A generalized recursive formulation for constrained flexible multibody dynamics

This research develops a relative co-ordinate formulation for the multibody exible dynamics.The velocity transformation method is notationally compact, because the Cartesian generalized velocities are simultaneously transformed to the relative generalized velocities in a matrix form. However, inherent computational e ciency in the recursive kinematics between two adjacent bodies has not been exploited. This research presents a recursive formulation which is both notationally compact and computationally e cient. The velocity transformation method is used to derive the equations of motion and their derivatives. Matrix operations associated with the velocity transformation matrix in the resulting equations of motion and their derivatives are classi ed into several categories. A joint library of the generalized recursive formulas is developed for each category. When one category is encountered in implementing the equations of motion and their derivatives, the corresponding recursive formulas in the category are invoked. When a new force or joint module is added to a general purpose programme in the relative co-ordinate formulation, the modules for the rigid body are not reusable for the exible body. Since the exible body dynamics handles additional generalized co-ordinates associated with deformation, implementation of the exible dynamics is generally complicated and prone to coding mistakes. A virtual rigid body is introduced at every joint and force reference frames. A virtual exible body joint is introduced between two body reference frames of the virtual and original bodies. This makes a exible body subjected to only the kinematic admissibility condition for the virtual exible body joint. As a result, the only extra work to handle the exible bodies is to add the virtual exible body joint modules in all recursive formulas. Since computation time in a relative co-ordinate formulation is approximately proportional to the number of relative co-ordinates, computational overhead due to the additional virtual bodies and joints are minor. Meanwhile, implementation convenience is dramatically improved