Current approaches to compute the arc length of a parametric curve rely on table lookup schemes. We present an approximate closed-form solution to the problem of computing an arc length parametrization for any given parametric curve. Our solution outputs a one or two-span Bézier curve which relates the length of the curve to the parametric variable. The main advantage of our approach is that we...

This work is concerned with the analysis of vibro-impact responses observed in large-scale nonlinear geared systems. Emphasis laid on interactions between high-frequency internal excitation generated by meshing process, i.e. static transmission error and time-varying mesh stiffness, low-frequency external excitations. To this end, a three-dimensional finite element model pump equipped reverse s...

A new algorithm is proposed to combine the split-frequency harmonic balance method (SFHBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number ...

During arc welding, the arc heats and melts the workpiece as heat flux. When the welding current is given, the distribution and the intensity of the heat flux are determined by the length of the arc. The measurement and control of the arc length are fundamental in robotic and automated welding operations. Length of welding arc determines the distribution of the arc energy and thus the heat inpu...

BACKGROUND: Though the development and fitting of scleral contact lenses are expanding steadily, there is no simple method to provide scleral metrics for scleral contact lens fitting yet. The aim of this study was to establish formulae for estimation of the axial radius of curvature (ARC) of the anterior sclera using ocular biometric parameters that can be easily obtained with conventional de...