Conceptual design method of link mechanisms based on topology optimization and concept of micropolar continuum theory

Abstract

This paper presents a conceptual design approach for planar link mechanisms by utilizing continuum topology optimization based on micropolar continuum theory. To effectively simulate the behavior of link mechanisms as continuum elasticity, we introduce a mathematical model utilizing micropolar elasticity. Although topology optimization is commonly used for single mechanical components, extending it to mechanisms with multiple interconnected parts presents inherent challenges. To address these challenges, we model the link mechanism using micropolar elasticity, leveraging its bendiness-related material property, which can apply to topology optimization. Subsequently, we formulate a topology optimization problem to generate link mechanisms using our proposed model. The optimized structure achieves the desired motion and deformation characteristics like traditional linkages with proper degrees of freedom while minimizing the objective function that considers both output motion error and link compliance. The design variables of the topology optimization problem are defined using the Solid Isotropic Material with Penalization (SIMP) method, which is further updated using a gradient-based optimizer. The governing equations of linear micropolar elasticity are solved using the Finite Element Method (FEM). The effectiveness and validity of our proposed method are evaluated through numerical examples, which conclusively demonstrate its ability to synthesize the number, dimensions, and structure of link mechanisms.