Dynamic Analysis Of Multibody Systems Research Articles

A New Exoskeleton Prototype for Lower Limb Rehabilitation

This paper presents a new solution for an exoskeleton robotic system that is used for locomotor assistance in people with locomotor disabilities. As novel features of the present research, a novel structural solution of a plane-parallel kinematic chain, intended to be used as the leg of an exoskeleton robot, is proposed. A virtual prototype is made, on the basis of which kinematic and dynamic studies are carried out using ADAMS software for the dynamic analysis of multibody systems. The dynamic simulation of the exoskeleton is performed in two simulation situations: walking on a horizontal plane, as well as the simulation of motion assistance when climbing stairs. Following this analysis, it is noted that the robotic system achieves angular variations in the hip and knee joints similar to that of a human subject. As a result, the constructive solution is feasible, and the next stage of the study is to realize an experimental prototype by the rapid prototyping technique. The kinematic elements of the exoskeleton are designed to provide structural strength, to be easily manufactured by 3D printing and to be easy to assemble. For this purpose, the structural optimization is performed with the finite element method to eliminate stress concentrators. Finally, an experimental prototype of the exoskeleton robot is manufactured and assembled, whose motion is analyzed using ultrafast-camera-based video analysis.

EFFICIENCY ASSESSMENT OF THE DIRECT INTEGRATION METHOD BY CENTRAL DIFFERENCES (DIMCD)

The direct integration method by central differences (DIMCD) is an explicit method of order two for integrating the equations governing the dynamic analysis of multibody systems. So far, development has focused only on verifying the quality of the results. In this paper, it is shown that in addition to providing optimal results, it is also competitive from the point of view of computational efficiency, at least for systems with up to six bodies. For this purpose, an appropriate implementation of the method in a compiled language is presented. In turn, it is shown that the methodology is suitable for modeling in sparse matrices, although the proposed implementation is based on dense matrices. The resulting code is applied to different benchmark examples. Results from various commercial software are also included. Keywords: Computational efficiency, multibody dynamics, central differences, null space, dense matrices, quaternions

A formulation for the dynamic analysis of multibody systems using non‐redundant unified local velocity coordinates

AbstractIn this paper, we present a formulation for the dynamic analysis of multibody systems using non‐redundant unified local velocity coordinates. The motivation for the present work is the result of an earlier investigation of unified local velocity coordinates of Holzinger et al. [1]. The equations of motion presented by the authors allow the description of the rigid body motion in space by local, purely translational velocity coordinates. However, the earlier investigations are limited to the description of the spatial motion of a free rigid body. Therefore, constraints are incorporated in the present paper.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

ADAMS-MATLAB co-simulation for kinematics, dynamics, and control of the Stewart–Gough platform

The mechanical structure known as Stewart–Gough platform is the most representative parallel robot with a wide variety of applications in many areas. Despite the intensive study on the kinematics, dynamics, and control of the Stewart–Gough platform, many details about these topics are still a challenging problem. In this work, the use of automatic dynamic analysis of multibody systems software for the kinematic and dynamic analysis of the Stewart–Gough platform is proposed. Moreover, a co-simulation automatic dynamic analysis of multibody systems (ADAMS)-MATLAB is developed for motion control of the Stewart–Gough platform end-effector. This computational approach allows the numerical solution for the kinematics, dynamics, and motion control of the Stewart–Gough platform and a considerable reduction on the analytical and programming effort. The obtained results in the three topics (kinematics, dynamics, and control) are validated by comparing them with analytical results reported in the literature. This kind of computational approach allows for the creation of virtual prototypes and saves time and resources in the development of Stewart–Gough platform-based robots applications.

Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations

Computational kinematics is a fundamental tool for the design, simulation, control, optimization and dynamic analysis of multibody systems. The analysis of complex multibody systems and the need for real time solutions requires the development of kinematic and dynamic formulations that reduces computational cost, the selection and efficient use of the most appropriated solvers and the exploiting of all the computer resources using parallel computing techniques. The topological approach based on group equations and natural coordinates reduces the computation time in comparison with well-known global formulations and enables the use of parallelism techniques which can be applied at different levels: simultaneous solution of equations, use of multithreading routines, or a combination of both. This paper studies and compares these topological formulation and parallel techniques to ascertain which combination performs better in two applications. The first application uses dedicated systems for the real time control of small multibody systems, defined by a few number of equations and small linear systems, so shared-memory parallelism in combination with linear algebra routines is analyzed in a small multicore and in Raspberry Pi. The control of a Stewart platform is used as a case study. The second application studies large multibody systems in which the kinematic analysis must be performed several times during the design of multibody systems. A simulator which allows us to control the formulation, the solver, the parallel techniques and size of the problem has been developed and tested in more powerful computational systems with larger multicores and GPU.

A new partitioned staggered scheme for flexible multibody interactions with strong inertial effects

In generic flexible multibody interaction problems, the differences in the mass, damping and stiffness of the bodies can be very large. Of particular interest is a small change in the higher mass structure which triggers relatively large inertial effects on the lower mass structure. In this work, a new partitioned staggered time integration scheme is developed and its applicability is extended to the problems involving low mass ratios in coupled multibody problems. The equation of motion of body with larger inertia is integrated by implicit Newmark method, whereas the smaller inertia is solved using a robust self-starting explicit integration procedure. The coupled formulation includes explicit correction terms that adjusts the amount of interfacial velocity, which plays a key role in the stability and accuracy of the simulations. A wide range of mass (10−6–10−1), damping and stiffness (10−3–103) ratios are chosen to assess the stability and accuracy characteristics of the proposed scheme. The closed-form expressions for the coupling parameter have been constructed for both matching and non-matching time stepping through the Godunov–Ryabenkii normal mode analysis. The stability of the proposed method is observed as a function of the relative properties and temporal discretisation of the coupled system. The time step of the heavier body significantly influences the stability more than the lighter body. To maintain the staggering error minimal, an optimal range of the coupling parameter is identified. The error computed with uniform variation in the time step revealed that the present method is more accurate than the existing methods. The partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems. As a potential application of this scheme, flexible multibody problems in the field of offshore engineering, viz., wave energy converter and floater–mooring systems are presented and validated with experimental measurements.

Vector form intrinsic finite element method for planar multibody systems with multiple clearance joints

A new computational methodology is presented for the dynamic analysis of multibody systems with multiple clearance joints by vector form intrinsic finite element method. A joint model is developed to simulate the motion of ideal and clearance joints for multibody systems. The dynamic behaviour of a four-bar mechanism with three clearance joints in continuous contact mode is analysed. The results show that the dynamic performance of the mechanism with three clearance joints in continuous contact mode is not similar to that with ideal joints and is fluctuating and affected by the clearance size of the joints and input crank speed.

Wear Analysis of Two Revolute Joints With Clearance in Multibody Systems

The wear of multiple joints with clearance is one of the main impacts on the life of mechanical systems while very limited study has been done on this subject. To be different with many existed researches focused on the dynamic analysis of multibody systems with multiple clearance joints, the wear of two revolute joints with clearance in multibody systems is analyzed in this paper by coupling dynamics with tribology. Based on a planar slider crank mechanism with two clearance joints, it is observed that the clearance sizes nonlinearly influence the wear depths of the two joints with clearance. Meanwhile, an appropriate relationship between the two joints' clearance sizes can significantly decrease the wear of the joints, which would greatly improve the system life. Both the independent and interactive influences of the two joints with clearances on the wear are investigated in this paper. The relation equations of the two clearances obtained in this work will significantly decrease the wear of the two clearance joints.

Dynamic analysis of deployable structures using independent displacement modes based on Moore-Penrose generalized inverse matrix

Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.

다물체계 운동 방정식 선형화를 통한 해상 풍력 발전기 동적 거동의 주파수 영역 해석 방법에 관한 연구

In this study, we describe a method to analysis dynamic behavior of an offshore wind turbine in the frequency domain and expected effects of the method. An offshore wind turbine, which is composed of platform, tower, nacelle, hubs, and blades, can be considered as multibody systems. In general, the dynamic analysis of multibody systems are carried out in the time domain, because the equations of motion derived based on the multibody dynamics are generally nonlinear differential equations. However, analyzing the dynamic behavior in time domain takes longer than in frequency domain. In this study, therefore, we describe how to analysis the system multibody systems in the frequency domain. For the frequency domain analysis, the non-linear differential equations are linearized using total derivative and Taylor series expansions, and then the linearized equations are solved in time domain. This method was applied to analysis of double pendulum system for the verification of its effectiveness, and the equations of motion for the offshore wind turbine was derived with assuming that the wind turbine is rigid multibody systems. Using this method, the dynamic behavior analysis of the offshore wind turbine can be expected to take less time.

Dynamic analysis of a slider-crank mechanism with two types of non-ideal revolute joints

Rolling element bearings and journal bearings are typical components comprising a revolute joint in a mechanical system. In the traditional dynamic analysis of multi-body systems, these two types of bearings are generally treated as ideal revolute joints and are modelled by kinematic constraints. The non-linearity of such bearings including internal radial clearance, local contact deformation, friction, lubrication and other phenomena associated with real joints are routinely ignored. In this work, an approach to the dynamic modelling of a multi-body system with these two types of non-ideal revolute joints is outlined. These non-ideal joints were modelled by their force interaction. In rolling element bearings, the frictionless multi-point contacts and bearing kinematics are considered. In the case of a journal bearing, the normal contact force and tangential dry friction force are considered. A planar slider-crank mechanism with multiple non-ideal revolute joints including a rolling ball bearing and two journal bearings is presented as a numerical example to demonstrate application of this approach. The variations of slider kinetic characteristics and the bearing reaction force are used to expound the dynamic characteristics of the mechanism when multiple non-ideal revolute joints are considered.

A Formulation on the Special Euclidean Group for Dynamic Analysis of Multibody Systems

This paper presents a finite element approach of multibody systems using the special Euclidean group SE(3) framework. The development leads to a compact and unified mixed coordinate formulation of the rigid bodies and the kinematic joints. Flexibility in the kinematic joints is also easily introduced. The method relies on local description of motions, so that it provides a singularity-free formulation and exhibits important advantages regarding numerical implementation. A practical case is presented to illustrate the method.

Dynamic response analysis of heavy load lifting operation in shipyard using multi-cranes

To increase the lifting capacity and minimize the cost and time for building a ship and offshore structure, block lifting with multi-cranes becomes more and more important. In this paper, therefore, dynamic response analysis of the multi-cranes is performed for block lifting operation. By this simulation, one can confirm the dynamic effects, such as dynamic motion and load, to prevent fatal accidents during the multi-crane operation.There are several types of crane and the crane systems consist of several rigid bodies. These rigid bodies are connected with various types of joints and wire rope, and the crane system is called as multibody system. To carry out the dynamic simulation of the crane system, therefore, the program for dynamic analysis of multibody system is developed.Among the several types of the cranes, the floating crane is operated on the sea water. Therefore, the developed program includes the function for calculating the hydrostatic and hydrodynamic forces. Using the dynamics simulation program developed in this paper, a dynamic response simulation of several cases of block lifting with multi-cranes are carried out, and the simulation results are validated by comparing them with the measured data from the shipyard.

Numerical efficiency of CUDA based parallel programming for dynamic analysis of multi-body systems with multi-joints and multi-force elements

The graphic processor unit (GPU) is an ideal solution to problems involving parallel data computations. A serial CPU-based program of dynamic analysis for multi-body systems is rebuilt as a parallel program that uses the GPU’s advantages. We developed an analysis code named GMAP to investigate how the dynamic analysis algorithm of multi-body systems is implemented in the GPU parallel programming. The numerical accuracy of GMAP is compared with the commercial program MSC/ADAMS. The numerical efficiency of GMAP is compared with the sequential CPU-based program. Multiple pendulums with bodies and joints and the net-shape system with bodies and spring-dampers are employed for computer simulations. The simulation results indicate that the accuracy of GMAP’s solution is the same as that of ADAMS. In the net type system that has 2370 spring-dampers, GMAP indicates an improved efficiency of about 566.7 seconds (24.7% improvement). It is noted that the larger the size of the system, the better the time efficiency.

DYNAMIC ANALYSIS OF MULTIBODY SYSTEMS WITH PROBABILISTIC PARAMETERS

Dynamic analysis of multibody systems with probabilistic parameters was presented. Dynamic modeling of multibody systems was obtained by Lagrange's method. The probabilistic differential algebraic equations were transformed into pure probabilistic differential equations by generalized coordinate partitioning method. The Newmark step-by-step integration method was used to calculate the results. Using the method of random factor method, the numerical characteristics of the system response were derived, and the results were expressed in statistic view. As an illustrating example, dynamic modeling of a rotating bar and sliding block system considering the probabilistic of load, geometric and physical parameters was presented. Compared with the result of Monte-Carlo numerical simulation method, the accuracy and efficiency of the method are verified. The results illustrate that the probabilistic parameters affect the dynamic response of the multibody system and the dynamic modeling with probabilistic parameters can objectively reflect the dynamic behavior of the objective systems.

Recursive dynamics simulator (ReDySim): A multibody dynamics solver

Recursive formulations have significantly helped in achieving real-time computations and model-based control laws. The recursive dynamics simulator (ReDySim) is a MATLAB-based recursive solver for dynamic analysis of multibody systems. ReDySim delves upon the decoupled natural orthogonal complement approach originally developed for serial-chain manipulators. In comparison to the commercially available software, dynamic analyses in ReDySim can be performed without creating solid model. The input parameters are specified in MATLAB environment. ReDySim has the capability to incorporate any control algorithm with utmost ease. In this work, the capabilities of ReDySim for solving open-loop and closed-loop systems are shown by examples of robotic gripper, KUKA KR5 industrial manipulator and four-bar mechanism. ReDySim can be downloaded for free from http://www.redysim.co.nr and can be used almost instantly.

Automatic generation of equations of motion for multibody system in discrete event simulation framework

In this paper, the development of a simulation program that can automatically generate equations of motion for mutibody systems in the discrete event simulation framework is presented. The need to analyze the dynamic response of mechanical systems that are under event triggered conditions is increasing. General mechanical systems can be defined as multibody systems that are collections of interconnected rigid bodies, consistent with various types of joints that limit the relative motion of pairs of bodies. For complex multibody systems, a systematic approach is required to efficiently set up the mathematical models. Therefore, a dynamics kernel was developed to automatically generate the equations of motion for multibody systems based on multibody dynamics. The developed dynamics kernel also provides the numerical solver for the dynamic analysis of multibody systems. The general multibody dynamics kernel cannot deal with discontinuous state variables, event triggered conditions, and state triggered conditions, though. To enable it to deal with multibody systems in discontinuous environments, the multibody dynamics kernel was integrated into a discrete event simulation framework, which was developed based on the discrete event system specification (DEVS) formalism. DEVS formalism is a modular and hierarchical formalism for modeling and analyzing systems under event triggered conditions, which are described by discontinuous state variables. To verify the developed program, it was applied to an block-lifting and transport simulation, and dynamic analysis of the system is carried out.

Motion planning for multi-HUG formation in an environment with obstacles

Hybrid-driven underwater glider (HUG) is a new type of autonomous underwater vehicles (AUVs). An HUG fleet can extend the ability of individual vehicles and increase mission efficiency. This paper presents motion planning and obstacle avoidance of multi-HUG formation using the artificial potential field (APF) method and Kane's method. The artificial potential fields used for formation motion control are constructed for particular mission requirement, ocean environment, and formation geometry. Multi-HUG formation with the artificial potential fields is regarded as a multibody system, in which HUGs are constrained by the virtual forces derived from the artificial potential fields. Kane's method for dynamic analysis of multibody systems is used to study the dynamic characteristics of motion of the multi-HUG formation. Combination of the APF method and Kane's method offers the advantage that coordinated control and motion planning of the formation can be implemented simultaneously. A case of a three-HUG formation is provided to demonstrate the methodology for clarity.

A Gyrobondgraph Method of Dynamic and Static Force Analysis for Spacial Multibody Systems

In order to increase the efficiency and reliability of dynamic and static force analysis for spatial multibody systems containing the coupling of multi-energy domains, a method based on gyrobondgraph is introduced. The procedure of modeling spacial multibody systems by bond graphs and its dynamic principle are described. The unified formulae of driving moment and constraint forces at joints are derived based on gyrobondgraph, they are easily generated on a computer in a complete form. As a result, the very difficult algebraic problem caused by differential causality and nonlinear junction structure can be overcome, and the automatic dynamic analysis of multibody systems on a computer is realized. By a practical example, the validity of this procedure is illustrated.