In this paper, we describe the nonlinear models of a rod in three-dimensional space based on the Cosserat theory. Using the pseudo-rigid body method and variational principle, we obtain the motion equations of a Cosse...In this paper, we describe the nonlinear models of a rod in three-dimensional space based on the Cosserat theory. Using the pseudo-rigid body method and variational principle, we obtain the motion equations of a Cosserat rod including shear deformations.展开更多
Continuum robots actuated by flexible rods have large potential applications,such as detection and operation tasks in confined environments,since the push and pull actuation of flexible rods withstand tension and comp...Continuum robots actuated by flexible rods have large potential applications,such as detection and operation tasks in confined environments,since the push and pull actuation of flexible rods withstand tension and compressive force,and increase the structure's rigidity.In this paper,a generalized kinetostatics model for multi-module and multi-segment continuum robots considering the effect of friction based on the Cosserat rod theory is established.Then,the model is applied to a two-module rod-driven continuum robot with winding ropes to analyze its deformation and load characteristics.Four different in-plane configurations under the external load term as S1,S2,C1,and C2 are defined.Taking a bending plane as an example,the tip deformation along thex-axis of these shapes is simulated and compared,which shows that the load capacity of C1 and C2 is generally larger than that of S1 and S2.Furthermore,the deformation experiments and simulations show that the maximum error ratio without external loads relative to the total length is no more than 3%,and it is no more than 4.7%under the external load.The established kinetostatics model is proven sufficient to accurately analyze the rod-driven continuum robot with the consideration of internal friction.展开更多
In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables： time t and arc coordinate s. Starting from the Lagrange equations of Cosserat ro...In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables： time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals.展开更多
The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical ...The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.展开更多
Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff＇s kinetic analogy is an effective approach to the stability analysis of e...Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff＇s kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff＇s theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler＇s angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov＇s stability of the helical equilibrium is discussed in static category. Euler＇s critical values of axial force and torque are obtained. Lyapunov＇s and Euler＇s stability conditions in the space domain are the necessary conditions of Lyapunov＇s stability of the helical rod in the time domain.展开更多
基金supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry of China
文摘In this paper, we describe the nonlinear models of a rod in three-dimensional space based on the Cosserat theory. Using the pseudo-rigid body method and variational principle, we obtain the motion equations of a Cosserat rod including shear deformations.
基金Supported by National Natural Science Foundation of China(Grant No.51875033)Fundamental Research Funds for the Central Universities of China(Grant No.2021YJS137).
文摘Continuum robots actuated by flexible rods have large potential applications,such as detection and operation tasks in confined environments,since the push and pull actuation of flexible rods withstand tension and compressive force,and increase the structure's rigidity.In this paper,a generalized kinetostatics model for multi-module and multi-segment continuum robots considering the effect of friction based on the Cosserat rod theory is established.Then,the model is applied to a two-module rod-driven continuum robot with winding ropes to analyze its deformation and load characteristics.Four different in-plane configurations under the external load term as S1,S2,C1,and C2 are defined.Taking a bending plane as an example,the tip deformation along thex-axis of these shapes is simulated and compared,which shows that the load capacity of C1 and C2 is generally larger than that of S1 and S2.Furthermore,the deformation experiments and simulations show that the maximum error ratio without external loads relative to the total length is no more than 3%,and it is no more than 4.7%under the external load.The established kinetostatics model is proven sufficient to accurately analyze the rod-driven continuum robot with the consideration of internal friction.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11262019 and 10972143)
文摘In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables： time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals.
基金Project supported by the National Natural Science Foundation of China (Grant No 10472067)
文摘The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.
基金supported by the National Natural Science Fundation of China(No.10972143)
文摘Helical equilibrium of a thin elastic rod has practical backgrounds, such as DNA, fiber, sub-ocean cable, and oil-well drill string. Kirchhoff＇s kinetic analogy is an effective approach to the stability analysis of equilibrium of a thin elastic rod. The main hypotheses of Kirchhoff＇s theory without the extension of the centerline and the shear deformation of the cross section are not adoptable to real soft materials of biological fibers. In this paper, the dynamic equations of a rod with a circular cross section are established on the basis of the exact Cosserat model by considering the tension and the shear deformations. Euler＇s angles are applied as the attitude representation of the cross section. The deviation of the normal axis of the cross section from the tangent of the centerline is considered as the result of the shear deformation. Lyapunov＇s stability of the helical equilibrium is discussed in static category. Euler＇s critical values of axial force and torque are obtained. Lyapunov＇s and Euler＇s stability conditions in the space domain are the necessary conditions of Lyapunov＇s stability of the helical rod in the time domain.
