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In this investigation, different computational methods for the analytical development and the computer implementation of the differential-algebraic dynamic equations of rigid multibody systems are examined. The analytical formulations considered in this paper are the Reference Point Coordinate Formulation based on Euler Parameters (RPCF-EP) and the Natural Absolute Coordinate Formulation (NACF). Moreover, the solution approaches of interest for this study are the Augmented Formulation (AF) and the Udwadia–Kalaba Equations (UKE). As shown in this paper, the combination of all the methodologies analyzed in this work leads to general, effective, and efficient multibody algorithms that can be readily implemented in a general-purpose computer code for analyzing the time evolution of mechanical systems constrained by kinematic joints. This study demonstrates that multibody algorithm based on the combination of the NACF with the UKE turned out to be the most effective and efficient computational method. The conclusions drawn in this paper are based on the numerical results obtained for a benchmark multibody system analyzed by means of dynamical simulations.

A large group of real mechanical problems can be modeled and analyzed using the approaches of flexible multibody dynamics. The computational models in the form of differential–algebraic equations can be quite complex, and therefore, it is suitable to develop efficient approaches for the analysis of such models. This paper deals with the development of fast and efficient computational techniques for the analysis of flexible and thin mechanical structures modeled using the absolute nodal coordinate formulation (ANCF). The first original contribution of this paper is the introduction of fast evaluation of nonlinear elastic forces of the ANCF cable element based on the pre-computation of various terms that are constant when evaluated numerically at Gaussian points. The second part of the paper is aimed at the usage of quasi-Newton methods, which led to the reduction in iteration matrix re-evaluations in case of Newmark type of numerical integration methods for equations of motion. Proposed improvements are implemented in an in-house software in MATLAB environment, and their effects are tested on the cable-mass system considered as a flexible multibody system. The numerical results shown in the paper have proven the efficiency of the proposed algorithms. Real behavior of testing mechanical systems was supported by presented experimental results.

Higher-order error terms (HOET) occur inevitably during the geometric error modelling and compensation of a machine tool using both screw theory and multi-body system (MBS) theory. Though the HOET has little influence on machining accuracy, it will make analysis and compensation of geometric errors complicated and tedious. Especially, it is necessary to eliminate the higher-order error terms artificially when deriving the analytical expressions for geometric error compensation. Hence, a novel geometric error modelling and compensation algorithm without the interference of HOET is proposed in this paper. Taking a three-axis CNC machine tool as an example. A new summation operation rule for geometric error modelling was defined according to the homogeneous transformation matrix (HTM) method, which has no multiplication between error matrices. And the analytical expressions of motion-axis commands for error compensation could be calculated directly according to the new modelling algorithm without manual deletion of HOET. Active elimination of HOET can simplify the process of geometric error modelling and compensation and can significantly improve efficiency. The results show that the acquisition efficiency of symbolic compensation expressions can be improved by at least 70% compared to the traditional actual inverse kinematics. Moreover, the HOET are automatically eliminated and has a small influence on the compensation accuracy. Finally, a cutting experiment was conducted and analyzed to verify the high efficiency and effectiveness of the proposed method.

The stability of vehicles is influenced by the suspension system. At present, there are many studies on the suspension of traditional passenger vehicles, but few are related to agricultural mobile robots. There are structural differences between the suspension system of agricultural mobile robots and passenger vehicles, which requires structural simplification and modelling concerning suspension of agricultural mobile robots. This study investigates the optimal design for an agricultural mobile robot’s suspension system designed based on a double wishbone suspension structure. The dynamics of the quarter suspension system were modelled based on Lagrange’s equation. In our work, the non-dominated sorting genetic algorithm III (NSGA-III) was selected for conducting multi-objective optimization of the suspension design, combined with the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) to choose the optimal combination of parameters in the non-dominated solution set obtained by NSGA-III. We compared the performance of NSGA-III with that of other multi-objective evolutionary algorithms (MOEAs). Compared with the second-scoring solution, the score of the optimal solution obtained by NSGA-III increased by 4.92%, indicating that NSGA-III has a significant advantage in terms of the solution quality and robustness for the optimal design of the suspension system. This was verified by simulation in Adams that our method, which utilizes multibody dynamics, NSGA-III and TOPSIS, is feasible to determine the optimal design of a suspension system for an agricultural mobile robot.

This paper proposes a parallel direct solution of flexible multibody systems based on block Gaussian elimination. The Craig–Bampton method is utilized to model flexible bodies within the multibody system, resulting in a reduction in the size of the system equations. To address the time integration problem, an implicit stiff scheme is adopted to obtain large time step sizes. When forming the linearized systemic equations, global sparsity in the Jacobian matrix and similar local sparsity in submatrices can be observed. Subsequently, block Gaussian elimination is introduced for the direct solution of these linearized equations. The algorithm is designed to be parallelizable at the algorithm level, with a specific processing order for the submatrices of the constraints. The stability of the method is guaranteed by the positive definite and symmetric properties in the diagonal matrices in the Craig–Bampton method. The parallel efficiency and numerical stability of the method are confirmed through numerical examples in homemade codes parallelized by OpenMP.

This paper deals with periodic motions and their stability of a flexible connected two-body system with respect to its center of mass in a central Newtonian gravitational field on an elliptical orbit. Equations of motion are derived in a Hamiltonian form, and two periodic solutions as well as the necessary conditions for their existence are acquired. By analyzing linearized equations of perturbed motions, Lyapunov instability domains and domains of stability in the first approximation are obtained. In addition, the third- and fourth-order resonances are investigated in linear stability domains. A constructive algorithm based on a symplectic map is used to calculate the coefficients of the normalized Hamiltonian. Then, a nonlinear stability analysis for two periodic solutions is performed in the third- and fourth-order resonance cases as well as in the nonresonance case.

Robot-assisted surgical systems have been widely applied for minimally invasive needle biopsies thanks to their excellent accuracy and superior stability compared to manual surgical operations, which lead to possible fatigue and misoperation due to long procedures. Current needle biopsy robots are normally customed designed for specific application scenarios, and only position-level kinematics are derived, preventing advanced speed control or singularity analysis. As a step forward, this paper aims to design a universal needle biopsy robot platform which features 6 DoF 3-RRRS (Revolute–Revolute–Revolute–Spherical) parallel structure. The analytical solutions to its nonlinear kinematic problems, including forward kinematics, inverse kinematics, and differential kinematics are derived, allowing fast and accurate feedback control calculations. A multibody simulation platform and a first-generation prototype are established next to provide comprehensive verifications for the derived robotic model. Finally, simulated puncture experiments are carried out to illustrate the effectiveness of the proposed method.

The current research of real-time observation for vehicle roll steer angle and compliance steer angle(both of them comprehensively referred as the additional steer angle in this paper) mainly employs the linear vehicle dynamic model, in which only the lateral acceleration of vehicle body is considered. The observation accuracy resorting to this method cannot meet the requirements of vehicle real-time stability control, especially under extreme driving conditions. The paper explores the solution resorting to experimental method. Firstly, a multi-body dynamic model of a passenger car is built based on the ADAMS/Car software, whose dynamic accuracy is verified by the same vehicle’s roadway test data of steady static circular test. Based on this simulation platform, several influencing factors of additional steer angle under different driving conditions are quantitatively analyzed. Then ɛ -SVR algorithm is employed to build the additional steer angle prediction model, whose input vectors mainly include the sensor information of standard electronic stability control system(ESC). The method of typical slalom tests and FMVSS 126 tests are adopted to make simulation, train model and test model’s generalization performance. The test result shows that the influence of lateral acceleration on additional steer angle is maximal (the magnitude up to 1°), followed by the longitudinal acceleration-deceleration and the road wave amplitude (the magnitude up to 0.3°). Moreover, both the prediction accuracy and the calculation real-time of the model can meet the control requirements of ESC. This research expands the accurate observation methods of the additional steer angle under extreme driving conditions.

A new and efficient computational method for constrained multibody systems is proposed. In the proposed method, local parametrization method is employed to apply the same solution method for position, velocity, and acceleration analyses since the coefficient matrices for each analysis have an identical matrix pattern. The skyline solution method is used to overcome numerical inefficiency when solving large scaled equations. Also, subsystem mpartitioning method is derived systematically to perform parallel processing for real time simulation. To show the numerical accuracy and efficiency of the proposed method, three numerical problems are solved.

In a companion paper (Part 1, J. Optim. Theory Appl. 137(3), [ 2008 ]), we determined the optimal starting conditions for the rendezvous maneuver using an optimal control approach. In this paper, we study the same problem with a mathematical programming approach. Specifically, we consider the relative motion between a target spacecraft in a circular orbit and a chaser spacecraft moving in its proximity as described by the Clohessy-Wiltshire equations. We consider the class of multiple-subarc trajectories characterized by constant thrust controls in each subarc. Under these conditions, the Clohessy-Wiltshire equations can be integrated in closed form and in turn this leads to optimization processes of the mathematical programming type. Within the above framework, we study the rendezvous problem under the assumption that the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given. In particular, we consider the rendezvous between the Space Shuttle (chaser) and the International Space Station (target). Once a given initial distance SS-to-ISS is preselected, the present work supplies not only the best initial conditions for the rendezvous trajectory, but simultaneously the corresponding final conditions for the ascent trajectory.