Stewart platforms, compared with two conventional methods, this method improves computational efficiency and precision significantly. The computation time of the first platform is reduced by 97.54% and 98.07% respectively, while that of the second platform is cut by 80.84% and 81.80% respectively. In terms of precision, the first platform demonstrates 95.83% and 78% improvement respectively, and the second platform attains 99.99% improvement over two conventional methods. Full article

Kinematic modeling is essential for planning and controlling continuum robot motion. The traditional Denavit Hartenberg (DH) model involves complex matrix multiplication operations, resulting in computationally intensive inverse solutions and trajectory planning. Solving position and orientation changes in continuum robots using the double quaternion rule can reduce computational complexity. However, existing dual quaternion methods are direct equational transformations of DH rules and do not give a complete modeling process. They usually require more interpretability when applying continuum robot kinematic modeling. This paper uses the dual quaternion method to establish a kinematic model of a continuum robot. It uses a two-section continuum robot model to compare the advantages of dual quaternion and traditional modeling methods. In addition, this paper proposes a five-polynomial interpolation algorithm based on the dual quaternion method for trajectory planning of continuum robots. This method accurately models spatial bending and torsional motions of singularity-free continuum robots. Full article

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. Full article