Static balancing of mechanical systems is useful and required in many situations. The objective of such balancing is the compensation of gravitational forces in order to achieve a static equilibrium. A balanced system becomes safer and actuators are reduced in size. However, balancing a system requires numerous complex mechanical add-ons or unavoidable addition of mass. This is the reason why methods of partial static balancing have been developed and applied in practice. In this paper, a newly designed parallel robot for medical 3D-ultrasound imaging is required to be statically balanced without complicated design modifications. Simple mechanical add-on that is optimally designed can reduce substantially the effect of gravity. The efficiency of these suggested solutions is illustrated by numerical simulation of the robot.