Finite element modeling of an origami inspired delta mechanism

Abstract

Incorporating origami principles into engineering practices has proven valuable for the construction, assembly, and functionality of structures in aerospace, robotics, and related domains. With the increasing complexity of origami structures in terms of geometry and material considerations, the development of computational models and design methodologies has become essential to enhance their engineering applicability. One particularly popular parallel mechanism employed in robotic applications is the Delta mechanism. This research makes significant contributions to the field of origami-inspired engineering and delta mechanism design. One key objective is to showcase the wide-ranging applicability of the origami-inspired delta mechanism across various industries, such as robotics, manufacturing, and aerospace. This mechanism's remarkable attributes, such as exceptional precision, adaptability, and energy efficiency, make it highly suitable for tasks involving precise positioning, swift movement, and compact designs. Additionally, the study highlights the efficacy of finite element modeling for analyzing origami-inspired structures. Through numerical simulations, valuable insights into complex folding patterns and their engineering applications are obtained, allowing for a detailed examination of deformation and overall performance. The integration of FEM modeling and experimental validation enables a thorough understanding of mechanical behavior and performance of origami-inspired delta mechanisms. Furthermore, the findings contribute to enhancing the design of the mechanism, bolstering its precision, adaptability, and efficiency. Incorporating origami-inspired design methodologies and 2D monolithic layered production techniques, this study employs the Delta mechanism, a commonly utilized component in small-scale robotics systems. The objective is to develop a streamlined assembly process that preserves the planar structure while minimizing intermediate steps such as folding and bonding, which lie outside the core procedures of the selected techniques. Leveraging the 2D fabrication approach, the mechanism's assembly can be simplified to a single cycle of cutting, bonding, and repetition. For this project, the chosen fabrication method is called "Smart Composite Microstructures" (SCM). This method involves cutting sheets with different properties and arranging them in a specific pattern, forming a five-layered structure consisting of rigid, adhesive, flexible, adhesive, and rigid layers. The rigid layer employs 400-gram American Bristol paper, while the flexible layer utilizes PET plastic. Additionally, the inclusion of one or two layers of 3D printed TPU material further enhances the design. The mechanisms patterns are generated using innovative origami-inspired design approaches. The research demonstrates the successful modeling of the trajectory behavior of a novel Delta mechanism, constructed using layer-by-layer origami, by incorporating the dimensions of the actual fabricated mechanism. Tensile testing experiments provided crucial material properties for the four distinct materials utilized in the mechanism. Leveraging finite element method (FEM) simulations, an in-depth analysis of deformations and overall performance was conducted under diverse loading conditions. The numerical results yielded valuable insights into the mechanism's behavior. Validation of the FEM simulations was performed through displacement measurements on a physical prototype of the origami-inspired Delta mechanism, comparing numerical and experimental results. The FEM analysis demonstrated remarkable precision in positioning and movement, underscoring its potential for high-precision applications. The experimental validation provided robust evidence of the strong agreement between the experimental and numerical results, thereby affirming the accuracy of the numerical simulations and enriching our understanding of the mechanism's real-world behavior and performance. By comparing finite element simulations, we determined that the mechanism closely followed the trajectory with a maximum error of 0.05 in normalized root-mean-square (RMS) values, in comparison to the kinematic model. Employing FEM simulations, we analyzed the impact of fabrication and instrumentation errors on the trajectory and meticulously evaluated the contribution of each factor to the overall error. Incorporating uniaxial test data into the hyperelastic material model, the novel numerical results are compared to previous existing models. The novel model displays significantly reduced RMS errors and highlights critical joint regions in folding zones. To mitigate strain, eight inventive joints are formulated. Comparative study reveals strain reduction in all novel mechanisms. This guides mechanism selection for specific goals like joint strain reduction. About half of the novel mechanisms are deemed optimal designs based on RMS errors in the standard trajectory. Exploring novel mechanisms under diverse loads identifies optimal of models. Numerical results, involving strain deviations, and trajectory RMS errors for an 8 mm radius and 50 mm elevation, mirror standard trends closely. At Z=50 mm, Org_〖30〗^◦and Org_〖45〗^◦are promising. For 10 mm radius and 40 mm elevation, Nov1_〖30〗^◦is the evident choice, maintaining coherent deviation and error patterns. Strain reduction in each joint facilitates optimal sensor placement within folding joints. This approach effectively diminishes sensor failure rates and mitigates sensor cracking issues. Leveraging this validated numerical representation, future simulations of origami-inspired mechanisms can be conducted with confidence, facilitating the design of innovative mechanisms.