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This Chapter deals with the optimal balancing of gravitational forces. In Sect. 8.1, the balancing methods of manipulator mechanisms with the reduced number of springs, which are based on the copying properties of the pantograph mechanism, are presented. Then, in Sect. 8.2, a newly designed parallel robot for medical 3D-ultrasound imaging is considered for an optimum static balancing. The optimum solutions reduces substantially the effect of gravity with simple mechanical system. The efficiency of the suggested solutions is illustrated by numerical simulations.
Section 8.3 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-free length springs, the stiffness coefficient of the springs is determined from a quadratic equation and for non-zero-free 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.
The last Section (Sect. 8.4) improves the known design concepts permitting the dynamic decoupling of serial manipulators with an optimal balancing schemes permitting relatively small increase in the total mass of the moving links.
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- Gravitational Force Balancing of Robotic Systems
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