Three-Dimensional Dynamics of a Rigid Body with Wheels on a Moving Base

Abstract

For reasons more related to functionality than safety, it is not uncommon for heavy mechanical and electrical equipment to be placed on wheels. Examples of such devices are medical carts, mechanical equipment in hospitals, electrical transformers, and recently, even supercomputers. Although wheels facilitate the operation of these devices, they also affect the response of these objects during earthquakes, but not necessarily in a beneficial way. While a wheel rolling favors the translational displacement of the body in the horizontal direction parallel to its plane over rocking, rocking is still possible along the plane perpendicular to the plane of the wheel. Moreover, because the plane of the wheel is in most cases free to rotate with respect to the body, it is not easy to identify the directions that favor rocking or displacement at any time. The problem becomes even more complicated, if one considers that one of the wheels, which can swivel, may be locked. Thus, in the most general case, a body on wheels experiences three-dimensional displacements and rotations along with the three-dimensional dynamics of the wheels. In this work, a model for the dynamic behavior of bodies on wheels is presented and the corresponding response behavior is examined for several common cases.