A regularization method for solving dynamic problems with singular configuration

2021 ◽  
pp. 146441932110619
Author(s):  
Liusong Yang ◽  
Shifeng Xue ◽  
Xingang Zhang ◽  
Wenli Yao
Keyword(s):  
Regularization Method ◽  
Null Space ◽  
Mechanical Energy ◽  
Iteration Step ◽  
Dynamic Simulations ◽  
Gauss Principle ◽  
Space Formulation ◽  
Singular Configuration ◽  
Multi Body ◽  
Four Bar Linkage

In the simulation process for multi-body systems, the generated redundant constraints will result in ill-conditioned dynamic equations, which are not good for stable simulations when the system motion proceeds near a singular configuration. In order to overcome the singularity problems, the paper presents a regularization method with an explicit expression based on Gauss principle, which does not need to eliminate the constraint violation after each iteration step compared with the traditional methods. Then the effectiveness and stability are demonstrated through two numerical examples, a slider-crank mechanism and a planar four-bar linkage. Simulation results obtained with the proposed method are analyzed and compared with augmented Lagrangian formulation and the null space formulation in terms of constraints violation, drift mechanical energy and computational efficiency, which shows that the proposed method is suitable to perform efficient and stable dynamic simulations for multi-body systems with singular configurations.

Dynamic Modeling and Numeration of Flexible Multi-Body System with Closed Loop

2010 ◽  
Vol 44-47 ◽  
pp. 1519-1524
Author(s):  
Shu Qing Liu ◽  
Xing Song Wang
Keyword(s):  
Dynamic Model ◽  
Closed Loop ◽  
Narrow Range ◽  
Null Space ◽  
Orthogonal Basis ◽  
Natural Coordinates ◽  
Body System ◽  
Multi Body ◽  
Four Bar Linkage ◽  
Flexible Linkage

The dynamic model of flexible multi-body system with closed loop is described with natural coordinates. The method is formulaic and especially appropriate to the modeling of system with repetitive substructures, but Lagrange multipliers as unknown variables are contained in the model. The dynamic model is reduced to a system with minimum dimensions by means of null-space orthogonal basis of constraint Jacobin. The result is correspondence with the dynamic model of rigid multi- body system while the rigid and flexible coupling is considered. The numerical method and the simulation steps are given in detail. Numerical example dealing with a flexible parallel four-bar linkage widely used in engineering illustrates the performance of the proposed method. The dynamic response of the angle between flexible linkage and horizontal axis are presented. The results indicate that there are clearly fluctuation in the angular velocity and acceleration of crank. The motion of connecting linkage contains not only translation but also narrow range rotation especially in the start instant.

A Design Methodology for System Parameters Synthesis of Elastic Planar Linkages: Theory

1992 ◽  
Vol 114 (4) ◽  
pp. 536-541 ◽  
Author(s):  
Zine-Eddine Boutaghou ◽  
A. G. Erdman
Keyword(s):  
Design Methodology ◽  
Design Sensitivity ◽  
Element Analysis ◽  
System Parameters ◽  
Sensitivity Equations ◽  
The Finite Element Analysis ◽  
Planar Linkages ◽  
Multi Body ◽  
Four Bar Linkage ◽  
Theoretical Considerations

Existing formulations predict the displacement and stresses in multi-body systems that result from known system parameters. In contrast, the proposed design methodology enables structured selection of system parameters necessary to produce desired elastic displacements, stresses, and frequencies. This design process involves the development of inverse design equations, the finite element analysis, and the design sensitivity equations to obtain converged solutions satisfying desired design constraints. Part 1 (Theory) considers the theoretical considerations involved. Part 2 (Applications) applies the methodology to design a four-bar linkage and a six-bar linkage.

Distributed Operational Space Formulation of Serial Manipulators

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Kishor D. Bhalerao ◽  
James Critchley ◽  
Denny Oetomo ◽  
Roy Featherstone ◽  
Oussama Khatib
Keyword(s):  
Parallel Algorithms ◽  
Time Complexity ◽  
Degrees Of Freedom ◽  
Null Space ◽  
Divide And Conquer ◽  
Serial Manipulators ◽  
Divide And Conquer Algorithm ◽  
Operational Space ◽  
Space Formulation ◽  
Space Dynamics

This paper presents a new parallel algorithm for the operational space dynamics of unconstrained serial manipulators, which outperforms contemporary sequential and parallel algorithms in the presence of two or more processors. The method employs a hybrid divide and conquer algorithm (DCA) multibody methodology which brings together the best features of the DCA and fast sequential techniques. The method achieves a logarithmic time complexity (O(log(n)) in the number of degrees of freedom (n) for computing the operational space inertia (Λe) of a serial manipulator in presence of O(n) processors. The paper also addresses the efficient sequential and parallel computation of the dynamically consistent generalized inverse (J¯e) of the task Jacobian, the associated null space projection matrix (Ne), and the joint actuator forces (τnull) which only affect the manipulator posture. The sequential algorithms for computing J¯e, Ne, and τnull are of O(n), O(n2), and O(n) computational complexity, respectively, while the corresponding parallel algorithms are of O(log(n)), O(n), and O(log(n)) time complexity in the presence of O(n) processors.

A mechanical integral steering system for increasing the stability and handling of motor vehicles

2015 ◽  
Vol 231 (8) ◽  
pp. 1465-1480 ◽  
Author(s):  
Cătălin Alexandru
Keyword(s):  
Modeling And Simulation ◽  
Steering System ◽  
Motor Vehicles ◽  
Steering Wheel ◽  
Dynamic Simulations ◽  
Translational Movement ◽  
Steering Law ◽  
The Stability ◽  
Input Motion ◽  
Multi Body

The article deals with the design, modeling, and simulation of an innovative four-wheel steering system for motor vehicles. The study is focused on the steering box of the rear wheels, which is a cam-based mechanism, while the front steering system uses a classical pinion—rack gearbox. In the proposed concept, the four-wheel steering aims to improve the vehicle stability and handling performances by considering the integral steering law, which is formulated in terms of correlation between the steering angles of the front and rear wheels. In this regard, a double-profiled cam is designed, in correlation with the input motion law applied to the steering wheel. The cam profile dictates (prescribes) the translational movement of the rear follower, which is connected to the left and right steering tierods, turning—as appropriate—the rear wheels in the same direction (for stability) or in opposite (for handling) to the front wheels. The cam-based mechanism is able to carry out complex motion laws, providing accurate integral steering law. The dynamic modeling and simulation of the four-wheel steering vehicle was performed by using the Multi-Body Systems package Automatic Dynamic Analysis of Mechanical Systems of MSC.Software, the full-vehicle model containing also the front and rear wheels suspension systems, as well the vehicle chassis (car body). The dynamic simulations in virtual environment have resulted in important results that demonstrate the handling and stability performances of the proposed four-wheel steering system by reference to a classical two-wheel steering vehicle.

scholarly journals Toward a Computational Model of the Upper Extremity

2017 ◽  
Vol 7 (2) ◽  
pp. 40 ◽  
Author(s):  
Hooshang Hemami
Keyword(s):  
Rigid Body ◽  
Upper Extremity ◽  
Soft Tissues ◽  
Euler Method ◽  
Co Activation ◽  
Computational Testing ◽  
The Central Nervous System ◽  
Space Formulation ◽  
Circular Surface ◽  
Multi Body

A basic 22-segment model of the upper extremity is formulated that can allow computational testing of hypotheses about the control and coordination of the upper extremity by the central nervous system. The formulation allows for further analytical, anatomical, physiological, and bio-mechanical expansion and improvement of the model. It allows for inclusion of all passive structures: ligaments, membranes, soft tissues, and cartilages. The formulation is based on the state space formulation of the Newton-Euler method applied to multi-body systems. Extensive use is made of three-segment rigid body modules, constraints, reduction of dimensionality, projection, and matrices of large dimensions.An example, gliding motion of a rigid body on a circular surface (as in wiping a dish with a pre-specified force of contact) shows the application of some of the concepts and feasibility of the developed routines. The control is based on analogous strategies in living systems where co-activation of agonist-antagonist muscular systems and precise reference inputs implement the desirable trajectories of motion and where an integral feedback of the force implements the desired forces of contact.

scholarly journals Big in Japan: Regularizing Networks for Solving Inverse Problems

2019 ◽  
Vol 62 (3) ◽  
pp. 445-455
Author(s):  
Johannes Schwab ◽  
Stephan Antholzer ◽  
Markus Haltmeier
Keyword(s):  
Neural Networks ◽  
Inverse Problems ◽  
Regularization Method ◽  
Deep Neural Networks ◽  
Convergence Rates ◽  
Null Space ◽  
Space Network ◽  
Special Cases ◽  
Data Problem ◽  
Sparse Data Problem

Abstract Deep learning and (deep) neural networks are emerging tools to address inverse problems and image reconstruction tasks. Despite outstanding performance, the mathematical analysis for solving inverse problems by neural networks is mostly missing. In this paper, we introduce and rigorously analyze families of deep regularizing neural networks (RegNets) of the form $$\mathbf {B}_\alpha + \mathbf {N}_{\theta (\alpha )} \mathbf {B}_\alpha $$Bα+Nθ(α)Bα, where $$\mathbf {B}_\alpha $$Bα is a classical regularization and the network $$\mathbf {N}_{\theta (\alpha )} \mathbf {B}_\alpha $$Nθ(α)Bα is trained to recover the missing part $${\text {Id}}_X - \mathbf {B}_\alpha $$IdX-Bα not found by the classical regularization. We show that these regularizing networks yield a convergent regularization method for solving inverse problems. Additionally, we derive convergence rates (quantitative error estimates) assuming a sufficient decay of the associated distance function. We demonstrate that our results recover existing convergence and convergence rates results for filter-based regularization methods as well as the recently introduced null space network as special cases. Numerical results are presented for a tomographic sparse data problem, which clearly demonstrate that the proposed RegNets improve classical regularization as well as the null space network.

Dynamics of Flexible Slider-Crank Mechanism Based on the Floating Frame Reference Formulation

2013 ◽  
Vol 456 ◽  
pp. 330-333
Author(s):  
Wei Fang Sun ◽  
Xiang Zhou Zheng ◽  
Jing Rui Liang
Keyword(s):  
Compliant Mechanisms ◽  
System Modeling ◽  
Reference Formulation ◽  
Flexible System ◽  
Flexible Parts ◽  
Floating Frame ◽  
Multi Body ◽  
Four Bar Linkage ◽  
Special Case ◽  
Crank Mechanism

The slider-crank mechanism is a special case of the four bar linkage which is widely used in reciprocating machines. Flexible multi-body mechanisms that gain some motion through the deflection of flexible elements are classified as compliant mechanisms. Dynamics of flexible slider-crank mechanisms is presented in this paper. Both rigid and flexible parts are included in the slider-crank mechanisms. As one of the widely accepted dynamic analytical method for the multi-body system modeling, floating frame reference formulation has been applied to derive dynamic formulations. Simulations of dynamics of flexible slider-crank mechanisms have been carried out using Matlab. It was shown that flexibility of parts has a certain extent effects on mechanical properties of flexible system that disagree with that of rigid ones. Keywords: Floating frame reference formulation; Slider-crank; Deformation; Flexible multi-body

Motorcycle Dynamics Modeling and Simulation Based on Road Simulation

2009 ◽  
Vol 16-19 ◽  
pp. 307-312
Author(s):  
Xi Hong Zou ◽  
Xiao Hui Shi ◽  
Quan Shi ◽  
Shun Li Xiao
Keyword(s):  
Lagrange Equation ◽  
Dynamics Modeling ◽  
Load Spectra ◽  
Simulation Based ◽  
Simulation And Experiment ◽  
Space Formulation ◽  
Multi Body ◽  
Motorcycle Dynamics ◽  
Body Dynamic ◽  
Driving Signal

Based on the stimulation and restriction of road simulation, the 5-DOF motorcycle multi-body dynamic model is derived, and the differential equation of motion and state-space formulation are developed according to Lagrange Equation. By iterating the load spectra, which was sampled on Hainan Proving Ground, the driving signal of motorcycle road simulation is obtained. With the driving signal as input, the motorcycle dynamics is simulated using MATLAB program, then the simulation and experiment are compared. The result shows that motorcycle dynamics can be analyzed and estimated precisely by combining road simulation with computer simulation.

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