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This paper presents a simplified algorithm for the profiling of the rack gear tool to generate the active profile associated with rolling centrodes. The algorithm is based on the enveloping surfaces principles and reduces the computational problem by proposing an approximate representation of tool’s profile using only three or four points on the profile to be generated by using Bezier representations of the surfaces. The algorithm computes the coefficients of a Bezier substitution polynomial instead of computing hundreds of points on the active profile. This simplifies the solution methodology and requires only a limited number of points along the profile to be generated. The algorithm is computationally efficient and can also be used in the case when the active profile to be generated is physically measured at a few points. Examples include mill tools, splined shafts, and gears. [ABSTRACT FROM AUTHOR]

In this paper, we use the Ehlich-Zeller-G9ärtel inequality to derive an algorithm for finding the global minima of polynomials over hyperrectangles as well as to provide a bounding method for the branch-and-bound algorithm. The latter application of the inequality results in an improved algorithm which gives simultaneously a decreasing upper bound and an increasing lower bound for the global minimum at each iteration. The algorithm can be used also to find the Lipschitz constant of a polynomial. [ABSTRACT FROM AUTHOR]