A Concise and Geometrically Exact Planar Beam Model for Arbitrarily Large Elastic Deformation Dynamics.

Area of Science:

• Robotics and Control Systems
• Continuum Mechanics
• Computational Mechanics

Background:

• Exploiting large elastic deformations in dynamic control applications, particularly robotic manipulation, remains challenging due to complex, computationally intensive continuum models.
• Existing control approaches often rely on simplified assumptions like small deflections or quasi-static conditions, limiting their applicability to complex dynamic scenarios.

Purpose of the Study:

• To develop a geometrically exact, yet concise, beam model suitable for control applications involving large elastic deformations in dynamic contexts.
• To enable the exploitation of elastic properties in planar beam dynamics for advanced robotic manipulation and control.

Main Methods:

• Reduced the general 3D Simo-Reissner beam model to a planar, shear- and torsion-free case without elongation.
• Utilized the assumption of inextensibility to simplify planar Cartesian parameters in relation to the beam's centerline tangent angle.
• Formulated the model within a finite element method (FEM) framework, incorporating position-related boundary conditions and tangent angle parametrization.

Main Results:

• Derived a concise, geometrically exact beam model for planar dynamics with large elastic deformations.
• Successfully incorporated boundary conditions and tangent angle parametrization within the FEM formulation.
• Validated the model's expressions against analytic initial value solutions and dynamic simulation energy analysis.

Conclusions:

• The presented beam model offers a computationally feasible approach for controlling large elastic deformations in planar systems.
• This model facilitates the design of online feedback control structures, enabling the full utilization of elasticity in dynamic robotic applications.