The balancing of robotic systems is an important issue because it allows significant reduction of torques. However the literature review shows that the gravity balancing of robotic systems is carried out by weightless springs. For many balancing schemes it is the source of errors. This paper deals with an analytically tractable solution for the gravity balancing considering the spring mass. For this purpose, the relationship between the stiffness coefficient of the spring and its mass is provided. Then this relationship is introduced into the balancing equation and spring elastic force is determined taking into account its mass. For zero length springs, the stiffness coefficient of the springs is determined from a quadratic equation and for non-zero length springs from a cubic equation. In this way, an exact balancing of gravitational forces is achieved, which allows improving the balancing accuracy of robotic systems. The efficiency of the suggested approach is illustrated by numerical examples. An application to the balancing of the leg orthosis for robotic rehabilitation is also presented.

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