Balancing is another efficient way to improve the performance of robot motions. In literature, it is extensively considered as a modification and/or addition of passive elements such as links, counterweights [11], or springs [12], and is divided into two major types: complete and partial balancing [13]. In complete balancing, all the gravitational, velocity-based coupling terms and inertial couplings are released [14], which results in heavy counterweights and counter rotors that make balancing impossible for usual applications. On the other hand, a few researchers have defined a performance index for partial balancing problem [15] based on some predefined trajectories or some dynamical properties. Since the choice of balancing parameters changes dynamics and optimal trajectory of the system, the balancing parameters, and optimal trajectories cannot be designed individually. This hint motivates the idea of optimal balancing method (OBM) proposed by Nikoobin and Moradi [16] as the most general mathematical theory about partial balancing. Moreover, it has been shown that the static balancing is a special case of OBM [17]. In OBM, some unknown parameters are found simultaneously with trajectory unknowns such as position waypoints and velocity profiles. In the previous studies on the application of OBM for balancing [16,17], only one stage of motion was considered, making it hard to make a decision about overall performance improvement. For instance, the values of payload for carrying and returning phases are different. So, applying OBM to a carrying phase is not necessarily the optimal choice for the overall motion.