Cycloid drives are widely used in the industries because of their excellent characteristics, namely, high gear ratio, smooth transmission, compact size, high efficiency, low noise and long service life. In this paper, a mathematical model of an epitrochoid gear for a cycloid drive with a small tooth number difference has been proposed. Computerized simulation of the generated epitrochoid gear has also been developed. In this paper, the pressure angle, which has an important role in the analysis of cycloid drives as it influences the direction and magnitude of force transmission in gears, is derived based on the theory of differential geometry. The rack cutter profile, which is the fundamental tooth profile of a hob cutter, which in turn is the main manufacturing process of epitrochoid gear, has been obtained based on the theory of gearing. It is anticipated that the results from this paper will be beneficial to the design, analysis and manufacture of cycloid drives.

In this paper viscous boundary layer flows above and inside a permeable wavy bed are studied. The flow motions are driven by an oscillatory horizontal velocity just outside the Stokes boundary layer above the bed. Analytical and numerical solutions are obtained for both the oscillatory velocity component and the steady streaming inside the permeable bed, the Stokes boundary layer and the outer boundary layer. Two specific situations are examined: (1)Weak oscillatory motions over a wavy bed with finite slope and (2) strong oscillatory motions over a small wavy slope. In both situations, the slip (tangential) velocity and the normal velocity do not vanish on the wavy surface because of the permeability. The magnitude of the bed shear stress decreases as the permeability increases. The permeability can also affect significantly the steady streaming patterns; they could change from having two pairs of recirculating cells above an impervious wavy bed to one pair of recirculating cells above a wavy permeable bed.

This paper aims to investigate the failure probability of short high-strength concrete tied columns using the Monte Carlo technique. The random variables considered in this study are the strength of concrete, the strength of steels, the cross-section dimensions, the location of the steel reinforcement, the variability of strength model and the loads. The results show that the failure probabilities of high-strength concrete columns designed according to the ACI Code are relatively high. The current ACI Code may not be conservative for design of short high-strength concrete tied columns.

This research is focused in the measurement and modelling of the dispersion relations of Lamb waves propagating in a piezoelectric plate. A theoretical model based on a partial wave analysis is used to provide numerical calculations for the dispersion relations of Lamb waves propagating in an LiNbO3 plate with different propagating directions. The dispersion relations are presented in an innovative image format. A non-contact laser ultrasound technique operated in B-scan mode with the aid of double Fast Fourier transform signal-processing scheme is used to measured multi-mode dispersion realtions. Among all the propagation angles, the measured dispersion curves show good agreement with the theoretical calculations. The Rayleigh wave speeds are extracted from the measured and calculated dispersion curves, showing favorable comparison with classical theory by Campbell.

In this paper, spline collocation method (SCM) is successfully extended to solve the generalized problems of beam structures. The spline functions in SCM are re-formulated by finite difference method in a systematical way that is easily understood by engineers. The manipulation of SCM is further simplified by the introduction of quintic table so that the matrix-vector governing equation can be easily formulated to solve the weighting coefficients. SCM is first examined by the problems of a generalized single-span beam undergoing various types of loadings and boundary conditions, and it is then extended to the problems of continuous beam with multiple spans. By comparing with available analytical results, differential quadrature method (DQM), if any, excellent accuracy in deflection is achieved.

In this paper, EndoFEM integrated methodology developed for fatigue crack growth under constant amplitude load, was extended successfully to investigate the Kumar's experimental observations, especially in the increasing severity of delayed retardation due to increasing overload ratio. This phenomenon was accompanied with an increasing max. crack closure load (Pcl) within 0.5mm crack extension after overload, and then followed by a longer recovery stage with lower fatigue crack propagation (FCP) rate.

In the methodology, the EndoFEM with rc controlled node-released strategy was employed to produce a 2mm fatigue crack length from 6% prestrained SEN specimen. To simulate the delayed retardation of overload with/without instant crack extension, five strategies of nodal release were proposed, and then the CMOD method was employed to determine Pcl. The resulting variations of Pcl during crack extension had the same tendency as those of experimental findings. These results allowed one to propose a quadratic relationship between Pcl and Kmax under a fixed overload ratio. As a consequence, a conventional formula of crack closure model could be preserved with a modified coefficient, i.e., da/dN = C(UΔK)m. The formula proposed could predict both the a vs. N crack growth data and the da/dN vs. ΔK data under fixed overload ratios quite well.