Smoothly Blending Of Two Tubes Whose Axes Are Non-coplanar

This paper proposes a method of constructing cylindrical helix tube whose axis is cylindrical helix, conical helix tube whose axis is conical helix and Bezier tube whose axis is space Bezier curve. When non-coplanar axes of two tubes can be smoothly blending by cylindrical helix or conical helix or space Bezier curve, we achieve the aim of smoothly blending two tubes whose axes are non-coplanar by constructed tubes.In this paper, we define generalized cylindrical helix tube, generalized conical helix tube and generalized Bezier tube in the third chapter. They all regard fixed axis as the axis of rotation. We obtain some smoothly blending conditions of two generalized tubes whose axes are non-coplanar at section of paralleling to the horizontal plane by the generalized tubes. Then, we establish a proper coordinate system in the fourth chapter. Under the new coordinate system, we consider equations which the axes were met and the position and tangent continuous conditions of two tubes whose axes are non-coplanar were blent by cylindrical helix tube and elliptical helix tube respectively as smoothly blending conditions.We get a set of nonlinear equations by combining the smoothly blending conditions and the initial conditions. Then, we employ effective computing method and computing equipment to make sure every parameters of constructed tubes meet all conditions. And then we give some specific examples. Ultimately, we achieve the fact that smoothly blending of two tubes whose axes are non-coplanar by maple software...