可展面在平面上的展开及其在工程上的应用

论述了可展面在平面上展开的理论方法 ,即以可展面上一条已知曲线为基础 ,将可展面展开的方法。并以此为依据 ,探讨了工程中应用很广泛的一种可展面——渐开线螺旋面的展开问题 ,为解决工程实际问题奠定基础     

复杂曲面的可展化及其展开方法

提出了一种复杂曲面可展化及其展开的新方法 ,在依附于复杂曲面的两条空间曲线之间 ,构造可展面 ,逼近复杂曲面 ,使复杂曲面可展化并展开。该方法以计算机辅助服装原型设计过程中的前片服装原型的可展化及其展开作为应用实例 ,证明其完全附和工业设计实际要求     

汽车变速比齿轮齿条式转向器的啮合原理(Ⅰ)

对汽车变速比齿轮齿条式转向器的啮合原理进行了系统研究。首先讨论了转向器采用变速比的必要性及速比选择原则,在已知齿轮齿面（渐开线螺旋面）和给定速比规律下,应用共轭曲面原理给出了齿条齿面方程,并发现：瞬时接触线为直线;齿条齿面为可展面;该可展面的腰线为定倾曲线等,最后讨论了端截面齿形。     

可展曲面的计算机辅助设计

基于三维射影空间中点和平面间的对偶性,提出了计算机辅助设计五次样条上可展曲面的一种简单且有效的方法,通过采用该方法,可利用具有B啨zier和B样条基的控制平面设计可展曲面。基于将可展曲面作为平面单参数族包络面的思想,给出在B啨zier和B样条基下可展曲面的参数表示形式。讨论了所设计可展曲面的特点和几何构造,研究结果表明,所提出的设计方法具有现有曲线设计方法的特征,现有的对于曲线的一些几何构造技术可延伸到可展曲面的设计。     

可展面的连接与组合

探讨了可展面连接的两种类型:相交连接与相切连接。通过定理论证,得出重要结论:两个可展面只有在直母线上才能实现相切的接触。该结论为服装设计及其它工程领域构造组合式可展面问题的解决提供了理论依据。     

汽车变速比齿轮条式转向器的啮合原理（Ⅰ）

对汽车变速比齿轮齿条式转向器的啮合原理进行了系统研究。首先讨论了转向器采用变速比的必要性及速比选择原则，在已知齿轮齿面（渐开线螺旋面）和给定速比定律下应用共轭曲面原理给出了齿条面方程，并发现：瞬时接触线为直线；齿条齿面灰可展面；该呆展面的腰线为定倾曲线等，最后讨论了端截面齿形。     

基于投影法的过渡曲面构造方法

在采用组合函数法构造过渡曲面方法的基础上,提出了一种在基曲面上构造G1连续的过渡切触线的方法。该方法只需给定曲面上的一组点列及其点上的切矢,在此基础上构造一条空间曲线,并基于正交投影法将这条曲线投影到基曲面上得到一条G1连续的过渡切触线,使得设计人员可以根据需要直接在基曲面上确定过渡曲面与基曲面的切触线的位置,并以此为边界构造过渡曲面。还提出了新的构造过渡辅助面和重新参数化局部基曲面的方法,以适应过渡切触线为分段曲线的情况,并将其应用于翼身融合面的构造中,实例证明了该方法的可行性,效果令人满意。     

离心式叶轮三元可展面叶片解析展开法及叶片型面模成型方法

本文从可展面的特点出发,提出了有关可展面叶片与轮盖、轮盘回转面相贯线的准确解法;可展面叶片展成平面的方法及简单易行的型面模成型方法,并且通过模型机的制造过程,验证了求解方法的正确及模型机制造的经济性。     

线面共轭啮合原理及齿面构建方法

定义曲线与曲面共轭啮合的概念,即给定运动的两构件上的一条光滑曲线和一个光滑曲面始终保持连续相切接触,并给出由共轭啮合副齿面形成曲线与曲面共轭啮合的一般方法,在共轭啮合副的一个齿面上构建啮合管齿面与另一齿面相啮和;提出以适当半径的球体沿啮合曲线的指定等距线包络出管状曲面的齿面构建新方法,推导啮合管齿面方程、接触曲线方程等,给出啮合曲线选取的条件以及啮合管齿面半径的选取范围,从而建立以啮合曲线为脊线构建管状共轭齿面的理论;以摆线针轮行星传动为例,构建针齿螺旋管齿面,讨论线面共轭摆线针轮行星传动的特性;分析表明,线面共轭具有点接触特性,通过构建合适的线面共轭啮合副,可获得近似纯滚动啮合,齿面滑动率小,传动效率高。     

基于四面体单元的新型可展机构自由度分析

基于3RR-3URU四面体单元构造对称和非对称两种可展组合单元机构,提出3UU-3URU四面体单元机构,并基于此单元构造可展组合单元机构,对这三种可展机构进行自由度分析。首先,基于拆杆等效法分析3RR-3URU四面体单元的自由度数目及性质,进一步将基本单元组合成对称组合单元和非对称组合单元两种形式,定义这两种组合单元的结构及需要满足的几何约束条件,并应用螺旋理论和G-K公式分析两种组合单元的自由度。其次,针对基于3RR-3URU构成的组合单元无法组网成大型可展天线机构的问题,提出3UU-3URU四面体单元及其组合单元机构,根据G-K公式得到其自由度数。最后,应用ADAMS仿真软件建立三种组合单元机构的仿真模型,对三种组合单元进行运动仿真,仿真结果验证其自由度分析的正确性。研究结果为四面体可展天线机构的设计与分析提供重要理论依据。     

基于控制顶点的Bezier曲面交线算法

Bezier曲面求交问题是CAGD的核心问题之一。利用Bezier曲面片的控制顶点构造可展直纹面片,将Bezier曲面的求交问题转化为可展直纹面的求交问题,从而获得一种简单快捷的求交算法。     

PRINCIPLE AND TRANSMISSION TECHNOLOGY OF BERTRAND CONJUGATE SURFACES

Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic of Bertrand surface is that normals along generator are coplanar. Bertrand conjugate principle is studied and its basic characteristic is that the instantaneous contact line between a pair of Bertrand conjugate surfaces is generator. Bertrand conjugate can be divided into three kinds of typical conjugation forms in terms of the generators that are general plane curve, circular-arc and straight line. Basic conjugate condition is given respectively, and structure condition, which reflects transmission forms and directrix characteristic of this kind of conjugation, is researched. As typical engineering application of Bertrand conjugate surface principle, transmission technology of loxodromic-type normal circular-arc bevel gear is studied.     

Analytical envelope surface representation of a conical cutter undergoing rational motion

Flank milling with a taper cutter is widely used in industry. The analytical representation of the envelope surface generated by a conical cutter undergoing rational motion is derived by bringing together the theories of line geometry and kinematics. Based on the projective duality between a point and a plane in line geometry, a cone surface is represented as two pieces of rational quadratic Bézier developable surfaces in terms of the plane coordinates instead of the traditional point coordinates. It provides a way to describe and calculate the envelope surface exactly by analyzing the trajectory of a plane undergoing a two-parameter rational motion. The rotation around the axis of the cone is adopted to ensure that the characteristic curve is located on the same piece of rational quadratic Bézier developable surface of the cone. The degenerate cases that the characteristic curve does not exist are also discussed. Examples are provided, in which the envelope surfaces of a conical cutter undergoing rational Bézier and B-spline motions are computed. The results can be applied to tool-path planning and error analysis for five-axis flank milling machining.     

Tool path planning for five-axis flank milling with developable surface approximation

This paper presents a novel approach that automatically generates an interference-free tool path for five-axis flank milling of a ruled surface. A boundary curve of the machined surface is subdivided into curve segments. Each segment works as a guide curve in the design method for developable Bézier surface that controls a developable patch for approximating the surface with available degrees of freedom. Geometric algorithms are proposed for calculating consecutive patches with G¹ continuity across the patch boundary. A tapered tool can move along the rulings of these patches without inducing local tool interference as a result of their developability. The machining deviation is controlled by the surface approximation error. A machining test is conducted with the generated CL data and the result verifies the feasibility of the proposed approach. This work successfully transforms avoidance of tool interference into a geometric modeling problem and provides a simple solution. It thus demonstrates a good potential for the developable surface theory of five-axis flank machining .     

NURBS curve and surface fitting for reverse engineering

Reverse engineering is an approach for constructing a computer-aided design (CAD) model from a physical part through dimensional measurement and surface modelling. This paper presents alternatives for reverse engineering of free-form parts using Non-Uniform Rational B-Spline (NURBS) surfaces. A two-step linear approach is employed for fitting NURBS curves and surfaces using the measured points. During the first step, the weights of the control points are identified from a homogeneous system using symmetric eigenvalue decomposition. The control points are further processed in a way similar to B-spline curve and surface fitting. Some examples are presented to illustrate both the steps of reverse engineering and the process of NURBS curve and surface fitting.     

基于单元等变形的复杂曲面展开算法研究

针对板壳类零件展开问题提出了一种基于单元等变形的复杂曲面展开算法。首先利用有限元网格生成算法将零件曲面划分成三角形单元 ,然后按照单元等变形假设将三角形单元映射到平面上 ,从而得到曲面的展开形状与尺寸 ,并通过重新计算单元的变形率得到曲面内的应变分布。该算法可以将各种可展曲面和不可展曲面采用统一的形式展开 ,实际应用表明采用该算法展开复杂曲面时具有快速准确的特点 ,可以显著缩短零件从设计造型到求取其毛料外形的时间 ,适用于航空航天及汽车制造等工业领域内具有复杂曲面的金属板料零件的数字化展开。     

A method of the determination of a developable ruled surface

Using dual vector calculus, a method of determination of a developable ruled surface is presented. The dual vectorial expression of a developable ruled surface m(t, u)=p(t)+ux(t), p(t) is called the base curve of m(t, u), obtained from the coordinates and the first derivatives of the base curve.