###### Abstract
This innovative design employed interference plates to regulate localized stiffness without the need for additional devices, offering precise control over deformation and adaptability to complex scenarios. The study demonstrated the capability to efficiently adjust stiffness by preprogramming stiffness profiles, significantly reducing the reconstruction time and enhancing environmental compliance. However, challenges remain, particularly concerning the construction of the continuum model. The research work discussed above primarily focused on the flexible components of continuum robots, such as trunk-like structures, while largely excluding considerations of the rigid parts, such as the wrist or prearm, that are often critical for certain applications. The development of such models requires intricate design considerations, including balancing flexibility and structural integrity, accurately modeling the dynamic behavior of the system, and addressing the complexity of implementing effective trajectory-tracking algorithms. Additionally, a miniaturized and lightweight design, while advantageous for confined spaces, can result in limitations such as a reduced load capacity and increased susceptibility to external forces, which may compromise stability and precision during operation. These drawbacks highlight the need for further research to integrate rigid and flexible components into a unified framework, optimizing the construction and control strategies of continuum models for demanding applications. To address these complexities, the multibody system approach provides a robust framework for modeling the dynamics of systems comprising rigid and flexible components [8]. By integrating continuum mechanics within the multibody dynamics framework, formulations such as the Absolute Nodal Coordinates Formulation (ANCF) enable the precise modeling of large deformations and large rotation problems [9; 10]. Unlike simplified assumptions of constant curvature or discrete elastic rod models, the ANCF allows for the comprehensive representation of structural flexibility, geometric nonlinearities, and cross-sectional distortions. This approach not only enhances the accuracy of dynamic simulations but also supports the development of integrated kinematic and static models, enabling sophisticated applications in soft and continuum robotics. However, modeling the rigid-flexible interface in multibody systems presents significant challenges due to the contrasting dynamic characteristics of rigid and flexible bodies. Rigid bodies require simplified modeling, often focusing on positional and orientational coordinates, while flexible bodies necessitate a detailed representation of deformations, strain distributions, and dynamic interactions. This disparity introduces complexity in coupling these components within a unified framework. The strain-based nonlinear beam formulation, as presented in [11], provides an effective approach for analyzing complex rigid-flexible interfaces. It enhances computational efficiency and stability by employing strain measures and minimizing cross-sectional deformations, making it particularly suitable for slender, geometrically nonlinear systems. While it reduces the number of variables and achieves better convergence compared to the ANCF, its integration into multibody frameworks requires substantial modifications, and its applicability to complex or non-slender geometries remains unclear. The Natural Coordinates Formulation (NCF) [12; 13; 14] offers an effective method for modeling rigid bodies using Cartesian coordinates that inherently increase the number of shared coordinates among interconnected rigid-flexible bodies. This formulation is particularly effective in systems with Differential Algebraic Equations (DAEs), as it ensures the mass matrix remains constant and simplifies the integration of linear constraints.