Explore the vast range of titles available.

In this paper, a general error identification and compensation method is proposed for the position-independent geometric errors (PIGEs) of dual rotation axes of cradle-type five-axis machine tools with non-intersecting rotation axes. A unique hole machining specimen is designed to evaluate the compensation effect. First, the kinematic error model of the five-axis machine tool is established based on the dual quaternion, and the correlation between the PIGEs defined based on the dual quaternion and the PIGEs in ISO 230–7 is analyzed. Then, eight PIGEs of the two rotation axes are simultaneously identified by using a double-ball bar (DBB) through the synchronous motion trajectory of the A- and C-axes. Moreover, an error compensation strategy based on the principle of tool pose approximation is proposed, which preferentially compensates for the direction error. The direction and position vector errors of the tool are directly compensated by establishing the ideal and actual relative pose difference model between the tool and workpiece. Finally, a unique hole machining experiment on a circular cone surface is proposed according to the position structure of the rotation axis of the target machine tool. The machining of the hole on the conical surface is realized by controlling the tool through the motion of the rotation axis, thus effectively avoiding the influence of the translational axis. The effectiveness of the proposed compensation strategy is verified by the measurement and fitting of the points on the machining hole wall by a three-coordinate measuring machine. The average residual error after compensation is reduced by about 88.65% and 85.2% compared with that before compensation by using the established position error and direction error compensation evaluation function.

In this paper, we present an inexact multiblock alternating direction method for the point-contact friction model of the force-optimization problem (FOP). The friction-cone constraints of the FOP are reformulated as the Cartesian product of circular cones. We focus on the convex quadratic circular-cone programming model of the FOP, which is an exact cone-programming model. Coupled with the separable convex quadratic objective function, we recast the circular-cone-programming model as a multiblock separable cone model. A parallel inexact multiblock alternating direction method is used to solve the FOP. We prove the global convergence of the proposed method. Simulation results of the three-fingered FOP are reported, which verified the efficiency of the proposed method.

Grasping force optimization of multi-fingered robotic hands can be formulated as a convex quadratic circular cone programming problem, which consists in minimizing a convex quadratic objective function subject to the friction cone constraints and balance constraints of external force. This paper presents projection and contraction methods for grasping force optimization problems. The proposed projection and contraction methods are shown to be globally convergent to the optimal grasping force. The global convergence makes projection and contraction methods well suited to the warm-start techniques. The numerical examples show that the projection and contraction methods with warm-start version are fast and efficient.

The aim of this study is to investigate the effects of temperature-dependent viscosity on the natural convection flow from a vertical permeable circular cone with uniform heat flux. As part of numerical computation, the governing boundary layer equations are transformed into a non-dimensional form. The resulting nonlinear system of partial differential equations is then reduced to local non-similarity equations which are solved computationally by three different solution methodologies, namely, (i) perturbation solution for small transpiration parameter (ξ), (ii) asymptotic solution for large ξ, and (iii) the implicit finite difference method together with a Keller box scheme for all ξ. The numerical results of the velocity and viscosity profiles of the fluid are displayed graphically with heat transfer characteristics. The shearing stress in terms of the local skin-friction coefficient and the rate of heat transfer in terms of the local Nusselt number (Nu) are given in tabular form for the viscosity parameter (ε) and the Prandtl number (Pr). The viscosity is a linear function of temperature which is valid for small Prandtl numbers (Pr). The three-fold solutions were compared as part of the validations with various ranges of Pr numbers. Overall, good agreements were established. The major finding of the research provides a better demonstration of how temperature-dependent viscosity affects the natural convective flow. It was found that increasing Pr, ξ, and ε decrease the local skin-friction coefficient, but ξ has more influence on increasing the rate of heat transfer, as the effect of ε was erratic at small and large ξ. Furthermore, at the variable Pr, a large ξ increased the local maxima of viscosity at large extents, particularly at low Pr, but the effect on temperature distribution was found to be less significant under the same condition. However, at variable ε and fixed Pr, the temperature distribution was observed to be more influenced by ε at small ξ, whereas large ξ dominated this scheme significantly regardless of the variation in ε. The validations through three-fold solutions act as evidence of the accuracy and versatility of the current approach.

In this paper, we study the parabolic second-order directional derivative in the Hadamard sense of a vector-valued function associated with circular cone. The vector-valued function comes from applying a given real-valued function to the spectral decomposition associated with circular cone. In particular, we present the exact formula of second-order tangent set of circular cone by using the parabolic second-order directional derivative of projection operator. In addition, we also deal with the relationship of second-order differentiability between the vector-valued function and the given real-valued function. The results in this paper build fundamental bricks to the characterizations of second-order necessary and sufficient conditions for circular cone optimization problems.

In this paper, we consider complementarity problem associated with circular cone, which is a type of nonsymmetric cone complementarity problem. The main purpose of this paper is to show the readers how to construct complementarity functions for such nonsymmetric cone complementarity problem, and propose a few merit functions for solving such a complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also show that these merit functions provide an error bound for the circular cone complementarity problem. These results ensure that the sequence generated by descent methods has at least one accumulation point, and build up a theoretical basis for designing the merit function method for solving circular cone complementarity problem.

The objective of this study is to analyze the natural convection flow of nanofluid along a circular cone placed in a vertical direction. The generalized heat flux and mass flux models are commonly known as the Cattaneo–Christov heat flux model and mass flux models. In the present study, these models are used for both heat and mass transfers analysis in nanofluid flow. For the governing equations, the Buongiorno transport model is used in which two important slip mechanism, namely thermophoresis and Brownian motion parameters, are discussed. The resulting governing equations in the form of partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) due to similar flow along the surface of a circular cone. To solve these ODEs, a numerical algorithm based on implicit finite difference scheme is utilized. The effects of dimensionless parameters on heat and mass transfer in nanofluid flow are discussed graphically in the form of velocity profile, temperature profile, Sherwood number and Nusselt number. It is noted that in the presence of the Cattaneo–Christov heat flux model and mass flux model, the heat transfer rate decreases by increasing both thermal and concentration relaxation parameters; however, Sherwood number decreases by increasing the thermal relaxation parameter, and increases by increasing the concentration relaxation parameter.

We present a full step feasible interior-point algorithm for circular cone optimization using Euclidean Jordan algebras. The specificity of our method is to use a transformation similar to that introduced by Darvay and Takács for the centering equations of the central path of the linear optimization. The Nesterov and Todd symmetrization scheme is used to derive the search directions. The theoretical complexity bound of the algorithm coincides with the best-known iteration bound for small-update methods.

It is well known that the second-order cone and the circular cone have many analogous properties. In particular, there exists an important distance inequality associated with the second-order cone and the circular cone. The inequality indicates that the distances of arbitrary points to the second-order cone and the circular cone are equivalent, which is crucial in analyzing the tangent cone and normal cone for the circular cone. In this paper, we provide an alternative approach to achieve the aforementioned inequality. Although the proof is a bit longer than the existing one, the new approach offers a way to clarify when the equality holds. Such a clarification is helpful for further study of the relationship between the second-order cone programming problems and the circular cone programming problems.

Let L θ be the circular cone in R n which includes second-order cone as a special case. For any function f from R to R , one can define a corresponding vector-valued function f L θ on R n by applying f to the spectral values of the spectral decomposition of x ∈ R n with respect to L θ . The main results of this paper are regarding the H -differentiability and calmness of circular cone function f L θ . Specifically, we investigate the relations of H -differentiability and calmness between f and f L θ . In addition, we propose a merit function approach for solving the circular cone complementarity problems under H -differentiability. These results are crucial to subsequent study regarding various analysis towards optimizations associated with circular cone.