A new monolithic fully compliant gravity balancer is designed with help of a design approach based on shape optimization. The balancer consists of one single complex-shaped beam on which the weight is attached. The beam is modeled as a planar isogeometric Bernoulli beam. The goal function of the optimization consists of an energy based evaluation of the load path of the beam which is compared with a desired response. The best result of the shape optimization has been constructed out of polycarbonate sheet and has been tested on a compression test bench. The experimental results have good resemblance with the theoretical model.