Modeling of translational motion between two flexible bodies connected via three points

Abstract

A dynamic model is presented in this paper for modeling the translation of a flexible body over another flexible body with three load transmission points between them. The three contact points on one of the bodies continuously change as one body translates with respect to the other. No software tools currently exist for simulating the dynamic response of this two-body system. In the present model, six degrees of freedom are allowed between the two bodies and then contacts are modeled using constraints that account for the relative motion. The small, elastic deformation of each body is modeled using the method of assumed modes. Numerical results presented demonstrate the dynamic interactions. The steps needed for implementation in multibody dynamics codes are outlined. The Mobile Transporter-Space Station system is a direct application for the present model. YNAMICS formulations13 and software analysis tools such f as TREETOPS4 and DISCOS5 model the relative motion between two bodies in an articulated, flexible multibody system through a hinge that can permit up to six degrees of freedom (DOFs). In such models, the relative translational motion is defined as that occurring between two points, one each fixed in each of the bodies, and the relative rotational motion as that between two reference frames, one each attached at the same two points in the respective bodies. A typical hinge definition is shown in Fig. 1. This definition facilitates the modeling of open-loop, articulated flexible multibody systems such as the Shuttle Remote Manipulator System (SRMS) and typical spacecraft with articulating flexible solar arrays. In the case of closed-loop systems, a cut joint is introduced to render the system open loop, with the joint definition the same as above, and then loop closure constraints are imposed. A consequence of the above definition for a joint connecting two bodies is that the dynamics of a flexible beam translating over two rigid supports, studied by Buffinton and Kane,6 cannot be modeled using the above formulations or software. This is because the points on the flexible beam that are in contact with the two rigid supports continuously change as the beam translates. The translation joint modeling in Refs. 1-5 assumes that the translation occurs along a rigid appendage, although the bodies themselves may be flexible. Although not incorporated into TREETOPS,4 Li and Likins7 extended the approach of Singh et al.4 to include travel along a curved flexible path, with a single point contact between the flexible guide and the body traveling on it. Hwang and Haug8 modeled one- and two-point contacts between two flexible bodies but presented numerical results only for the single-point contact case. Another system that cannot be modeled using the above joint definition alone is shown in Fig. 2. Body j and body L(y) in this figure are in contact at three locations and body j travels over a pair of parallel tracks that are fixed to body L(j). Two of the three contacts between the bodies occur over one rail whereas the third contact occurs over the other rail. Both the bodies are flexible. The interaction dynamics with multipoint contact between flexible bodies and with a relative DOF has not been modeled in the literature and cannot be simulated using the available multibody dynamics software. Single- and multipoint contact studies in the literature912 investigate how a flexible body will react to a given set of moving point