General Kinetostatic Modeling and Deformation Analysis of a Two-Module Rod-Driven Continuum Robot with Friction Considered

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.

考虑轴向大拉伸下弹性模量对聚酯系泊动态响应的影响

Owing to the particularity of a polyester fiber material,the polyester mooring undergoes large axial tensile deformation over long-term use.Large axial tensile deformation significantly impacts the dynamic response of the mooring system.In addition,the degrees of large axial tension caused by different elastic moduli are also different,and the force on the mooring line is also different.Therefore,it is of great significance to study the influence of elastic modulus on the dynamic results of the mooring systems under large axial tension.Conventional numerical software fails to consider the axial tension deformation of the mooring.Based on the theory of slender rods,this paper derives the formula for large axial tension using the method of overall coordinates and overall slope coordinates and provides the calculation programs.Considering a polyester mooring system as an example,the calculation program and numerical software are used to calculate and compare the static and dynamic analyses to verify the reliability of the calculation program.To make the force change of the mooring obvious,the elastic moduli of three different orders of magnitude are compared and analyzed,and the dynamic response results after large axial tension are compared.This study concludes that the change in the elastic modulus of the polyester mooring changes the result of the vertex tension by generating an axial tension.The smaller the elastic modulus,the larger the forced oscillation motion amplitude of the top point of the mooring line,the more obvious the axial tension phenomenon,and the smaller the force on the top of the polyester mooring.

STRUCTURE OF ROD SHELL THEORIES IN HILBERT SPACE

This paper builds symmetrically general theories of rods and shells under mathematical frame of 'Hilbert Space', and successfully obtains the error estimate to the system of theory.

SUBSPACE VARIATIONAL PRINCIPLE OF RODS AND SHELLS

This paper builds the general forms of subspace variational principles of rods and shells which are taken as the controlled equations of the constitutive theories developed front the three-dimensional (non-polar) continuum mechanics. And the constitutive equations of rods and shells using the principles are satisfactory.

Correction Factors of the Approximate Theories for Axisymmetric Modes of Longitudinal Waves in Circular Rods

The longitudinal waves guided by rods are widely used in broad engineering fields.Approximate theories are required to improve the understanding of the longitudinal wave propagation in finite rods in particular.The correction factors are commonly used in the vibration analyses of beams and plates,but are seldom adopted to the longitudinal wave propagation in rods in a similar manner.In this paper,the longitudinal and radial displacements in axisymmetric problems of circular rods are expanded in infinite power series of the radial coordinate.By using Hamilton’s principle,an infinite one-dimensional system of equations of motion is established.The high-order components of stress and strain,and their relations are introduced to obtain the infinite one-dimensional system for the axisymmetric wave propagation in elastic rods.A proper truncation of the infinite equations leads to an approximate theory of a specific order.To improve the truncated equations,some high-order components of strain are multiplied by the correction factors.The correction factors for the first-to fourth-order approximations are systematically determined to ensure that the cutoff frequencies are the same as the exact values calculated by the Pochhmammer–Chree equation.The frequency spectra,via the well-known Pochhmammer–Chree equation and the approximate theories of order one to four,are presented for comparison in a region where the longitudinal wave is not attenuating and the wavelength in the axial direction is longer than the diameter of the rod.Compared to the approximate theories without correction factors,the approximate theories with correction factors show some advantages in accuracy when the branches are high.

Full time-domain nonlinear coupled dynamic analysis of a truss spar and its mooring/riser system in irregular wave

A new full time-domain nonlinear coupled method has been established and then applied to predict the responses of a Truss Spar in irregular wave. For the coupled analysis, a second-order time-domain approach is developed to calculate the wave forces, and a finite element model based on rod theory is established in three dimensions in a global coordinate system. In nu- merical implementation, the higher-order boundary element method （HOBEM） is employed to solve the velocity potential, and the 4th-order Adams-Bashforth-Moultn scheme is used to update the second-order wave surface. In deriving convergent solu- tions, the hull displacements and mooring tensions are kept consistent at the fairlead and the motion equations of platform and mooring-lines/risers are solved simultaneously using Newmark-fl integration scheme including Newton-Raphson iteration. Both the coupled quasi-static analysis and the coupled dynamic analysis are performed. The numerical simulation results are also compared with the model test results, and they coincide very well as a whole. The slow-drift responses can be clearly ob- served in the time histories of displacements and mooring tensions. Some important characteristics of the coupled responses are concluded.

MECHANICAL MODELING OF THE BISTABLE BACTERIAL FLAGELLAR FILAMENT

We extend the 2D Landau phase transition theory to the bacterial flagellar filament which displays the phase transition between the left handed normal form and the right handed semi-coiled form. The bacterial flagellar filament is treated as an elastic thin rod based on the Kirchhoff’s thin rod theory. Mechanical analysis is performed on the periodical phase transition of the filament between the two helical structures of the opposite charity. The curvature and twist are chosen as the order parameters in constructing the phase transition model of the filament. The established model is applied to study the instability properties of the filament and to investigate the loading and deformation conditions of the phase transition. In addition, the curvature and twist gradient energy are considered to describe the interface properties of the two phases.

Simulating an Elastic Ring with Bend and Twist by an Adaptive Generalized Immersed Boundary Method

Many problems involving the interaction of an elastic structure and a viscous fluid can be solved by the immersed boundary(IB)method.In the IB approach to such problems,the elastic forces generated by the immersed structure are applied to the surrounding fluid,and the motion of the immersed structure is determined by the local motion of the fluid.Recently,the IB method has been extended to treatmore general elasticity models that include both positional and rotational degrees of freedom.For such models,force and torque must both be applied to the fluid.The positional degrees of freedomof the immersed structuremove according to the local linear velocity of the fluid,whereas the rotational degrees of freedom move according to the local angular velocity.This paper introduces a spatially adaptive,formally second-order accurate version of this generalized immersed boundary method.We use this adaptive scheme to simulate the dynamics of an elastic ring immersed in fluid.To describe the elasticity of the ring,we use an unconstrained version of Kirchhoff rod theory.We demonstrate empirically that our numerical scheme yields essentially second-order convergence rates when applied to such problems.We also study dynamical instabilities of such fluid-structure systems,and we compare numerical results produced by our method to classical analytic results from elastic rod theory.