MBS Motion Equation Without Explicit Definition of Body-Fixed Reference Frames

Abstract

Any description of rigid body motions requires body-fixed RFRs since the latter kinematically represent the bodies and are necessary to define their inertia properties. Consequently there is no formulation without RFR. Nevertheless this does not necessarily mean that the definition of body-fixed RFRs is an indispensable step in MBS modeling. A formulation without body-fixed reference frames is one that does not involve explicit definition of body-fixed frames to express the kinematics and the inertia data of an MBS. In this paper a formulation is presented that only requires a single spatial inertial frame to model all kinematic and dynamic properties of the MBS. It only requires the joint kinematics (axis and position vector) as well as the inertia tensors w.r.t. the spatial inertial frame in a reference configuration the MBS. That is, the inertia tensors of all rigid bodies are expressed w.r.t. a virtual body-fixed references frame that coincides with the spatial inertia frame in the reference configuration. Avoiding the explicit introduction of body-fixed reference frames significantly simplifies the MBS modeling. This is not only beneficial for manual modeling but also gives rise to much simpler MBS codes. The approach is discussed for tree-topology MBS as well as for closed loop systems. It is demonstrated for a planar slider-crank examples.