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This paper presents a method for path generation synthesis of a four-bar linkage that includes both graphical and analytical synthesis and both cases of with and without prescribed timing. The advantage of the proposed method over available techniques is that it is easier and does not need the complicated process (especially in graphical case). In an analytical solution, this method needs the solution of the linear equations, unlike the previous methods, in that they have required the solution of the nonlinear equations. Moreover, in the current method, one can choose the shape of the coupler, while, in other methods, the shape of the coupler is the result of the solution process. The proposed algorithm can be used for path generation synthesizing of a four-bar linkage for three precision points. [ABSTRACT FROM AUTHOR]

Three approaches to calculating the boundaries of the core and zones of scattering of publications, and more specifically, the coordinates of three characteristic points, viz., A, C, and B, on the distribution curve are investigated. These are the analytical and graphical methods, as well as the method of least squares. The first two methods can be applied to any statistical rank-size distribution in the case of a homogeneous sample. Such distributions can be described by the second system of continuous distributions, which represents the universal law of scattering of publications. In a particular case, if Weibull's law can be met, the method of least squares is applied. Practical examples that confirm the high accuracy level of statistical rank-size distributions approximated by a second system of continuous distributions are presented. [ABSTRACT FROM AUTHOR]