Hyper-Redundant Manipulator Capable of Adjusting Its Non-Uniform Curvature with Discrete Stiffness Distribution

Hyper-redundant manipulators are widely used in minimally invasive surgery because they can navigate through narrow passages in passive compliance with the human body. Although their stability and dexterity have been significantly improved over the years, we need manipulators that can bend with appropriate curvatures and adapt to complex environments. This paper proposes a design principle for a manipulator capable of adjusting its non-uniform curvature and predicting the bending shape. Rigid segments were serially stacked, and elastic fixtures in the form of flat springs were arranged between hinged-slide joint segments. A manipulator with a diameter of 4.5 mm and a length of 28 mm had been fabricated. A model was established to predict the bending shape through minimum potential energy theory, kinematics, and measured stiffnesses of the flat springs. A comparison of the simulation and experimental results indicated an average position error of 3.82% of the endpoints when compared to the total length. With this modification, the manipulator is expected to be widely used in various fields such as small endoscope systems and single-port robot systems.

Buckling Analysis of a Bi-Directional Strain-Gradient Euler–Bernoulli Nano-Beams

Investigated herein is the buckling of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. Since the transport matrix cannot be calculated analytically, the problem was examined with the help of an approximate transport matrix (matricant). This method can be easily applied with buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on gradient elasticity theory. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The diagrams and tables of the solutions for different end conditions and various values of the parameters are given and the results are discussed.

Evaluation of fractal dimension of star polymers with different numbers of arms in computer experiment

One of the important characteristics of a polymer molecule is its fractal dimension. Fractals are objects whose Hausdorff dimension is fractional and exceeds the topological dimension. The main distinguishing feature of such objects is self-similarity. The fractal characteristics of polymer macromolecules largely determine the chemical, physicochemical, and physical properties of these objects, such as the Mark-Kuhn-Houwink scaling parameters, toughness, tangent of the angle of mechanical losses, and dynamic modulus of elasticity. Today the fractal properties of topologically linear polymers are studied in detail, however, the fractal properties of practically significant star polymers are still poorly studied. This is probably due to the fact that computer simulation of polymer systems by methods of classical mechanics requires lengthy calculations even on supercomputers. In this regard, it is interesting to evaluate the possibility of using relatively simple software packages such as HyperChem in molecular modeling of polymers. The purpose of the research was to determine the fractal dimension for 3, 4, 5, and 6-arm star (-CH2-CH2-)n polymers in a state of minimum potential energy in an isolated system and in a state of thermodynamic equilibrium at a constant temperature, comparing the obtained values with the fractal dimension of linear polyethylene and to mfke an assessment of the appropriateness of using the HyperChem software package for macromolecular calculations. A computer experiment was conducted using the HyperChem package. To obtain isolated molecules in a state of minimum potential energy, a simulation by the conjugate gradient method was performed. To bring the macromolecules to a state of thermodynamic equilibrium at a constant temperature, the molecular modeling in the canonical ensemble was carried out. For the studied polymers, the values of the fractal dimension and critical Flory index were calculated. The data obtained confirm the relation between fractal dimension and conformation of the macromolecule and, within the accuracy achieved, indicate the absence of fractal properties for star macromolecules with a large number of arms.

Principles of minimum potential energy and complementary energy

With the displacement field taken as the only fundamental unknown field in a mixed-boundary-value problem for linear elastostatics, the principle of minimum potential energy asserts that a potential energy functional, which is defined as the difference between the free energy of the body and the work done by the prescribed surface tractions and the body forces --- assumes a smaller value for the actual solution of the mixed problem than for any other kinematically admissible displacement field which satisfies the displacement boundary condition. This principle provides a weak or variational method for solving mixed boundary-value-problems of elastostatics. In particular, instead of solving the governing Navier form of the partial differential equations of equilibrium, one can search for a displacement field such that the first variation of the potential energy functional vanishes. A similar principle of minimum complementary energy, which is phrased in terms of statically admissible stress fields which satisfy the equilibrium equation and the traction boundary condition, is also discussed. The principles of minimum potential energy and minimum complementary energy can also be applied to derive specialized principles which are particularly well-suited to solving structural problems; in this context the celebrated theorems of Castigliano are discussed.

Numerical study on contact force of paralleled beveloid gears using minimum potential energy theory

Using minimum potential energy theory and slicing method, a computational approach to calculate the magnitude and distribution of contact force for paralleled beveloid gear pair was proposed in this article. The theoretical tooth contact model was built based on spatial gearing theory to calculate the mesh parameters including the coordinates, normal vectors, and equivalent radius for meshing points. Then, the analytical contact force model of paralleled beveloid gear pair was derived based on minimum potential energy theory. Finite element contact analysis was conducted to verify the proposed model. Finally, the influences of macro-geometry design parameters on the contact force distribution were investigated. Results show that the pressure angle has a limited influence on the contact force distribution. The increase in helix and cone angles will observably increase the asymmetry of contact force distribution as well as the fluctuation of contact force distribution for a single tooth. A good correlation was obtained between the proposed analytical model and the finite element model for the distribution and magnitudes of contact force.

Static Mantle Density Distribution 2 Improved Equation and Solution

Using Archimedes Principle of Sink or Buoyancy (APSB), Newton’s universal gravity, buoyancy, lateral buoyancy, centrifugal force and Principle of Minimum Potential Energy (PMPE), this paper improves the derivation of equation of static mantle density distribution. It is a set of mutual related 2-D integral equations of Volterra/Fredholm type. Using method of matchtrying, we find the solution. Some new results are: (1) The mantle is divided into sink zone, neural zone and buoyed zone. The sink zone is located in a region with boundaries of an inclined line, angle α_0=35°15’, with apex at O(0,0) revolving around the z-axis, inside the crust involving the equator. Where no negative mass exists, while positive mass is uniformly distributed. The buoyed zone is located in the remainder part, inside the crust involving poles. Where no positive mass exists, while negative mass is uniformly distributed. The neural zone is the boundary between the buoyed and sink zones. The shape of core (in sink zone) is not a sphere. (2) The total positive mass is equal to the total negative mass. (3) The volume of BUO zone is near twice the volume of SIN zone. (4) No positive mass exists in an imagine tunnel passing through poles (the z-axis).

Formulation of the pextension finite elements for the solution of normal contact problems

This work deals with normal contact problems. After a wide literature review, we look for the possibility of achieving a high-precision solution using the principle of minimum potential energy and the Hellinger-Reissner variational principle with penalty and augmented Lagrangian techniques. By positioning of the border of the contact elements, the whole surfaces of the eligible elements fall in contact or in gap regions. This reduces the error of the singularity in the border of the contact domain. Computations with $h$-, $p$- and $rp$-versions are performed. For the $rp$-version, the pre-fixed number of finite elements are moved so that small elements are placed in one or two element layers at the ends of the contact zone. A number of diagrams and tables showing the convergence of the solution (by increasing the number of polynomial degrees p) demonstrate the high efficiency of the proposed solution procedure.

On the Derivation of Exact Solutions of a Tapered Cantilever Timoshenko Beam

A tapered beam is a beam that has a linearly varying cross section. This paper presents an analytical derivation of the solutions to bending of a symmetric tapered cantilever Timoshenko beam subjected to a bending moment and a concentrated force at the free end and a uniformly-distributed load along the beam. The governing differential equations of the Timoshenko beam of a variable cross section are firstly derived from the principle of minimum potential energy. The differential equations are then solved to obtain the exact deflections and rotations along the beam. Formulas for computing the beam deflections and rotations at the free end are presented. Examples of application are given for the cases of a relatively slender beam and a deep beam. The present solutions can be useful for practical applications as well as for evaluating the accuracy of a numerical method.