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A typical interpolation strategy for line segments consists of a transition scheme, a Look-ahead ACC/DEC scheduling, and an interpolation algorithm. In these three parts, the main computation occurs in the first and second part. Some research work has been carried out to decrease the computation in the previous literatures, but these methods occupy a lot of computing resources for the optimization process during the calculation of transition curve parameters and feed rates. Consequently, the computational efficiency of interpolation strategy is greatly reduced. To deal with the issue, a real-time interpolation strategy is proposed in this paper. In the transition scheme, a Bézier curve is utilized to smooth the line segments. Based on the relationship among the approximation error, the approximation radius, and the transition curve, the curve can be directly generated when the approximation error is given. In the ACC/DEC scheduling, a 3-segment feed rate profile with jerk continuity is constructed. Meanwhile, a Look-ahead planning based on Backward Scanning and Forward Revision (BSFR) algorithm is utilized to eliminate redundant computation. Compared with Zhao’s and Shi’s strategy, the proposed strategy has the merits of C2 and G2 continuity for the tool path, jerk continuity for the tool movement, and distinguished real-time performance for interpolation. The experiments of 3D pentagram and 2D butterfly are carried out with different strategies and their results demonstrate that the interpolation efficiency can be greatly improved with the proposed strategy. [ABSTRACT FROM AUTHOR]

In this paper we propose a numerical procedure for the prediction of capillary forces in polydisperse granular assemblies at a degree of moisture content that corresponds to the so-called pendular regime. The capillary force model is adopted within the Laplace-Young framework with a toroidal approximation of the liquid bridge geometry. Governing equations are first derived in a form that highlights the role of intrinsic parameters such as inter-particle separation distance, ratio of particle radii and liquid volume. A proper scaling of these equations is adopted so that the solution applies to any particle pair configuration. Numerical integration algorithms are provided in a way that facilitates implementations in macroscopic procedures for computer simulations. A qualitative evaluation is undertaken to highlight model predictions of the effects on capillary force of various intrinsic parameters that characterise the particle pair and liquid bridge. The model is validated against the experimental results provided by Willet et al. (Langmuir 16:9396-9405, ) for a wide range of liquid volumes and particle-pair polydispersity. [ABSTRACT FROM AUTHOR]

The paper is devoted to schemes of approximation of attainability sets of nonlinear controlled differential systems where the problem of program control optimization is an 'elementary operation.' The results of numerical experiments are represented. [ABSTRACT FROM AUTHOR]

This paper deals with the real-time NURBS interpolation method in which the interpolation error between the ideal curve and the interpolated curve is compensated within the machine basic length unit (BLU). Parametric curve interpolation methods are based on the Taylor series expansion of curve parameters and an approximation. This approach enables effective feed command generation following the target curve. However, the interpolation error caused by the curve segmentation cannot be controlled. In this research, a two-stage interpolation method that compensates for interpolation errors within machine BLU is proposed. The interpolation result was filtered by an acceleration/jerk limitation equation. Through this two-stage interpolation, both the interpolation error condition and the motion dynamics can be satisfied. Using computer simulations in which interpolation results are revaluated by a numerical iteration method, it is shown that the two-stage interpolation algorithm can interpolate target curves precisely with geometric and dynamic contentment. The proposed algorithm was implemented in the CNC simulator system and an experimental run was conducted to identify the real-time adaptation. [ABSTRACT FROM AUTHOR]

This paper describes a numerical procedure for solving two-dimensional elastostatics problems with multiple circular holes and elastic inclusions in a finite domain with a circular boundary. The inclusions may have arbitrary elastic properties, different from those of the matrix, and the holes may be traction free or loaded with uniform normal pressure. The loading can be applied on all or part of the finite external boundary. Complex potentials are expressed in the form of integrals of the tractions and displacements on the boundaries. The unknown boundary tractions and displacements are approximated by truncated complex Fourier series. A linear algebraic system is obtained by using Taylor series expansion without boundary discretization. The matrix of the linear system has diagonal submatrices on its diagonal, which allows the system to be effectively solved by using a block Gauss-Seidel iterative algorithm. [ABSTRACT FROM AUTHOR]