In this paper a dynamic system consisting of a robot manipulator and a target is analyzed. The target is considered in a general way as a dynamic subsystem having finite mass and moments of inertia (e.g. a rigid body or a second robot). The situation investigated is when the robot establishes interaction with the target in such a way that it intercepts and captures a reference element of the target. The greatest attention is paid to the analysis of the phase of transition from from ‘free’ to constrained motion at the time of interception and capture (impulsive motion). Based on the use of impulsive constraints and the Jourdanian formulation of analytical dynamics, a novel approach is proposed for the modeling of target capture by a robot manipulator. The proposed approach is suitable to handle both finite and impulsive motions in a common analytical framework. Based on the dynamic model developed and using a geometric representation of the system’s dynamics, a detailed analysis and a performance evaluation framework are presented for the phase of transition. Both rigid and structurally flexible models of robots are considered. For the performance evaluation analyses, two main concepts are proposed and corresponding performance measures are derived. These tools may be used in the analysis, design and control of time varying robotic systems. The dynamic system of a three link robot arm capturing a rigid body is used to illustrate the material presented.