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At present, the mainstream method is directly reduced the platform of the six series branch to six drive rods for analysis and modeling refers to inverse kinematic of the parallel six-degree-of-freedom (6-DOF) Stewart platform, and ignored the influence of the joints that excluded the driving leg on the Stewart platform, resulted in the mathematical model lack of accuracy, there is error in the actual platform. In this paper, the mathematical analysis method of inverse kinematic of the parallel six-degree-of-freedom Stewart platform based on homogeneous coordinate transformation is studied. The relationship of spatial coordinate system is worked up by using the Denavit-Hartenberg (DH) method on the upper and lower platforms and each branch of parallel 6-DOF Stewart platform. Considering the influence among the series branch joints, the transfer relationship is established by using the three-dimensional vector and the homogeneous coordinate transformation matrix between the adjacent joint coordinate systems. The length of the branch drive lever is treated as a variable, the vector equation of the platform system is deduced based on the geometric relation of the parallel 6-DOF Stewart platform. The application of this method in the kinematic inverse solution of parallel 6-DOF Stewart platform is given, verified the correctness of this method. Thinks to the data validation of the actual Stewart platform, it is proved that the proposed method can be applied to the kinematic inverse of parallel 6-DOF Stewart platform that composed of series branch. [ABSTRACT FROM AUTHOR]

Ferroelastic lead phosphate-type (LP) crystals undergo a sequence of phase transition $\bm{R\bar{\hbox{\bi 3}}m - C\hbox{\bi 2}/c}$ and $\bm{R\bar{\hbox{\bi 3}}m - P\hbox{\bi 2}_{\sb{\bi 1}}/c}$ [1]. The ferroic domain pattern depends on the spontaneous strain which can be diluted by the chemical composition. Light scattering from ferroelastic materials and its computer model was presented by T-matrix method at the structural phase transition. We discussed numerical procedure of T-matrix method and improved new computer program to calculate the scattering properties for domain structure of LP-type ferroelastic materials. Then, we report results of these calculations for polydispersive, randomly oriented spheroid with a refractive index, different semi-axis ratios and different size parameters. The calculation results are very close to our previous study of light scattering by spherical, cylindrical structures and convex particles. [ABSTRACT FROM AUTHOR]

A computer model of light scattering from the domain structure of Pb 3 MgNb 3 O 9 (PMN) was obtained by the T-matrix method. First we discuss numerical aspects of T-matrix computations specific for ellipsoids and present results of benchmark computations for a simple ellipsoid model. Then we report results of extensive computations for poly-disperse, randomly oriented ellipsoids with the refractive index of PMN [2.15 + ki, ( k = 0.01, 0.008, 0.015)] semi-axis ratios of 1/2, 1/1.5, 1/3, 1/4 and effective size parameters ranging from 0 to 15. These computations parallel to our previous study of light scattering by poly-disperse, randomly oriented spheroids are used to compare scattering properties of two classes of particles. [ABSTRACT FROM AUTHOR]

A calculation procedure for obtaining the complete set of scattering coefficients and incident, scattered and internal electric fields in terms of the vector spherical harmonics for a multilayered nonlinear structure (as model of polydomain ferroelectric) is proposed by using the T-matrix method. [ABSTRACT FROM AUTHOR]