Automated spacecraft docking is a technology that has long been pursued. Deep space explorers and small spacecraft can carry fewer resources for docking, such as navigation sensors or latching structures, than can their larger near-Earth counterparts. The concept of the probe-cone docking mechanism is an effective solution to this problem. In this approach, a probe attached to the chaser satellite is guided automatically to the connection part of the target satellite by a conical structure. It is important to have a shock attenuation mechanism at the docking interface to prevent the chaser from being bounced away from the target. In the present paper, an automated docking mechanism that uses a flexible and deployable boom as the probe is proposed, and results of an analysis of the multi-body system dynamics are presented. Although analytical investigations into docking dynamics have been reported, the dynamics depend on many interdependent design parameters, the interaction of which is yet to be investigated. The present work involved a numerical analysis of the effect of each design parameter on the satellite behavior. An energy-based index that can predict the success or failure of docking was also developed in this study. In addition, a design scheme for the parameters is presented based on the results of the analysis in which the optimal combination of the design parameters is determined by searching the solution space.