几何轨迹

Some basic equations of dual beam scan are derived,such as,the position vector for the incident point,the scalar expression for reflected ray,scan pattern on observation plane ect.

文摘：应用几何光学理论研究了多光束转镜扫描场的非对称性，导出多光束扫描入射点位置矢量、反射线标量表达式、观察面上的扫描轨迹方程，并研究了扫描远场的非对称性。

Through the new research methods, this thesis has made the following contributions in this field: 1. For the first time the curvature radii and relative angles of a planar continuous curve at discrete points are chosen as local parameters to represent the curve, which reflect clearly the local geometrical characteristics of the curve and are easy to be dealt with.

借助于新的研究方法，本文在这一领域作出如下贡献：（1）首次提出用曲线上离散点处曲率半径和相对转角作为局部参数表示平面连续曲线，直观地反映曲线各个局部的几何特征，且便于曲线的修改和变换，并通过机构运动分析，快速求出机构轨迹的这两个局部参数。

By analyses of geometry characteristies of various cutters and workpieces,the methed of application of the property to improving the algorithm on calculating the cutter－ contact point trace is presented.

对各种形式的刀具与工件的几何特性进行了分析，阐述了该性质在改进刀位点轨迹算法中的应用方法。

Based on the geometry constraint and dimensiondriving technique, a 3-UPU parallel simulation mechanism is created. Then a 3D free surface and a guiding plane of tool path are constituted, with the 3-UPU parallel machine tool combined, a novel 3-UPU simulation parallel machine tool for machining a 3D free surface is created.

通过几何约束和尺寸驱动技术，先建立3-UPU并联模拟机构，再构造任意3D自由曲面和刀具轨迹的引导平面，与3-UPU模拟并联机构合成，得到用于加工任意3D自由曲面的模拟并联机床。

Based on the geometry constraint and dimension-driving technique,a 3-UPU parallel simulation mechanism is created.Then a 3D free surface and a guiding plane of tool path are constituted,with the 3-UPU parallel machine tool combined,a novel 3-UPU simulation parallel machine tool for machining a 3D free surface is created.

通过几何约束和尺寸驱动技术，先建立3-UPU并联模拟机构，再构造任意3D自由曲面和刀具轨迹的引导平面，与3-UPU模拟并联机构合成，得到用于加工任意3D自由曲面的模拟并联机床。

In comparison with the computation point by point according to Hencky stress equations, determination of the stress in slip line field by use of the geometrical mapping is clear and simple.

文献〔1〕〔2〕〔3〕在Prager极点轨迹基础上提出了一种摆线映射法，这是滑移线场在口一，应力平面上的一种几何映射，其图形由两族相互正交的摆线构成。

Resorting to the Roberts-Chebyshev theorem,we replace the two cranks of a crank-rocker cognate mechanism with a double bar,which is required to satisfy certain geometrical and motion conditions,and we change the mechanism thus reformed into a geared five-bar mechanism so that one of its links can fully rotate with the link connected with it.

借助于Roberts-Chebyshev定理，将曲柄摇杆轨迹同源机构的两曲柄分别用一双杆组代替，并要求双杆组满足一定的几何尺寸条件和运动条件，使变形后的机构为齿轮五杆机构，且满足机构的一个连架杆以及与其相连的连杆能够整周转动。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。