Synthesis of discrete mechanisms: a hybrid approach based on geometric algebra and genetic algorithms

Subject of research: automated synthesis of workable kinematic schemes and mechanisms from a given discrete set of functional components. Purpose of research: to overcome the fundamental limitations of modern generative design and topological optimization methods, which are unable to operate with discrete components and guarantee kinematic closure, by developing a new hybrid design architecture. Research methods: hybrid Evolutionary-Symbolic AI architecture combining evolutionary modeling (genetic algorithms) for structural optimization and Projective Geometric Algebra (PGA, Clifford algebra) for analytical enforcement of kinematics. Objects of research: synthesis tasks for mechanisms with continuous and conditional closure. Research findings: an approach was developed that separates the generation of a "kinematic skeleton" (via PGA) and its material implementation from standard parts (via genetic algorithm). The method guarantees assemblability, filters out kinematically incorrect variants at early stages, and solves the problem of phase-dependent contacts (collision vs constraint). Testing showed an 85–90 % reduction in the search space and successful synthesis of mechanisms replicating complex trajectories and performing clamping functions.