Behavior Of Multibody Systems Research Articles

Dynamic Analysis of Planar Multibody Systems Considering Contact Characteristics of Ball Bearing Joint

A comparative study of dynamic analysis for planar multibody systems with ball bearing joints is conducted in this study. The transmission mechanism is used as the exemplar case for illustrating the effect of ball bearing joints on the dynamic behavior of multibody systems. To reflect the energy loss, the models of continuous contact force and modified Coulomb’s friction are considered in the kinematic equations for the multibody system with ball bearing joint. With this, the dynamic characteristics of the mechanism are studied. Meanwhile, an experimental platform is built to generate the test data for demonstrating the effectiveness and correctness of the proposed method. Moreover, the effects of driving speed and clearance size on the dynamic behavior of the multibody system are investigated. The numerical results indicate that the dynamic behavior of the mechanical system is sensitive to the variation of the design parameters and the selection of parameters can affect greatly the accuracy of the mechanism with clearance joints.

Tangential velocity during impact with friction in three-dimensional rigid multibody systems

This paper introduces an analysis of tangential velocity of the contact point during a single-point impact with friction in three-dimensional rigid multibody systems. Considering the normal component of impulse at the contact point as the independent variable, a system of nonlinear differential equations describing the progress of the tangential velocity is derived. Quartic algebraic equations for the invariant and the flow change directions are obtained. The system of differential equations could have a discontinuity problem if the tangential velocity instantaneously vanishes. Effectively, this problem is mathematically solved and the new sliding direction is specified. During impact, the sliding direction could continuously change or the sliding could stop and the non-sliding continues or the sliding could restart along a new direction. The stick-slip effect could also have its influence. Two friction models are used, and an appropriate numerical procedure is suggested that can handle all the possible sliding scenarios. To verify the proposed method, the numerical solution is compared to the analytical solution for a special case of a homogeneous ellipsoid that collides with a horizontal fixed rough surface. A case study of a four-degrees-of-freedom spatial robot that collides with its environment is considered. The bifurcation associated with the variation of the kinetic coefficient of friction is investigated, and a set of threshold values of it are determined. Some phase portraits are drawn, and the invariant directions and flow change directions are drawn for all portraits. Each portrait represents all the flow trajectories of the tangential velocity for different initial conditions with a specific kinetic coefficient of friction. This qualitative analysis not only helps in understanding the behavior of multibody systems in such situations but also it gives insight to the physical phenomenon of impact itself.

Application of the First Order Generalized-α Method to the Solution of an Intrinsic Geometrically Exact Model of Rotor Blade Systems

An energy decaying integration scheme for an intrinsic, geometrically exact, multibody dynamics model with composite, dimensionally reducible, active beamlike structures is proposed. The scheme is based on the first order generalized-α method that was proposed and successfully applied to various nonlinear dynamics models. The similarities and the differences between the mathematical structure of the nonlinear intrinsic model and a parallel nonlinear mixed model of chains are highlighted to demonstrate the effect of the form of the governing equation on the stability of the integration scheme. Simple C° shape functions are used in the spatial discretization of the state variables owing to the weak form of the model. Numerical solution of the transient behavior of multibody systems, representative of various rotor blade system configurations, is presented to highlight the advantages and the drawbacks of the integration scheme. Simulation predictions are compared against experimental results whenever the latter is available to verify the implementation. The suitability and the robustness of the proposed integration scheme are then established based on satisfying two conservational laws derived from the intrinsic model, which demonstrate the retained energy decaying characteristic of the scheme and its unconditional stability when applied to the intrinsic nonlinear problem, and the dependance of its success on the form of the governing equations.

349 テニススウィング時の人体の負担評価のための多体連成系の挙動解析

349 テニススウィング時の人体の負担評価のための多体連成系の挙動解析

Exact Equations for Tractrix Curves Associated with Vehicle Offtracking

Abstract Vehicle offtracking behavior at low speeds is closely approximated by a geometric entity called a tractrix. This paper presents differential equations for generalized coordinates of a planar multibody vehicle model based on tractrix behavior. The equations are exact, can be used with any type of input path, are valid for forward and backward movements, and are much simpler than previously published formulations used to compute transient offtracking. The differential equations can be integrated using conventional numerical integration algorithms to obtain plots of the low-speed tracking performance of articulated vehicles. The equations were formulated symbolically by a computer program used to analyze the kinematic and dynamic behavior of multibody systems. Example numerical results are plotted.

Optimal Design Of Multibody Systems

Dynamic simulation is often used to predict the behaviour of multibody systems but, it should be sometimes completed to optimize the choice of the design parameters by taking into account the expected performances of the mechanism. The aim of this paper is to propose an optimal design method adapted to mechanisms containing close loops and submitted to dynamic criteria. A formulation based on relative coordinates and Newton-Euler laws has been chosen, the constraint equations being expressed by the closing of the loops. A single value decomposition method is used to divide the set of differential and algebraic equations into two sub-spaces associated to the dependent and independent parameters. The equations of motion are integrated by the Newmark algorithm in its residual formulation. The optimization step is performed by the steepest descent method with constraint compensation. A special design sensitivity analysis has been developed by considering time dependent constraints, including first and second derivatives of the configuration parameters. The primary problem is reformulated so that integrals replace the time dependent functions. The classical adjoint variables are introduced to eliminate the state variables in the sensitivity formulation. The method has been applied to optimize the suspensions of an urban railway vehicle.