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1、Unit5 Part Programming Calculations,5.1 Introduction,Vocabulary,mathematical 7mAWi5mAtikEl adj. 数学的, 精确的 carry out 完成, 实现, 贯彻, 执行 calculation 7kAlkju5leiFEn n. 计算, 考虑 profile 5prEufail n. 剖面, 侧面, 外形, 轮廓 intersection intE5sekF(E)n n.交点；交叉线 competent 5kCmpitEnt adj. 有能力的, 胜任的,fairly 5fZEli adv. 相当地 so
2、und saund adv. 彻底地, 充分地 geometric dViE5metrik adj. 几何的, 几何学的 construction kEn5strQkFEn n. 建筑, 建筑物, 解释, 造句 accomplish E5kCmpliF vt. 完成, 达到, 实现 trigonometry triE5nCmitri n. 三角法，三角学 principle 5prinsEpl n. 法则, 原则, 原理,Notes,1Competent manual part programming is impossible without a fairly well developed
3、mathemat-ical ability and a sound understanding of geometric construction. 没有相当好的数学能力和对几何构造充分的理解，要想胜任手工编程是不可能的。其中：sound的含义不是我们十分熟悉的声音，而是表示彻底地，充分地。,2Many problems in CNC programming involve finding the X and Y coordinates of tool motion based on a given length and angle. These tasks can usually be ac
4、complished by using basic triangle trigonometry.,在CNC编程中常碰到根据已知长度和角度确定刀具运动的X,Y坐标问题，这些问题一般是通过基本的三角运算解决的。,5.2 Useful Angle Concepts,A circle contains 360. （一个圆周角是360。） Figure 5.1,Vertical angles（对顶角） Figure 5.2,Alternate interior angles（内错角） Figure 5.3,Four equally spaced holes （圆周均布的4个孔） Figure 5.4,F
5、our equally spaced holes. （周围均布的4个孔。） Figure 5.5,Vocabulary,vertical angles 对顶角 alternate interior angles 内错角 fraction 5frAkFEn n. 小部分, 片断, 分数 trigonometric 7triEnE5metrik adj. 三角法的, 据三角法的,Notes,1The following facts concerning angles are of use when dealing with problem involving triangles. 在处理三角形的问
6、题时，下面这些关于角的定理非常有用。,2A minute () is defined as 1/60 of a degree. Convert minutes to fractions of a degree before using the trigonometric functions: 一分等于1/60度。在进行三角运算之前，要把分转换为度的分数形式。,3Because the machine has no rotary table, hole 2 cannot be located by directly inputting its angle from 0 and distance
7、from the center of rotation C. Instead, its X2 and Y2 absolute coordinates must be determined.,因为机床没有回转工作台，所以加工孔2时不能直接输入它相对0线的角度以及相对圆心C的距离，而是必须计算出绝对坐标X2，Y2。,4A circle contains 360 and there are four equally spaced holes in the circular pattern. Thus, each hole makes an angle of 360/4 = 90 with its n
8、eighbor. 圆周为360，沿圆周均布4个孔。所以相邻两孔间的角度为360/4 = 90。,5.3 Types of Angles and Triangles,Vocabulary,right triangle 直角三角形 acute E5kju:t adj. 成锐角的，敏锐的 obtuse Eb5tju:s adj. 钝的，成钝角的，迟钝的 oblique E5bli:k adj. 倾斜的, 间接的, 不坦率的, 无诚意的 define di5fain vt. 定义, 详细说明 definition 7defi5niFEn n. 定义, 解说,share FZE vt. 分享, 均分,
9、共有, 分配 cousin 5kQzn n. 堂兄弟姊妹, 表兄弟姊妹 isosceles ai5sRsili:z adj. 等腰的 unlikely Qn5laikli adj. 未必的, 不太可能的, 靠不住的 dimension di5menFEn n. 尺寸, 尺度, 维(数), 度(数), 元 equilateral 7i:kwi5lAtErEl adj. 等边的 equiangular 7i:kwi5ANjulE adj. 等角的,Notes,1In addition, there is also an oblique angle, which is not a new type
10、of an angle. Just a new definition. 另外，还有一个斜角，它不是一个新类型的角度，而仅仅是一种新的定义。,2These triangles can be solved only if at least three dimensions are known, and one of them must always be a side. 对于三角形只有当至少已知三个参数，而且其中一个必为边长时，这些三角形才是可解的。,3Two sides and the angle opposite one of them. 两边及其一个对角。 4Two sides and th
11、e included angle. 两边及其夹角。,5Isosceles triangle has two sides of equal length. Each side or leg is joined by a line called the base. 等腰三角形有两条长度相等的边，这两条边由一条叫做底边的线相连。,6A triangle that has all sides of equal length is called an equilateral triangle. An equilateral triangle is also always an equiangular t
12、riangle, because all internal angles are the same - each angle is 60.,三条边长都相等的三角形叫做等边三角形。等边三角形也就是等角三角形，因为所有内角都相等，均为60。,5.4 Right Triangle,Vocabulary,remain ri5mein vi. 保持, 逗留, 剩余, 残存 hypotenuse hai5pCtinju:z n. 直角三角形之斜边 opposite 5CpEzit adj. 相对的, 对面的, 对立的, 相反的, 对等的, 对应的n.相反的事物 leg le n. 直角三角形之直角边 il
13、lustration 7ilEs5treiFEn n. 例子, 图表, 插图 mathematician 7mAWimE5tiFEn n. 数学家 Pythagoras pai5WAErEs n. 毕达哥拉斯,Pythagorean pai7WAE5ri:En adj. 毕达哥拉斯的 theorem WiErEm n. 定理，法则 emphasize 5emfEsaiz vt. 强调, 着重 trigonometric 7triEnE5metrik adj. 三角法的, 据三角法的 relate to 涉及 trigonometry triE5nCmitri n. 三角法 solution s
14、E5lju:FEn n. 解答, 解决办法, 溶解, 溶液, 解决方案 available E5veilEbl adj. 可用到的, 可利用的, 有用的, 有空的, 接受探访的,Notes,1There is a number of mathematical relationships that form the base of all calculations. 一些数学关系构成了所有计算的基础。,2Learn these relationships well enough to be able to apply them to daily situations. Keep in mind
15、that 99.9 of all triangles to be solved are right triangles. 学好这些关系就足以将它们应用到日常情况之中。记住，99.9要求解的三角形都是直角三角形。,3This mathematical theory relates to the solution of right triangles and states: In any right triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides. 这个数学定理
16、涉及直角三角形问题的解决方法，内容为：对任意直角三角形来说，其斜边的平方等于另外两个边的平方和。,4In trigonometry, any triangle can be solved, providing one of the two data sources is known 在三角学中，加入已知下面两种数据中的任一种，那么任何三角形问题都可以得到解决。,5If more than a single solution is available, use both methods to double check the result. 如果解决方案不止一种，那么可以用两种方法再次检验一下结果。,5.5 Similar Triangles,Similar triangle（相似三角形） Fig
