A time-domain substructure synthesis for finite rotations of flexible mechanical systems

This paper presents a floating IBS method for dynamic prediction of structures with finite rotations. The conventional IBS (impulse-based substructuring) method is efficient and accurate in structural transient impact analysis. When facing about finite rotations, the conventional IBS method will generate unreasonable results due to the lack of consideration of geometric nonlinearity. In this paper, the idea of floating frame of reference is introduced. The motions of structures are divided into the moving of floating frame of reference and local vibrations which are described using the idea of IBS method. Two numerical examples validate that the proposed method is available for unconstrained single-body system (free-free rotating beam) and constrained multibody system (a slider-crank system). Meanwhile, to some extent the local elastic vibration degrees of freedom can be reduced by employing interpolation matrixes

Efficient Approach for Constraint Enforcement in Constrained Multibody System Dynamics

We present an efficient and robust approach for enforcing the loop closure constraint at acceleration, velocity and position level in modeling multi-rigid body system dynamics. Our approach builds on the seminal ideas of the Divide and Conquer Algorithm (DCA) and the Augmented Lagrangian Method (ALM). The order-independent hierarchic assembly-disassembly process of the DCA provides an excellent opportunity for modularizing the system topology such that the loop closure constraints can be elegantly handled using constraint enforcement ideas motivated by the ALM. We present a non-iterative, user controlled constraint enforcement approach that enables robust constraint enforcement within the DCA. This approach eliminates the need for the iterative scheme found in many ALM motivated approaches. Similarly, it enables the use of relative or internal coordinates to model kinematic joint constraints not involved in the loop closure, thereby enforcing the constraints exactly for these joints. The approach also enables computationally very efficient serial and parallel implementations. Results from a number of test cases with single and couple closed loops are presented to demonstrate verification of the algorithm.

Walking Pattern Generation for a Biped Robot Using Polynomial Approximation

In this paper, a stable walking pattern generation method for a biped robot is presented. A biped robot is considered as constrained multibody system by several kinematic joints. The proposed method is based on the optimized trunk motion along the moving direction. Foot motions can be designed according to the ground condition and walking speed. To minimize the deviation from the desired ZMP, the trunk motion is generated by the fifth order polynomial approximation. Walking simulation for the virtual biped robot is performed to demonstrate the effectiveness and validity of the proposed method. The method can be applied to the biped robot for stable walking pattern generation.

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.

A Symbolic Formulation for Linearization of Multibody Equations of Motion

This paper presents a method for obtaining linearized state space representations of open or closed loop multibody dynamic systems. The paper develops a symbolic formulation for multibody dynamic systems which result in an explicit set of symbolic equations of motion. The symbolic equations are then used to perform symbolic linearizations. The resulting symbolic, linear equations are in terms of the system parameters and the equilibrium point, and are valid for any equilibrium point. Finally, a method is developed for reducing a linearized, constrained multibody system consisting of a mixed set of algebraic-differential equations to a reduced set of differential equations in terms of an independent coordinate set. An example is used to demonstrate the technique.