Kinematic and Kinetic Derivatives in Multibody System Analysis

Analytical formulas for kinematic and kinetic derivatives needed in multibody system analyses are derived. A broad spectrum of problems, including implicit numerical integration, dynamic sensitivity analysis, and kinematic workspace analysis, require evaluation of first derivatives of generalized inertia and force expressions and at least three derivatives of algebraic constraint functions. In the setting of a formulation based on Cartesian generalized coordinates with Euler parameters for orientation, basic identities are developed that enable practical and efficient computation of all derivatives required for a large number of multibody mechanical system analyses. The formulation is verified through application to a spatial slider crank mechanism and a 14 body vehicle model. Efficiency of computation using the expressions derived is compared with results obtained employing finite differences, showing significant computational advantage using the analytically derived expressions.

<div class="htmlview paragraph">In this paper methods for the nonlinear dynamic analysis of multibody vehicle systems are presented. A total Lagrangian finite element formulation for deformable bodies of the vehicle systems that undergo large translational and rotational displacements is developed. A set of nonlinear dynamic differential equations are developed in a closed form for each finite element in terms of the reference as well as the nodal elstic coordinates and their time derivatives. These equations are expressed in terms of a set of element invariants that depend on the assumed displacement field. The invariants of the deformable body that undergoes large reference translational and rotational displacements can be obtained by assembling the invariants of its elements using a standard finite element procedure. The nonlinear dynamic equations of the deformable body can then be obtained by assembling the nonlinear element equations. Both the consistent and lumped mass finite element formulations are discussed. The dynamic formulations presented in this paper are exemplified using multibody vehicle systems that consist of interconnected rigid and deformable bodies. Numerical results are obtained using the general purpose computer program <b>DAMS</b> (Dynamic Analysis of Multibody Systems).</div>

The double pendulum, a simple system that exhibits complex dynamics, is used to demonstrate a method based on Hamilton’ s weak principle (HWP) for assembling and solving the maximum coordinate set equations for a multibody system. Results calculated using HWP are compared to a reference solution obtained by integrating the ordinary differential equations (ODE) in minimum coordinate set form. The HWP solution is shown to be comparable to the ODE solution in accuracy and computational efe ciency. These results suggest an alternative architecture for multibody system analysis, which implements the maximum coordinate set form of the system equations, and a simple, efe cient, and robust solution algorithm.

Computational structural analysis of spatial multibody systems based on mobility criteria

This chapter provides a brief and very selective survey of some software useful for solving problems in analytical dynamics. I have chosen to include only software intended for academic and industrial use that has been validated for modeling accuracy. Consequently, I have omitted the many dynamics engines used for video games and entertainment purposes. General Purpose Mathematical Software A number of powerful tools for mathematical analysis exist. Two of the most popular are Mathematica by Wolfram Research Inc. and MATLAB by The MathWorks Inc. They provide capabilities for both symbolic manipulation of expressions (i.e., computer algebra systems) and numerical computation and evaluation of expressions. While the basic Mathematica and MATLAB applications do not provide high-level programming abstractions specific to multibody system modeling and analysis, they are extremely useful for the low-level symbolic and numerical processing required in solving problems in analytical dynamics (see Figure 10.1 for a screenshot of Mathematica). This has a benefit in the learning process, as they require the student to understand the central concepts of analytical dynamics and to set up the solution procedure in a detailed manner, while alleviating much of the tedium of the algebraic and numerical work. Packages and Extensions for Multibody Dynamics Wolfram Research and MathWorks both provide domain-specific extensions for analyzing multibody systems. This gives the user access to high-level abstractions for modeling, simulating, and analyzing multibody systems. These high-level abstractions can be accessed through a programming language or through a diagrammatic interface supporting both acausal and causal modeling. Acausal modeling involves component-based schematic representations of the physical system, whereas causal modeling involves block diagram representations of the underlying mathematical description of the system. Simscape Multibody (formerly SimMechanics) by The MathWorks Inc. allows users to model multibody systems using a library of blocks associated with bodies, joints, constraints, spatial transformations, force elements, and sensors (see Figure 10.2 for a screenshot of Simscape Multibody). Entire CAD assemblies can be imported along with associated geometry, inertial properties, joint parameters, and constraints. Simscape Multibody then formulates and integrates the equations of motion for the multibody system. Animations are generated during simulation to allow visualization of the motion of the system.

This paper presents the validation of a novel code for the dynamic analysis of flexible multibody systems, which leverages projective geometric algebra for the kinematic description of the system. The theoretical foundations of geometric algebra are introduced briefly. A closed-form solution for the interpolation of motion is derived within the proposed framework and a finite element formulation of geometrically exact beams is developed. The accuracy of this code is assessed by comparing its prediction with those of eight multibody dynamics codes developed by independent researchers. Results are presented for three benchmark problems: the flexible four-bar mechanism, the lateral buckling of a thin beam, and the stability of a rotating shaft. Excellent agreement is found between the predictions of the proposed code and the previously published results, confirming the accuracy of the PGA-based approach. These findings demonstrate the potential of geometric algebra as a robust and elegant basis for the analysis of complex multibody systems.

This paper describes the design of a multibody systems analysis program that implements the principles of object-oriented programming to simplify the architecture of the code. A minimum coordinate set approach is used to generate the equations of motion. The principal features of the program include a unified treatment of rigid, flexible, and generic bodies, and the use of a single algorithm for both open-loop and closed-loop systems.

The aim of this work is to implement a new nondestructive testing (NDT) method based on the metal magnetic memory (MMM) effect into comprehensive diagnostic approach for power-line connectors, which is of great practical importance. Essence of this method lies in detection of stress concentration zones (SCZs) in material of the considered element during its operation (before micro-cracks and fracture occurs). If to compare with the traditional NDT methods, which indicate SCZs after the failure (post factum), this method provides major progress in the field of NDT. In this paper an approach of connection of numerical structural simulation (static and dynamic) with MMM-based testing method is also proposed. SCZs in power-line mechanical connector were evaluated and dynamic analysis of a complete power line, which included the analyzed connector, was carried out by means of MSC.ADAMS. Uniqueness of this analysis consist in integration of FEM analysis, MSC.ADAMS multibody system analysis (for testing of working conditions in advance - during virtual prototyping) and verification using MMM method. This hybrid approach enables to accomplish diagnostic analysis of selected construction elements and provides the possibility to take into consideration actual working conditions (e.g. vibrations) of the element. Proposed diagnostics method can substantially increase operational safety of electrical connectors and lines.

This paper introduces MBSVT (Multibody Systems at Virginia Tech), as a software library for the kinematic and dynamic simulation of multibody systems, with forward kinematics and dynamics, direct and adjoint sensitivity analysis, and optimization capabilities. The MBSVT software was developed in Fortran 2003 as a collection of Fortran modules and it was tested on several different platforms using multiple compilers. The kinematic library includes dot-1 constraint, revolute, spherical, Euler, and translational joints, as well as distance and coordinates driving constraints. The forward dynamics uses the penalty formulation to write the equations of motion and both explicit and implicit Runge-Kutta numerical integrators are implemented to integrate the equations. The library implements external forces, such as translational spring-damper-actuator, bump stop, linear normal contact, and basic tire force. Direct and adjoint sensitivity equations are implemented for the penalty formulation. The L-BFGS-B quasi-Newton optimization algorithm [1] is integrated with the library, to carry out the optimization tasks. MBSVT also provides a connection with Matlab by means of the Matlab engine. 3D rendering is available via the graphic library MBSVT-viz based on OpenSceneGraph. The collection of benchmark problems provided includes a crank-slider mechanism, 2D and 3D excavators models, a vehicle suspension, and full vehicle model. The distribution includes a Cmake list, gfortran make files, MSV2010 project files, and a collection of training problems. Detailed doxygen documentation for the MBSVT library is available in html and pdf formats.

Multibody system dynamics is already a well developed branch of theoretical, computational and applied mechanics. Thousands of documents can be found in any of the well-known scientific databases. In this work it is demonstrated that multibody system dynamics is built of many thematic communities. Using the Elsevier’s abstract and citation database SCOPUS, a massive amount of data is collected and analyzed with the use of the open source visualization tool Gephi. The information is represented as a large set of nodes with connections to study their graphical distribution and explore geometry and symmetries. A randomized radial symmetry is found in the graphical representation of the collected information. Furthermore, the concept of modularity is used to demonstrate that community structures are present in the field of multibody system dynamics. In particular, twenty-four different thematic communities have been identified. The scientific production of each community is analyzed, which allows to predict its growing rate in the next years. The journals and conference proceedings mainly used by the authors belonging to the community as well as the cooperation between them by country are also analyzed.

Clearance is inevitable for manufacture and assembly in the revolute joints of multibody systems. Excessive value of joint clearance will lead to the poor dynamic performance of mechanism, namely noise, vibration and fatigue failure. This paper presents the development of a dynamic model for planar multibody systems with clearance joints. Based on the continuous contact law, the contact force model proposed by Lankarani and Nikravesh is employed to describe the contact–impact phenomenon between pin and hole. And, the incorporation of the friction influence on revolute joint clearance is conducted by a modified friction force model. According to the geometric relationship between contact elements, the kinematics of the multibody systems is mapped into the global coordinate systems. Additionally, an experimental test platform is set up whereby a slider–crank mechanism with two clearance joints is used as an example to demonstrate the correctness and effectiveness of the proposed approach. Finally, the effects of joint clearance on the dynamic characteristics of planar multibody systems are investigated.

In general, joints are assumed without clearance in the dynamic analysis of multi-body echanical systems. When joint clearance is considered, the mechanism obtains two uncontrollable degrees of freedom and hence the dynamic response considerably changes. The joints’ clearances are the main sources of vibrations and noise due to the impact of the coupling parts in the joints. Therefore, the system responses lead to chaotic and unpredictable behaviors instead of being periodic and regular. In this paper, nonlinear dynamic behavior of a four-bar linkage with clearance at the joint between the coupler and the rocker is studied. The system response is performed by using a nonlinear continuous contact force model proposed by Lankarani and Nikravesh [1] and the friction effect is considered by a modified Coulomb friction law [2]. By using the Poincare portrait, it is proven that either strange attractors or chaos exist in the system response. Numerical simulations display both periodic and chaotic motions in the system behavior. Therefore, bifurcation analysis is carried out with a change in the size of the clearance corresponding to different values of crank rotational velocities. Fast Fourier Transformation is applied to analyze the frequency spectrum of the system response.

Application of the rigid finite element method to modelling of free vibrations of a band saw frame

Dynamic recursive decoupling method for closed-loop flexible mechanical systems

The kinematic and dynamic analysis of the high-degree of freedom (dof) hybrid systems that using serial and parallel robots together on fixed or mobile platform such as legged robots and service robots, is a rather difficult and complex, time consuming problem and a topic of great interest for researchers. There are many educational and commercial toolboxes which analyze serial and parallel robots separately. With the toolbox developed here, high-dof serial, parallel and hybrid robotics systems used on both fixed and mobile platforms can be designed and studied easily. Forward and inverse kinematics, Jacobian matrix, singularities, trajectory planning, torques and forces in joint and operational space can be examined with different robot designs. Using the toolbox that proposed in this paper, robot designer, researchers, students and educators can easily develop their own robotics systems and visualize them in the virtual reality environment provided by MATLAB. Also, it helps understanding fundamentals of high-dof multi-body hybrid robotics systems through user friendly interactive simulation. The most of existing toolboxes in the literature allow only user to analyze the predefined robots in their library with limited interactive capabilities. In some of them, the user can define a new robot with limited dof. But, the user must already have a prior knowledge about designing process of robots. In the proposed toolbox, designing and defining any new robotics systems become very easy. What makes this toolbox unique compared with the existing toolboxes is that any type of robot structures with high dof can be developed, analyzed and studied in detail.