Abstract: Bezier curves have useful properties for path
generation problem, for instance, it can generate the reference
trajectory for vehicles to satisfy the path constraints. Both algorithms
join cubic Bezier curve segment smoothly to generate the path. Some
of the useful properties of Bezier are curvature. In mathematics,
curvature is the amount by which a geometric object deviates from
being flat, or straight in the case of a line. Another extrinsic example
of curvature is a circle, where the curvature is equal to the reciprocal
of its radius at any point on the circle. The smaller the radius, the
higher the curvature thus the vehicle needs to bend sharply. In this
study, we use Bezier curve to fit highway-like curve. We use
different approach to find the best approximation for the curve so that
it will resembles highway-like curve. We compute curvature value by
analytical differentiation of the Bezier Curve. We will then compute
the maximum speed for driving using the curvature information
obtained. Our research works on some assumptions; first, the Bezier
curve estimates the real shape of the curve which can be verified
visually. Even though, fitting process of Bezier curve does not
interpolate exactly on the curve of interest, we believe that the
estimation of speed are acceptable. We verified our result with the
manual calculation of the curvature from the map.
Abstract: This paper presents the analysis of duct design using
static and dynamic approaches. The static approach is used to find
out applicability between the design and material applied. The
material used in this paper is Thermoplastic Olefins (TPO). For the
dynamic approach, the focusing is only on the CFD simulations. The
fatigue life in this design and material applied also covered.
Abstract: In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.
Abstract: The exploration of this paper will focus on the Cshaped
transition curve. This curve is designed by using the concept
of circle to circle where one circle lies inside other. The degree of
smoothness employed is curvature continuity. The function used in
designing the C-curve is Bézier-like cubic function. This function has
a low degree, flexible for the interactive design of curves and
surfaces and has a shape parameter. The shape parameter is used to
control the C-shape curve. Once the C-shaped curve design is
completed, this curve will be applied to design spur gear tooth. After
the tooth design procedure is finished, the design will be analyzed by
using Finite Element Analysis (FEA). This analysis is used to find
out the applicability of the tooth design and the gear material that
chosen. In this research, Cast Iron 4.5 % Carbon, ASTM A-48 is
selected as a gear material.