Balancing of Planar 5R Symmetrical Parallel Manipulators Taking into Account the Varying Payload

The shaking force balancing are carried out by an optimal redistribution of moving masses, which allows one to cancel or reduce the variable dynamic loads on the manipulator frame. The shaking force balancing mostly leads to an increase in the moving mass of the manipulator, which has negative impact on the input torques and the shaking moment. It was shown that the force balancing method based on the minimization of dynamic loads on the manipulator frame via reducing the acceleration of the common centre of mass of moving links is more optimal from this point of view. To minimize the acceleration of the manipulator’s common centre of mass, and subsequently, the shaking force, the “bang-bang” law is used. In this paper, it is shown that such a solution is also efficient when the manipulator must be balanced taking into account the varying payload. Numerical simulations illustrate the simplicity and the efficiency of the suggested balancing technique.