The reachable workspace of a robot carrying a payload is usually limited by the maximal value of the torque that each actuator can deliver. This results in limiting the zones for the robot to operate with the payload due to a possible division of its static-wrench workspace into several disconnected aspects. In order to increase the reachable workspace areas, this paper proposes to exploit the natural oscillations in dynamics, so that the robot can carry a payload which is out of its feasible static-wrench workspace, i.e. to perform motions between two disconnected aspects, while constraining the torques of the actuators. This is done thanks to the solution of a boundary value problem, which seeks to smartly exchange the gravity potential energy and the kinetic energy in order to connect two desired payload positions, which are placed in two disconnected aspects. Simulations of the suggested approach on a 2-degree-of-freedom robot are performed and show the efficiency of the proposed approach.