Many applications require mechanical systems to meet several performance specifications, achieved through the suitable design of their mechanisms and controllers. The mechanical design establishes the parts and components that make up a mechanism to obtain valuable mechanical properties in its motion. Control design, however, aims to ensure that the mechanical system performs its task with the highest possible performance. By their very nature, these design problems can be conceived in a bilevel hierarchical way, where any change in the components of a mechanism to achieve mechanical design goals is affected by the control parameters that govern its behavior, which aim to achieve its own control performance goals. This work develops the simultaneous mechanical and control design of systems under a Semi-Vectorial Bilevel Optimization (SVBO) approach for the first time to study its advantages and drawbacks compared to other design approaches used to date. In this approach, a single-objective mechanical design problem is considered at the upper level, and a multi-objective controller design problem is addressed at the lower level. A proposed Evolutionary Semi-Vectorial Optimizer (ESVO) handles the resulting design model. The approach is tested using two case studies: the mechanical and control design of two four-bar mechanisms, one Grashof and one non-Grashof. The results obtained with the proposed approach are compared with three representative design approaches (manual, multiobjective and sequential). The proposed SVBO approach obtained adequate mechanical design with valuable trade-off between control requirements. The complete approach developed can be extended to tackle concurrent designs of other relevant engineering domains.