For customized design of a hybrid manipulator for a specific application, selection of an appropriate configuration is always a challenge. To assist in this foremost decision in data-driven synthesis, a novel approach is proposed for modular formation of quick configurations. Majorly, a unified methodology is presented for the development of respective kinematic models and differential relations for their performance analyses. This unified modular approach utilizes modular primitives to define planar hybrid configurations. Three types of primitives are introduced as modular components, and the pattern study is detailed. Modeling results from the proposed approach are also compared with normally used partial differentiation with respect to the computational efforts, streamlined modular implementations, and applicability in optimal design approaches. The comparison highlights how the column-wise approach is appropriate for modular methodology. The strategy will help a designer as a tool for analyzing several configurations. Two realistic case studies are demonstrated in this article for application of the methodology in the medical robotics field.