Dynamic simulation of crankshaft multibody systems

General multibody system approaches are often not sufficient for specific situations in applications to yield an efficient and accurate solution. We concentrate on the simulation of the crankshaft dynamics which is characterized by flexible bodies and force laws describing the interaction between the bodies. The use of the floating frame of reference approach in our model leads to an index-2 DAE system. The algebraic constraints originate from the reference conditions and the normalization equation for the quaternions. For the time integration of this system, two aspects have to be taken into account: firstly, for efficiency exploiting the structure of the system and using parallelization. Secondly, consistent initial values also with respect to a related index-3 system have to be computed in order to compute missing initial velocities and to reduce transient phenomena. The work of C.B. Drab, J.R. Haslinger, and R.U. Pfau is supported by the “Bundesministerium für Wirtschaft und Arbeit” and by the government of Upper Austria within the framework “Industrielle Kompetenzzentren und Netzwerke”.     

Real-time inverse dynamics control of parallel manipulators using general-purpose multibody software

This work deals with the problem of computing the inverse dynamics of complex constrained mechanical systems for real-time control applications. The main goal is the control of robotic systems using model-based schemes in which the inverse model itself is obtained using a general purpose multibody software, exploiting the redundant coordinate formalism. The resulting control scheme is essentially equivalent to a classical computed torque control, commonly used in robotics applications. This work proposes to use modern general-purpose multibody software to compute the inverse dynamics of complex rigid mechanisms in an efficient way, so that it suits the requirements of realistic real-time applications as well. This task can be very difficult, since it involves a higher number of equations than the relative coordinates approach. The latter is believed to be less general, and may suffer from topology limitations. The use of specialized linear algebra solvers makes this kind of control algorithms usable in real-time for mechanism models of realistic complexity. Numerical results from the simulation of practical applications are presented, consisting in a “delta” robot and a bio-mimetic 11 degrees of freedom manipulator controlled using the same software and the same algorithm.     

A rotationless formulation of multibody dynamics: Modeling of screw joints and incorporation of control constraints

In the present work, a new energy-momentum conserving time-stepping scheme for multibody systems comprising screw joints is developed. In particular, it is shown that the underlying rotationless formulation of multibody dynamics along with a specific coordinate augmentation technique makes possible the energy-momentum discretization of the screw pair. In addition to that, control (or servo) constraints are treated within the rotationless framework of multibody dynamics. The control constraints are used to partially prescribe the motion of a multibody system. In particular, control constraints, in conjunction with the coordinate augmentation technique, make possible to solve inverse dynamics problems by applying the present simulation approach.     

On the optimal scaling of index three DAEs in multibody dynamics

We propose a preconditioning strategy for the governing equations of multibody systems in index-3 differential-algebraic form. The method eliminates the amplification of errors and the ill-conditioning which affect numerical solutions of high index differential algebraic equations for small time steps. We develop a new theoretical analysis of the perturbation problem and we apply it to the derivation of preconditioners for the Newmark family of integration schemes. The theoretical results are confirmed by numerical experiments.     

多体系统动力学Lie 群微分⁃代数方程约束稳定方法

针对多体系统动力学微分-代数方程求解问题,研究基于Lie群表达的约束稳定方法.首先引入新的Lagrange乘子,结合位移约束、速度级约束和加速度级约束方程,构造了新的Lie群微分-代数方程.然后使用向后差商隐式方法和CG(Crouch-Grossman)方法,对微分–代数方程进行离散求解,得到精确度较高的动力学仿真结果.该方法在精确保持各级约束方程的同时,保持旋转矩阵的正交性,并且使系统总能量误差较小.     

Research trends in multibody system dynamics

During the last decade, multibody dynamics was acknowledged as an independent branch of theoretical, computational and applied mechanics around the globe. The research topics have been widened as well as the applications. The research topics are discussed with respect to the subjects and countries dealing with multibody dynamics. A community of multibody dynamicists is identified by their contributions and services to the journal Multibody System Dynamics. Commemorative Contribution.     

基于微分/代数方程的多体系统动力学设计灵敏度分析的伴随变量方法

基于多体系统动力学微分/代数方程数学模型和通用积分形式的目标函数,建立了多体系统动力学设计灵敏度分析的伴随变量方法,避免了复杂的设计灵敏度计算,对于设计变量较多的多体系统灵敏度分析具有较高的计算效率.文中给出了通用公式以及具体的计算过程和验证方法,并将目标函数及其导数积分形式的计算转化为微分方程的初值问题,进一步提高了计算效率和精度.文末通过一曲柄-滑块机构算例对算法的有效性进行了验证.     

Developments of multibody system dynamics: computer simulations and experiments

It is an exceptional success when multibody dynamics researchers Multibody System Dynamics journal one of the most highly ranked journals in the last 10 years. In the inaugural issue, Professor Schiehlen wrote an interesting article explaining the roots and perspectives of multibody system dynamics. Professor Shabana also wrote an interesting article to review developments in flexible multibody dynamics. The application possibilities of multibody system dynamics have grown wider and deeper, with many application examples being introduced with multibody techniques in the past 10 years. In this paper, the development of multibody dynamics is briefly reviewed and several applications of multibody dynamics are described according to the author’s research results. Simulation examples are compared to physical experiments, which show reasonableness and accuracy of the multibody formulation applied to real problems. Computer simulations using the absolute nodal coordinate formulation (ANCF) were also compared to physical experiments; therefore, the validity of ANCF for large-displacement and large-deformation problems was shown. Physical experiments for large deformation problems include beam, plate, chain, and strip. Other research topics currently being carried out in the author’s laboratory are also briefly explained. Commemorative Contribution.     

A divide-and-conquer direct differentiation approach for multibody system sensitivity analysis

In the design and analysis of multibody dynamics systems, sensitivity analysis is a critical tool for good design decisions. Unless efficient algorithms are used, sensitivity analysis can be computationally expensive, and hence, limited in its efficacy. Traditional direct differentiation methods can be computationally expensive with complexity as large as O(n ⁴+n ² m ²+nm ³), where n is the number of generalized coordinates in the system and m is the number of algebraic constraints. In this paper, a direct differentiation divide-and-conquer approach is presented for efficient sensitivity analysis of multibody systems with general topologies. This approach uses a binary tree structure to traverse the topology of the system and recursively generate the sensitivity data in linear and logarithmic complexities for serial and parallel implementations, respectively. This method works concurrently with the forward dynamics problem, and hence, requires minimal data storage. The differentiation required in this algorithm is minimum as compared to traditional methods, and is generated locally on each body as a preprocessing step. The method provides sensitivity values accurately up to integration tolerance and is insensitive to perturbations in design parameter values. This approach is a good alternative to existing methodologies, as it is fairly simple to implement for general topologies and is computationally efficient.