Constrained Multibody Systems Research Articles

Dynamic Analysis of Constrained Multibody Systems Undergoing Collision with Friction

Dynamic Analysis of Constrained Multibody Systems Undergoing Collision with Friction

Dynamic Analysis of Constrained Multibody Systems Undergoing Collision

This paper presents a method for the dynamic analysis of constrained multibody systems undergoing abrupt collision. The proposed method uses a longer time interval to check collision than that of c onventional method. This reduces the computational effort significantly. To calculate collision points on two colliding rigid bodies, one may introduce constraints of contact. However, this causes reduction of degree of freedom and difficulty of numerical analysis. The proposed method can calculate collision points without above mentioned problems. Three numerical examples are given to demonstrate the computational efficiency and the usefulness of the proposed method

A Mathematical Corrector Method of Constrained Dynamic Systems.

This paper presents a numerical corrector method to find feasible state variables of the constrained multibody systems. For correcting state variables, the Lagrange-Newton method, a nonlinear optimization technique, is used. The iteration formulae derived from the quasi-Newton scheme do not update the Lagrange multipliers in the analysis steps and projects the state variables on the constraint manifold. Therefore, the cost due to the updating of Lagrange multipliers decreases. The method is verified through the convergence theorem denoting a convergence order of numerical solutions and as the corrections are performed along the constraint gradients, the system motion is formed in the null space tangent to the constraint manifold. The simulation example uses a three-dimensional full vehicle model, and the obtained numerical solutions are compared with the ADAMS solutions.

Dynamic Modelling and Simulation of Log-Hauling Trucks with Combined Tire-Cornering and Braking Forces

A general nonlinear procedure for yaw-roll-pitch models oflog-hauling trucks, with different configurations, is developed based onthe methodology of a general purpose computer code DYNOCOMBS (Dynamicsof Constrained Multibody Systems). To implement the constraint equationsfor the special design feature in log-hauling trucks, a procedure isdeveloped allowing the use of the code for general-purpose dynamicanalysis of the trucks. The BNPS (Bakker, Nyborg, and Pacejka andSmithers Scientific Services, Inc.) tire model for combinedtire-cornering and braking forces is used in the simulation. Thevalidation test is conducted by comparing the numerical results offree-rolling cornering responses of the system with both of the measuredresponses in field tests and the simulation results from CSTT (Centrefor Surface Transportation Technology) model. The simulation study iscarried out on three cases of evasive maneuvers with combined corneringand braking.

Interference Impact Analysis of Multibody Systems

A new computer aided analysis method for frictionless impact problems due to interference between two bodies in a constrained multibody system is presented in this paper. A virtual contact joint concept is used to detect interference between two bodies and calculate the jump in the body momenta, velocity discontinuities and rebounds. The interference surfaces can be described by the joint coordinates of the virtual contact joint, which are very useful for determining the impact time, the types and positions of two impact surfaces and impact initial conditions when an interference happens between two bodies.

Constraint Forces and Undetermined Multipliers in Constrained Multibody Systems

This paper addresses the relation between constraining forces, constraint equations, and undetermined multipliers, used in studying constrained multibody systems. A formalism is developed establishing the undetermined multiplier method through the concept of a generalized constraint force, partial velocities, and kinematic constraint equations.

A Decoupling Solution Method for Implicit Numerical Integration of Constrained Mechanical Systems*

A decoupling solution method is presented for implicit numerical integration of constrained multibody systems. Compared to implicit numerical integration methods, explicit numerical integration methods usually spend less computation time per iteration, since the equations of motion and an explicit integration formula coupled with the constraint manifolds are solved separately. However, the integration step size can be excessively small for highly nonlinear or stiff problems, due to the small stability region of the explicit method. In contrast, implicit numerical integration methods do not have the problem of excessive small step size. Implicit integration methods, however, generally require one to solve a large system equations simultaneously. The solution method proposed in this paper eliminates the problem of large system equations, while maintaining the advantage of the implicit method. Furthermore, the proposed method provides a well-conditioned iteration matrix for the implicit method, which is important to obtain accurate and stable solutions.

On the control of a constrained multibody system

This work deals with the modelling and control of the motion of a constrained multibody system. The system is composed of four uniform links, two torque actuated joints and three passive joints. All the links are moving in the horizontal plane, see Fig. 1. Given two configurations A and B of the system, and a time interval [0, t f ]. The problem dealt with in this work is to compute the control torques for each of the actuated joints such that the system will move during [0, t f ] from configuration A to configuration B subject to various constraints on the motion.

The control of the motion of a pantograph

This work deals with the modelling and control of the motion of a constrained multibody system which is a flexible version of a pantograph. The system is composed of four uniform links, two torque actuated joints and three passive joints. All the links are moving in the horizontal plane, see Figure 1. In the case of a pantograph, the joint p B is attached to the point p 4. See [1] for the description and equations of motion of a pantograph. Given two configurations A and B of the system, and a time interval [0, t f ]. The problem dealt with in this work is to compute the control torques for each of the actuated joints such that the system will move during [0, t f ] from configuration A to configuration B subject to various constraints on the motion.

Simulation of modular dynamic systems

A modular structure for dynamic systems is obtained by functional decomposition. This leads to an interconnected set of dynamic modules. A classification for modular dynamic systems is introduced, including constrained multibody systems with explicit joints, and several state space forms. The resulting mechanical differential-algebraic equations are treated by a post-stabilizing projection method. For most efficient simulation, a multi-rate-method is incorporated. The problem of algebraic loops is discussed and a method for its solution is proposed. The simulation program NEWMOS supplies all simulation strategies introduced. Several examples from different areas of dynamics show the power of the approach proposed.

Application of modified local parametrization method for the constrained multibody dynamic systems

This paper presents a corrector method for analyzing the dynamic behaviour of constrained multibody systems. For correcting the state variables this method uses Lagrange-Newton method, which is a nonlinear programming technique. The Lagrange-Newton method uses the Lagrangian function that is a combined form of state variables with constraints, and the iteration formulation for convergence can be derived by the Newton-Raphson method. This algorithm does not update the Lagrange multipliers in the iteration formulation, for correcting the state variables, and is to project the state variables on the constraint manifold, in contrast to the previous local parametrization method. The validity of the algorithm and numerical solutions is verified through the convergence theorem denoting the convergence order of numerical solutions and the dynamic analysis of the full vehicle 3D model. The numerical solutions are compared with the ADAMS solutions

Dynamic analysis of constrained multibody systems using Kane's method

A new formulation for the dynamic analysis of constrained multibody systems is presented in this paper. The formulation employs Kane's method along with the null space method. Kane's method reduces the dimension of equations of motion by using partial velocity matrix introduced in this study : it can improve the efficiency of the formulation. Three numerical examples are given to demonstrate the accuracy and efficiency of the formulation.

An Implicit Multistage Integration Method Including Projection for the Numerical Simulation of Constrained Multibody Systems

To be efficient, the simulation of multibody system dynamics requires fast and robust numerical algorithms for the time integration of the motion equations usually described by Differential Algebraic Equations (DAEs). Firstly, multistep schemes especially built up for second-order differential equations are developed. Some of them exhibit superior accuracy and stability properties than standard schemes for first-order equations. However, if unconditional stability is required, one must be satisfied with second-order accurate methods, like one-step schemes from the Newmark family.

Numerical integration of multibody system dynamic equations using the coordinate partitioning method in an implicit Newmark scheme

The modelling of constrained multibody systems has been widely studied, published and implemented into computer programs, using different formalisms and terminologies. The resulting equations are formally of a mixed nature, viz. differential-algebraic, and cannot be directly solved by classical integrator schemes. Among the various techniques proposed for solving differential-algebraic equations, none exhibits a real superiority in terms of reliability, generality and efficiency. Depending on subjective criteria related to his applications, the ‘user’ has to select the most suitable method among several whose range of application is limited: indeed most of the time, this choice is ‘problem dependent’. This paper proposes a method which conjointly takes advantage of the Coordinate Partitioning method and of the suitability of an implicit integration scheme regarding multibody systems containing flexible bodies. The top priority underlying this contribution is the rigorous resolution of the constraints during the simulation, whatever the application to be analysed.

Augmented lagrangian and mass-orthogonal projection methods for constrained multibody dynamics

This paper presents a new method for the integration of the equations of motion of constrained multibody systems in descriptor form. The method is based on the penalty-Augmented Lagrangian formulation and uses massorthogonal projections for the solution to satisfy the kinematic constraint conditions. The number of equations being solved is equal to the number of states, and does not depend on the number of constraint conditions. Therefore, the method is particularly suitable for systems with redundant constraints, singular configurations or topology changes. The major advantage of the new method relies on the fact that for a low computational cost, the constraints in positions, velocities and accelerations are satisfied to machine precision during the numerical integration. This process is efficiently done by means of a mass-orthogonal projection without the need for coordinate partitioning or reduction to a minimum set of coordinates. The projection scheme allows for a more accurate and robust integration of the equations of motion since constraint violations constitute one of the primary sources of numerical errors and instabilities during the integration process. The proposed projection is also applied to the classical Lagrangian approach, thus eliminating the need for further stabilization as well as the selection of parameters in Baumgarte's method.

Parameter Identification and Experimental Investigations of Unconventional Railway Wheelset Designs on a Scaled Roller Rig

SUMMARY In this paper a parameter identification method for multibody systems is applied to a 1:5-scaled two-axled railway vehicle with conical wheels on a roller rig with UIC 60 roller profiles. The aim is to demonstrate how parameter identification in connection with constrained multibody systems and dynamical measurements can be performed The process of mathematical modelling and solution approach is described, where emphasis is laid on the structure of equations, modelling of the wheel-roller contact, numerical methods and the representation of the parameter identification method for the determination of the unknown stiffness and damping parameters as well as uncertain parameters like the coefficient of friction and manufacturing imperfections of the vehicle Additionally it is indicated that the 1:s-scaled railway vehicle can be utilized for running behaviour experiments with unconventional wheelset designs.

An orthonormal tangent space method for constrained multibody systems

An automatic computer code for constructing an orthonormal basis of tangent (null) space for constrained multibody systems is proposed. The method uses the Gram-Schmidt vector orthogonalization process, adjusted to the Riemannian geometry formalism. An important and useful peculiarity of the formulation is that the minimal-order (purely differential) equations of the constrained motion are obtained directly in the resolved form, i.e. the mass matrix of the equations is the unity matrix. Some other interesting features of the formulation, leading to additional gain in efficiency of the dynamic analysis of constrained systems, are also reported.

A new approach to formulation of the governing equations of constrained multibody systems

In this paper a new method to formulate automatically the governing equations of constrained multibody systems is presented based on the property of constraints. In this method, the equations of motion for an unconstrained multibody system are converted into those of the associated constrained multibody system. Instead of introducing a set of Lagrange multipliers, the constraint forces are evaluated before integrating the governing equations; thus the process of finding an orthogonal-complement matrix of the constraint Jacobian matrix is avoided, which saves much computational time. Compared with other methods, more information about the dynamics of the multibody system is obtained by integrating the same number of differential equations. Additionally, a new stabilization technique is given in this paper.

An Orthogonal Complement Matrix Formulation for Constrained Multibody Systems

A method is proposed for the automatic generation of an orthogonal complement matrix to the constraint matrix for the dynamic analysis of constrained multibody systems. The clue for this method lies in the determination of local constraint matrices and their orthogonal complements relative to the local reference frames of particular constrained points. These matrices are then transformed into the system’s configuration space in order to form the final constraint matrix and its orthogonal complement. The avoidance of singularities in the formulation is discussed. The method is especially suited for the dynamic analysis of multibody systems with many constraints and/or closed-loops.

Computer-oriented closed-form algorithm for constrained multibody dynamics for robotics applications

An alternative computer-oriented algorithm for generating the equations of motion for constrained multibody systems subject to control is presented. The algorithm is derived from the principle of virtual work and includes the effect of a moving reference frame. The equations of motion are expanded in a closed form in terms of a minimum set of variables. Symbolic implementation, simplification and linearization are discussed. Computer-based models of a biped robot walking on a vibrating platform are generated. Dynamic behavior of the biped is simulated by implementing the optimal control theory. The study shows that this closed-form formalism holds promise in the simulation of constrained robotic systems.