Spur Gear Tooth Design and Transition Curve as a Spiral Using Cubic Trigonometric Bezier Function

In this paper, we construct an S-shaped transition curve and spur gear tooth model. The attempt has been made to use the circle to circle technique an S-Shaped transition curve by using Cubic Trigonometric Bezier function (TBezier, for short) with two shape parameters . The shape parameters are used to control the S-shaped transition curves and provide the more flexibility for the interactive design. We have used two curve segments for the completion of single gear teeth instead of four curve segments. This model is the introduction of new cost effective, more economical and computationally easy a more efficient for CAD and CAE systems than ever before. The smoothness of the curve is G
²
continuity.