In this work, the possibilities to approach various nonlinear moment-angle characteristics with a kinematically indeterminate rigid body balancer with torsion springs are examined. These torsion springs are mounted on the axes that intersect the rigid bodies. The rigid body balancer is coupled to an inverted pendulum. Although the kinematic indeterminate nature of the system enables the balancer to rotate non-proportionally along with the pendulum, the kinematics should correspond with the equilibrium configurations of the system. The required system parameters as spring stiffnesses and element lengths are obtained by optimization with a genetic algorithm. In addition to the standard optimization case, the effects of prestressed springs with contact release, nonlinear springs, optimizable initial configuration and an extra segment on the approximations are studied as well. Moreover, an extra objective function that concerns the distribution of energy among the springs is introduced. Eventually, the results that are obtained by the proposed method are verified with an experimental setup that contains a prototype of the system. The experimental results show agreement with the model with 93.47% work reduction. The corresponding model reduces the required work with more than 99%, which is higher than found in the state of the art.