<p>Inspired by the performance improvement of parallel mechanisms through redundant actuation, this paper proposes a novel redundantly actuated 4-RRR compliant spherical parallel mechanism (CSPM) by introducing a redundantly actuated branch into the compliant 3-RRR spherical parallel mechanism. First, the kinetostatic model of the redundantly actuated 4-RRR CSPM is derived using the compliance matrix method. Subsequently, the parasitic displacement model of the mechanism is further derived based on this model. Since the parasitic displacement model links the parasitic displacement and the output angular displacement through a compliance matrix (hereinafter defined as <Emphasis Type="BoldItalic">C</Emphasis>_<i>D-PD</i>), this paper proposes a structural optimization design method based on the compatibility theorem of Frobenius norms. This method aims to minimize the Frobenius norm of the compliance matrix <Emphasis Type="BoldItalic">C</Emphasis>_<i>D-PD</i>, thereby achieving the minimization of the overall parasitic displacements of the mechanism. In the simulation validation section, the correctness of the kinetostatic model and the parasitic displacement model is verified by comparing theoretical results with finite element simulations, using a specified spatial helical trajectory and a planar circular trajectory. Then, based on these two trajectories, the effectiveness of the structural optimization method is validated by comparing parasitic displacement changes before and after optimization. The structural optimization design method proposed in this paper, which aims to minimize the overall parasitic displacement, can also serve as a reference to the structural optimization of other similar parallel mechanisms.</p>