Variable Curvature Modeling Method of Soft Continuum Robots with Constraints

The inherent compliance of continuum robots holds great promise in the fields of soft manipulation and safe human–robot interaction.This compliance reduces the risk of damage to the manipulated object and its surroundings.However,continuum robots possess theoretically infinite degrees of freedom,and this high flexibility usually leads to complex deformations when subjected to external forces and positional constraints.Describing these complex deformations is the main challenge in modeling continuum robots.In this study,we investigated a novel variable curvature modeling method for continuum robots,considering external forces and positional constraints.The robot configuration curve is described using the developed mechanical model,and then the robot is fitted to the curve.A ten-section continuum robot prototype with a length of 1 m was developed in order to validate the model.The feasibility and accuracy of the model were verified by the ability of the robot to reach target points and track complex trajectories with a load.This work was able to serve as a new perspective for the design analysis and motion control of continuum robots.

Surface structures of equilibrium restricted curvature model on two fractal substrates

With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature （ERC） model on Sierpinski arrowhead and crab sub- strates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension dr, but possess different dynamic exponents of random walk Zrw. The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension df, but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk Zrw- The ERC model growing on the two substrates follows the well-known Family-Vicsek scaling law and satisfies the scaling relations 2a ~ df ~ z ~ 2Zrw. In addition, the values of the scaline exponents are in ~ood a^reement with the analytical orediction of the fractional Mullins-Herring equation.

Theoretical study of n-budding opening-up vesicle based on the spontaneous curvature model

N-budding lipid vesicles with single holes were analyzed theoretically by taking into account the line tension of membrane with a hole and the bending energy of membranes based on the Spontaneous-Curvature (SC) model. We solved numerically the Euler-Lagrange equation and the boundary conditions holding on the membrane edge to obtain axisymmetric vesicle shapes, which minimize the total energy. The numerical results show that the size of the opening-up vesicle is larger when the line tension is lower. In other words, additive protein molecules reduce the line tension of lipid membranes, such as talin dose.

EQUIVALENT NORMAL CURVATURE APPROACH MILLING MODEL OF MACHINING FREEFORM SURFACES

A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced. This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity. The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact, so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool. The practical results show that this new milling model is an effective method in machining complex three- dimensional surfaces. This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes. Some actual examples for manufacturing the freeform surfaces with this new model are given.

Internal co-seismic deformation and curvature effect based on an analytical approach

In this study, we present a new method to compute internal co-seismic deformations of a homoge- neous sphere, based on our previous approach （Dong et al. 2016）. In practical numerical computations, we consider a strike-slip point source as an example, and compute the vertical co-seismic displacement on different internal spherical surfaces （including the Earth surface）. Numerical results show that the internal co-seismic deformations are generally larger than that on the Earth surface; especially, the maximum co-seismic displacement appears around the seismic source. The co-seismic displacements are opposite in sign for the areas over and beneath the position of the seismic source. The results also indicate that the curvature effect of the internal deformation is pretty large, and larger than that on the Earth surface. The results indicate that the dislocation theory for a sphere is necessary in computing internal co-seismic deformations.

Large Deformation Analysis and Synthesis of Elastic Closed-loop Mechanism Made of a Certain Spring Wire Described by Free Curves

Recently novel mechanisms with compact size and without many mechanical elements such as bearing are strongly required for medical devices such as surgical operation devices. This paper describes analysis and synthesis of elastic link mechanisms of a single spring beam which can be manufactured by NC coiling machines. These mechanisms are expected as disposable micro forceps. Smooth Curvature Model（SCM） with 3rd order Legendre polynomial curvature functions is applied to calculate large deformation of a curved cantilever beam by taking account of the balance between external and internal elastic forces and moments. SCM is then extended to analyze large deformation of a closed-loop curved elastic beam which is composed of multiple free curved beams. A closed-loop elastic link is divided into two free curved cantilever beams each of which is assumed as serially connected free curved cantilever beams described with SCM. The sets of coefficients of Legendre polynomials of SCM in all free curved cantilever beams are determined by taking account of the force and moment balance at connecting point where external input force is applied. The sets of coefficients of Legendre polynomials of a nonleaded closed-loop elastic link are optimized to design a link mechanism which can generate specified output motion due to input force applied at the assumed dividing point. For example, two planar micro grippers with a single pulling input force are analyzed and designed. The elastic deformation analyzed with proposed method agrees very well with that calculated with FEM. The designed micro gripper can generate the desired pinching motion. The proposed method can contribute to design compact and simple elastic mechanisms without high calculation costs.

SIMULATION OF STRONG TURBULENCE FLOW WITH FREE SURFACE INCLUDING THE EFFECTS OF STREAMLINE CURVATURE

This paper is concerned with a mathematical model for two-dimensional strong turbulence flow with free surface including the effects of streamline curvature in orthogonal curvilinear coordinate system, with which the characteristics of the turbulence flow field on the ogee spillway was numerical simulated. In the numerical simulation, the flow control equations in orthogonal curvilinear coordinate system were discretized by the finite volume method, the physical parameters（ P, U,V,K,ε,γt , etc. ） were arranged on a staggered grid, the discretized equations were solved with the SIMPLEC method, and the complex free surface was dealt with VOF method. The computed results show that the velocity fields, pressure field, shear stress distribution and kinetic energy of turbulent flow on the ogee spillway are in agreement with experimental data. This confirms that the model can be used for numerieal simulation of the turbulence flow on ogee spillway.

Development and application of a throughflow method for high-loaded axial flow compressors

In this paper, a novel engineering platform for throughflow analysis based on streamline curvature approach is developed for the research of a 5-stage compressor. The method includes several types of improved loss and deviation angle models, which are combined with the authors' adjustments for the purpose of reflecting the influences of three-dimensional internal flow in high-loaded multistage compressors with higher accuracy. In order to validate the reliability and robustness of the method, a series of test cases, including a subsonic compressor P&W 3S1, a transonic rotor NASA Rotor 1B and especially an advanced high pressure core compressor GE E^3 HPC, are conducted. Then the computation procedure is applied to the research of a 5-stage compressor which is designed for developing an industrial gas turbine. The overall performance and aerodynamic configuration predicted by the procedure, both at design- and part-speed conditions, are analyzed and compared with experimental results, which show a good agreement. Further discussion regarding the universality of the method compared with CFD is made afterwards. The throughflow method is verified as a reliable and convenient tool for aerodynamic design and performance prediction of modern high-loaded compressors. This method is also qualified for use in the further optimization of the 5-stage compressor.