Rigid Multibody Dynamics Research Articles

Rigid multibody molecular dynamics algorithm in canonical ensemble

By specializing the Hamiltonian of Nose's extended system in rigid multibody systems, we develop rigorous motion equations for rigid multibody molecular dynamics in canonical ensemble. The equations are proved to generate correct canonical equilibrium distributions. The corresponding reversible and symplectic integrator is also given in this paper.

COUPLING ANALYSIS BASED ON JOINT-SPACE MODEL OF PARALLEL ROBOT

6-DOF hydraulically driven parallel robot mainly consists of two systems: mechanical subsystem and hydraulic subsystem. These two subsystems can be modeled as multi-rigid body dynamics and hydraulic dynamics respectively. According to a bilateral coupling between the two subsystems, the integrated dynamic model of 6-DOF parallel robot is set up in operating-space. Through mapping operating-space dynamic model onto joint-space using jacobian transformation, joint-space model of 6-DOF parallel robot is derived. And interactions characteristics among the channels are analyzed when 6-DOF parallel robot is in several typical poses. The results show that strong couplings exist among channels in the whole workspace and such couplings vary along with the poses of 6-DOF parallel robot. And such couplings will influence the equivalent load inertia acting on each channel which will bring difficulties to 6-DOF parallel robot control.

Root cause identification and physics of impact-induced driveline noise in vehicular powertrain systems

Numerical and experimental investigations shed light on the root causes leading to the emergence and persistence of an acute metallic noise in rear wheel drive light truck drivelines. Sudden demands in engine output torque combined with the presence of lash zones give rise to a phenomenon that is onomatopoeically referred to as clonk. Its multi physics nature requires a comprehensive study, which includes rigid multi-body dynamics, flexible body oscillations, and noise radiation computation. The verification of numerical results is achieved through the design and implementation of a transient dynamic experimental rig, which comprises the complete drivetrain from the engine flywheel to the rear axle. Parametric studies reveal high-frequency contributions in the driveline vibration response of certain structural modes of the driveshaft pieces, which are induced by remote impact of meshing transmission teeth through backlash. The numerically predicted spectrum of vibration is in good qualitative agreement with the experimental measurements. Combined study of the aforementioned results reveals the components that amplify the clonk noise.

Limiting performance analysis of biomechanical systems for optimal injury control – Part 1: Theory and methodology

The performance of safety devices for injury control is studied in this paper. The problem to be addressed is treated as the optimal control and optimization of a biomechanical system consisting of safety devices and occupants. The system performance is measured by injury criteria. The limiting performance analysis is utilized to find the best possible performance for the system. Parametric optimization is introduced for the optimal design of a safety device. Various techniques for the computational modeling of biomechanical systems are discussed. The use of nonlinear rigid multi-body dynamics software in the limiting performance analysis and parametric optimization is addressed. Best and worst disturbance analyses and a sensitivity analysis are also considered.

Optimization-based simulation of nonsmooth rigid multibody dynamics

We present a time-stepping method to simulate rigid multibody dynamics with inelastic collision, contact, and friction. The method progresses with fixed time step without backtracking for collision and solves at every step a strictly convex quadratic program. We prove that a solution sequence of the method converges to the solution of a measure differential inclusion. We present numerical results for a few examples, and we illustrate the difference between the results from our scheme and previous, linear-complementarity-based time-stepping schemes.

Impact-induced vibration in vehicular driveline systems: Theoretical and experimental investigations

The paper investigates the conditions leading to the emergence and persistence of an acute metallic noise in light-truck drivelines. Sudden demands in torque in the presence of lash zones give rise to this phenomenon, which is onomatopoeically referred to as clonk. The study of clonk requires combined rigid multi-body dynamics and flexible body oscillations. The results show high-frequency contributions in the driveline vibrational response of certain structural modes of the driveshaft pieces, which are induced by remote impact of meshing transmission teeth through backlash. The numerically predicted spectrum of vibration shows good correlation with experimental measurements of radiated noise from a dynamic drivetrain rig.

Convergence of Time-Stepping Method for Initial and Boundary-Value Frictional Compliant Contact Problems

Beginning with a proof of the existence of a discrete-time trajectory, this paper establishes the convergence of a time-stepping method for solving continuous-time, boundary-value problems for dynamic systems with frictional contacts characterized by local compliance in the normal and tangential directions. Our investigation complements the analysis of the initial-value rigid-body model with one frictional contact encountering inelastic impacts by Stewart [Arch. Ration. Mech. Anal., 145 (1998), pp. 215-260] and the recent analysis by Anitescu Optimization-Based Simulation for Nonsmooth Rigid Multibody Dynamics, Argonne National Laboratory, Argonne, IL, 2004] using the framework of measure differential inclusions. In contrast to the measure-theoretic approach of these authors, we follow a differential variational approach and address a broader class of problems with multiple elastic or inelastic impacts. Applicable to both initial and affine boundary-value problems, our main convergence result pertains to the case where the compliance in the normal direction is decoupled from the compliance in the tangential directions and where the friction coefficients are sufficiently small.

A Numerical Analysis of Inertial Torques in the Steering Maneuvers of Hovering Drosophila

A mathematical model of rigid multibody dynamics with one three bodies was built firstly, based on which, the contribution of inertial torques during the steering maneuvers of a hovering Drosophilawas analyzed systematically. To eliminate the contribution of aerodynamics, the flying maneuvers were simulated within vacuum. The wings’ kinematics schemes and morphological parameters were idealized in concordance with those of real Drosophila. Several kinds of wing kinematics were analyzed, and the simulation results imply that inertial torques may play a role in the steering maneuvers of insect free flight. For the symmetrical flapping motion of bilateral wings, the inertial pitch torque conducts the rotation tendency of nose-up climbing or nose-down falling. And for the asymmetrical flapping cases, all inertial torques can influence synthetically the attitude of whole insect and finally result in the corresponding steering maneuvers. The simulation also suggests that the inertial torques due to wings supination may effectively contribute to insect steering maneuvers.

Impact-induced vibration in vehicular driveline systems: theoretical and experimental investigations

The paper investigates the conditions leading to the emergence and persistence of an acute metallic noise in light-truck drivelines. Sudden demands in torque in the presence of lash zones give rise to this phenomenon, which is onomatopoeically referred to as clonk. The study of clonk requires combined rigid multi-body dynamics and flexible body oscillations. The results show high-frequency contributions in the driveline vibrational response of certain structural modes of the driveshaft pieces, which are induced by remote impact of meshing transmission teeth through backlash. The numerically predicted spectrum of vibration shows good correlation with experimental measurements of radiated noise from a dynamic drivetrain rig.

Second–order multivalued stochastic differential equations on Riemannian manifolds

The existence and uniqueness of solutions to multivalued stochastic differential equations of the second order on Riemannian manifolds are proved. The class of problem is motivated by rigid body and multibody dynamics with friction and an application to the spherical pendulum with friction is presented.

A constraint‐stabilized time‐stepping approach for rigid multibody dynamics with joints, contact and friction

AbstractWe present a method for achieving geometrical constraint stabilization for a linear‐complementarity‐based time‐stepping scheme for rigid multibody dynamics with joints, contact, and friction. The method requires the solution of only one linear complementarity problem per step. We prove that the velocity stays bounded and that the constraint infeasibility is uniformly bounded in terms of the size of the time step and the current value of the velocity. Several examples, including one for joint‐only systems, are used to demonstrate the constraint stabilization effect. Copyright © 2004 John Wiley & Sons, Ltd.

An Energy-Conserving and Filtering Method for Stiff Nonlinear Multibody Dynamics

The conservation of energy is necessary for accuracy oflong-term simulations, and also guarantees energystability, which is sought to alleviate any stabilityrestrictions on the time integration step size. We discusssome issues regarding the integration of stiff nonlineardynamics with traditional dissipative and energy andmomentum conserving methods and we introduce a new 2-stagemethod which is an adaptation of the time integrationscheme presented in [1] for rigid multibody dynamics. Bycombining an energy conserving scheme with a substageacceleration filter, we devise an implicit method thatpreserves the energy map and is capable of integratingstiff flexible multibody systems that require numericaldissipation. In order to avoid the artificial stiffnessand the resulting instabilities caused by the enforcementof kinematic constraints, a joint coordinate formulationis adopted to model the rigid components of the system,while a total Lagrangian approach is adopted to model theflexible elements in the system. As the resulting model istypically characterized by a large number of degrees offreedom, we also demonstrate how the method may beextended to incorporate a form of domain decomposition.

A Unified Formulation for Massively Parallel Rigid Multibody Dynamics of O(log2n) Computational Complexity

A novel algorithm for the solution of the inverse dynamics problem is presented and augmented to the solution of the equations of motion (EOM) for rigid multibody chains using explicit constraint components of force. The unified model corresponds to an optimal, strictly parallel, time, space, and processor lower bound solution to the dynamics of accelerated rigid multibodies, i.e., computation time of O(log2n) using O(n) processors for an n body system. Complex topological structures are supported in the form of multiple degree-of-freedom (DOF) joints/hinges, free-floating, hyper-branched, and/or closed-chain systems, with applications ranging from multibody molecular dynamics simulations and computational molecular nanotechnology, to real-time control and simulation of spatial robotic manipulators. In addition to the theoretical significance, the algorithms presented are shown to be very efficient for practical implementation on MIMD parallel architectures for large-scale systems.

A Multibody/Finite Element Analysis Approach for Modeling of Crash Dynamic Responses

Computer models of the human body are robust tools for gaining insight into the gross motion of ground vehicle or aircraft occupants and evaluating the loads and, deformations of their critical parts. The knowledge of occupant responses will help in the determination of the type and probable causes of injuries that may he sustained during a crash. An important aspect in crash analysis is how the large motion of the relatively rigid segments of an occupant, such as the limbs, and the small deformations of flexible segments, such as the spine column, are interrelated. To this end, a general methodology for kineto-static analysis of multibody systems with flexible structures undergoing large motion and structural deformations is developed. Rigid multibody dynamics is used to predict the gross motions and displacements at the boundaries between the relatively bulky (rigid) bodies and relatively flexible ones. A mixed boundary-condition finite-element analysis is formulated and solved at every numerical integration time to determine the corresponding reaction forces and moments at the boundaries and also the structural deformations. Based on this methodology, a multibody model of the occupant with a nonlinear finite element model of the lumbar spine is developed for a Hybrid II anthropomorphic crash test dummy. The analytical results obtained are compared with the experimental results from the impact sled tests. Comparison of the results has shown better correlation between the analyses and the experiments compared with earlier studies.

Matrix Formulation of Order-N-Algorithm for Constrained Multirigid-body Dynamics.

The calculation time of constrained multirigid-body dynamics by conventional methods is proportional to the cube of the model size. Compared with this, the calculation time of Order-N-Algorithm is directly proportional to the model size. Rosenthal showed this method, but his paper explained only step by step procedure of an example, and thus it was hard to grasp the whole aspect of the algorithm. The mathematical formulation of the algorithm, and simple examples of investigations about the calculation load are given in this paper.

A nonlinear viscoelastic bushing element in multibody dynamics

This paper presents a formulation for incorporating nonlinear viscoelastic bushing elements into multibody systems. The formulation is based on the assumption that the relaxation function can be expressed as a sum of functions which are nonlinear in deformation and exponentially decreasing in time. These forces can represent elastomeric mounts or bushings in automotive suspension systems. The numerical implementation of the nonlinear viscoelastic bushing model into a general purpose rigid multibody dynamics code is described, and an extension of the formulation is also presented wherein component flexibility is included. Model validation was performed by comparing experimental data to simulation results obtained using the nonlinear viscoelastic model and a nonlinear elastic model. The experimental data were obtained at the Center's facilities by testing an automotive lower control arm/bushing system, subjected to a simulated road load event. The comparison demonstrates the better load prediction capability of the viscoelastic bushing model compared to the conventional model.

Sensitivity of Occupant Response Subject to Prescribed Corridors for Impact Testing

A technology to study the sensitivity of impact responses to prescribed test conditions is presented. Motor vehicle impacts are used to illustrate the principles of this sensitivity technology. Impact conditions are regulated by specifying either a corridor for the acceleration time history or other test parameters such as velocity change, static crush distance, and pulse duration. By combining a time domain constrained optimization method and a multirigid body dynamics simulator, the upper and lower bounds of occupant responses subject to the regulated corridors were obtained. It was found that these prescribed corridors may be either so wide as to allow extreme variations in occupant response or so narrow that they are physically unrealizable in the laboratory test environment. A new corridor based on specifications for the test parameters of acceleration, velocity. crush distance, and duration for frontal vehicle impacts is given.

A general formulation in rigid multibody dynamics

AbstractThe dynamics of rigid multibodies is traditionally formulated by means of either minimal or redundant co‐ordinates methods. An alternative approach is here proposed whereby a highly redundant set of coordinates is adopted. As a result, the equations of motion of the constrained bodies are decoupled. Several meaningful parameters are directly available and the constraint conditions are enforced in a very natural way. The first part of the paper presents the basic meanings and the theoretical developments of the formulation. The second develops a numerical approximation for the methodology proposed in the first part. The non‐linear system of differential‐algebraic equations governing the motion of the multibody is reduced to its weak form. It is linearized by applying a Newton–Raphson procedure and approximated through the method of finite elements in time. The details of the numerical application of this method are discussed and a solution procedure is presented. Finally, some numerical examples involving tree and closed loop topologies prove the capability of the present formulation in handling multibody dynamics.

Rotations in computational solid mechanics

A survey of variational principles, which form the basis for computational methods in both continuum mechanics and multi-rigid body dynamics is presented: all of them have the distinguishing feature of making an explicit use of the finite rotation tensor. A coherent unified treatment is therefore given, ranging from finite elasticity to incremental updated Lagrangean formulations that are suitable for accomodating mechanical nonlinearities of an almost general type, to time-finite elements for dynamic analyses. Selected numerical examples are provided to show the performances of computational techniques relying on these formulations. Throughout the paper, an attempt is made to keep the mathematical abstraction to a minimum, and to retain conceptual clarity at the expense of brevity. It is hoped that the article is self-contained and easily readable by nonspecialists. While a part of the article rediscusses some previously published work, many parts of it deal with new results, documented here for the first time.

Flexible Multibody Dynamics Based on a Fully Cartesian System of Support Coordinates

In this paper we present an extension to flexible multibody systems of a system of fully cartesian coordinates previously used in rigid multibody dynamics. This method is fully compatible with the previous one, keeping most of its advantages in kinematics and dynamics. The deformation in each deformable body is expressed as a linear combination of Ritz vectors with respect to a local frame whose motion is defined by a series of points and vectors that move according to the rigid body motion. Joint constraint equations are formulated through the points and vectors that define each link. These are chosen so that a minimum use of local reference frames is done. The resulting equations of motion are integrated using the trapezoidal rule combined with fixed point iteration. An illustrative example that corresponds to a satellite deployment is presented.