Multibody Dynamics Formulation Research Articles

A recursive formulation for flexible multibody dynamics, part II: Closed loop systems

A recursive formulation for dynamics of closed loop flexible multibody systems is presented. Joints in closed loops in a flexible mechanism are cut to form a spanning tree structure. Cut joint constraint equations and associated Lagrange multipliers are introduced to represent cut joint reaction force and torque. A recursive formulation for closed loop systems is derived by extending the method presented in Part I of the paper. A flexible four-bar mechanism and a space robot system are studied to demonstrate efficiency of the recursive formulation.

A recursive formulation for flexible multibody dynamics, part I: Open-loop systems

This paper presents a recursive formulation for dynamics of flexible multibody systems. Deformation modes are used to represent elastic deformation of each body, relative to a body reference frame that is permitted to undergo large displacement and rotation in space. Kinematic relations between contiguous bodies that are connected by articulated joints are defined by relative joint coordinates. A recursive variational vector calculus method is presented for efficient formulation and solution of the equations of motion on parallel processors. A manipulator and a rotating blade with geometric nonlinear effects are studied to illustrate computational efficiency of the recursive formulation.

On the equivalence of Kane's equations and Gibbs' Equations for multibody dynamics formulations

On the equivalence of Kane's equations and Gibbs' Equations for multibody dynamics formulations