对原型的精确重构和基于原型的再设计是反求工程的应用目标之一。在制造业中,由于制造误差、测量误差、三维拟合精度等多种因素,使得依据实物原型重构而形成的制造数据与原型参数有较大的差距,在某种情况下,反求出的产品将会失去使用性能。针对此问题,提出了反求工程中存在有实物原型参数、重构参数和原始设计参数的参数体系,阐述了在不同的场合根据不同的要求应求出不同的参数,并提出了应用在制造业中的反求工程应逆求出制造实物原型所依据的原始设计参数,并依此作为制造新产品的依据。分析结果对强化反求工程在制造业的应用、突出反求工程的＂创新＂功能具有重要意义。

Accurate reconstruction of prototype and redesign based on prototype is one of the application goals of reverse engi-neering. In manufacture industry,because of many kinds of facts,such as,manufacturing errors,measuring errors and three-dimen-sional fitting precision,and so on,there was obvious gap between prototype parameter and manufacturing data that was formed based on objective prototype reconstruction,in some cases,the product to be reversed lost its using performance. Aimed at this problem,it puts forward that there is a parameter system that includes the objective prototype parameters,reconstruction parameters and original design parameters in the reverse engineering,and expounds that the different parameters must be obtained according to the different demands in a different situation. It proposed that the reverse engineering used in manufacture industry should find reversely the original design parameters that are foundation of making objective prototype,and should u

在实际应用中,为对曲线的形状做局部的修改,通常需要通过给定型值点反求曲线的控制顶点,通过个别控制顶点的调整来达到调整曲线形状的目的。在实际的形状表示与设计中,三次均匀B样条较为常见。而型值点与控制顶点之间,可由方程组确定。本文根据反求问题所对应方程组的特点,利用迭代的思想,构造易于计算机实现的反求方法。

Modifying the Curves need to use curve points to reverse calculating the control points of the curves. The Cubic uniform B-spline curves are common in shape expressing and designing. The relation between curve points and control points can be determined by equations. We find an iterative method can be used on computer.

为反求出烟草包装机中的凸轮机构，并建立起一种凸轮机构的反求方法，本文利用现代测绘技术和计算机模拟技术，构建了凸轮机构的模拟模型。通过对凸轮机构进行运动学模拟分析，得到了它的位移曲线、速度曲线和加速度曲线，计算出了凸轮机构的设计参数，并应用最小二乘法计算出了从动件的运动规律函数。同时，还以平行分度凸轮为例，验证了该反求方法的可靠性。结果显示：拟合出的从动件运动规律与模拟得到的各项性能曲线比较吻合；反求出的凸轮轮廓与测绘出的凸轮轮廓比较吻合。因此，该种凸轮反求方法比较准确，可近似计算出凸轮的设计运动规律。

In order to inverse evaluate the cam mechanism in tobacco packaging machine ,a method of inverse evaluation w as built .T he method used modern measuring technique and computerized simulation technology to create the simulation model of cam mechanism ,and gained its displacement diagram ,velocity diagram and acceleration diagram and calculated its several design parameters ,for calculating the follower′s movement function with least square method .The indexing cam was taken for an example to prove the reliability of the method . The results showed that the follower′s movement diagrams were in accordance with the ones from simulation .The cam′s figure calculated with inverse evaluation method matched the one from measuring .So the method of inverse evaluation for cam mechanism is reliable and can approximately confirm the cam′s motion in design .

反求技术作为模具开发的一种重要设计手段，越来越受到工程技术人员的重视。随着计算机技术、激光测量技术和数控技术的飞速发展，反求技术不再仅仅满足对已有产品进行简单复制，而是已发展成为船舶、汽车、航空和模具等工业领域重要的产品创新设计方法，是工程技术人员通过实物样件快速获取工程设计概念和设计模型的基本技术手段。反求技术能将实物样件或手工模型转化为CAD模型，并对CAD模型进一步优化和再设计，有力地促进了模具设计数字化与制造技术更紧密的结合，更好地为模具设计创新服务。

As a vital means of mould development, reverse technology has been very highly regarded by engineering technical personnel. With the rapid evolution of computer science ,laser measurement technology,and numerical control technique,reverse technology could not only satisfied the simple copy of the existent product ,but also became an innovative design method for high-tech areas such as marine,automotive,aerospace and mould industries. It is a basic technology method that engineers could fast access to the concept of engineering and mould design through physical sample. Reverse technology was able to transform the physical sample or hand-crafted model to CAD model. After that,it could optimize and redesign the CAD model as well which improves the compact combination of mould digitalization with manufacture techniques ,better served the mould innovation design.

为了求Sylvester矩阵方程AXB＋CXTD=E自反（或反自反）的最佳逼近解，提出了一种利用复合最速下降法的迭代算法。不论矩阵方程AXB＋CXTD=E是否相容，对于任给初始自反（或反自反）矩阵Xo，此算法都可以计算出该方程自反（或反自反）的最佳逼近解X。最后，通过两个数值例子验证了算法的可行性。

Presents an iterative algorithm to compute the optimal approximation solutions of the generalized Sylvester matrix equations AXB+CX T D=E over reflexive (anti-reflexive) matrices with the hybrid steepest descent method. Whether the matrix equations AXB+CX T D=E are consis-tent or not,for arbitrary initial reflexive(anti-reflexive)matrix X0 ,the given algorithm can be used to compute the reflexive(anti-reflexive)optimal approximation solutions X . The effectiveness of the proposed algorithm is verified by two numerical examples.