The inverse trochoid problem

If a circle in the plane is to roll along a track so that a given point on the circle traces out another circle, what must the shape of the track be? In this paper we give a full answer to this question. This question arises in the design of internal combustion engines and other machines. It is a sort of inverse problem to the classical problem of the trajectories of points on circles rolling inside other circles; the problem whose solution is hypocycloids and hypotrochoids. We derive a system of nonlinear differential equations for the coordinates of the track regarded as a parametric curve. We express the solution of this differential equation in terms of an elliptic integral. We establish the uniqueness of this solution for a given choice of the relevant parameters, the radius of the circle to be traced out and the location on the rolling circle of the tracing point. We show that if we allow the rolling circle to intersect the track, there is at least one track for any circle. We find all possible tracks, and we derive formulas to determine, for a given radius of the circle to be traced out, how many different tracks produce circles of that radius; there is always a finite number, and the number increases roughly linearly with the radius. We characterize those tracks that are mathematical solutions but are not practical physical solutions; tracks that the rolling circle intersects in such a way that it would get stuck.     

新手与专家问题

在科学实践和生活世界中,针对某一个问题,面对两个专家给出的不一致的或相矛盾的专家意见,外行或新手是否能又如何能获得辩护地相信一个专家意见而不是另一个专家意见,本文给出了这方面的分析。     

某大型火电站解决汽轮机喷油试验不成功问题的实践

文章根据人机材料方法环境,分析在中国北方的大型火力发电站失败的几个蒸汽涡轮机燃油喷射试验,同时阐述如何解决。     

The compound cylinder and the strength problem

A general discussion is given of the effects of various strength theories on the design of compound cylinders composed of as many as four tubes. Departing from the usual practice in problems of this type, the more modern theories of strength are included.The problem considered is limited to simultaneous, yielding in all component tubes of the cylinder under the action of bore pressure. In addition, new short design procedures employing graphical means are discussed which will considerably reduce the time ordinarily required in such calculations. The methods used are flexible since component tubes of different materials following different strength theories can be treated as easily as cylinders composed of tubes of one material.