High-precision systems often comprise many individual systems, each operating at its own frequency. However, the vibrations from one system can be transmitted to another, which yields a response. In high-tech applications where precision is crucial, such as compliant transmission systems, these responses are undesired as they result in a loss in precision. Topology optimization can be employed to directly include these unwanted vibrations in the design process of compliant mechanisms. However, the current literature only concerns simple beam structures and suffers from issues such as premature convergence and large intermediate-density areas. This thesis aims to employ topology optimization to design compliant transmission systems whilst simultaneously attenuating the effects of unwanted external vibrations in the form of base excitations. This is done by using an objective function capable of minimizing the displacement response of a structure whilst not suffering from the aforementioned issues. The found objective function relies on the principle of global minimization, which minimizes the largest displacements inside the structure resulting from the applied excitation. An extension of the current research is done by only minimizing a subset of the domain, obtaining a localized minimization whilst other areas of the domain are allowed to exhibit larger responses. These two minimization principles are then applied to the design of a compliant inverter mechanism, with local minimization considering two areas of interest: the entire mechanism area and the regions around the input and output of the mechanism. The results show that global minimization is able to obtain discrete results for a large range of frequencies. Local minimization of the mechanism area yields lower displacement responses and, for higher frequencies, resulting topologies with displacement behaviour similar to the principles of vibration absorption and vibration isolation. Decreasing the response area to be minimized only to cover the input and output regions of the mechanism yields inconclusive results in terms of obtaining lower displacement responses compared to local minimization of the mechanism area. A proof of concept for designing a compliant transmission system whilst minimizing the response to harmonic base excitations is established, demonstrating potential benefits for future research in this domain.