【正文】 處理矢量在一個(gè)非常抽象的層次上的數(shù)量和經(jīng)常使用向量定義相對(duì)于在表達(dá)不同的坐標(biāo)系統(tǒng)。小寫的變量的標(biāo)量。在某些點(diǎn)，稱為奇點(diǎn)，這映射是不使轉(zhuǎn)化。除了處理靜態(tài)定位問題，我們不妨分析機(jī)器人的運(yùn)動(dòng)。同時(shí)，對(duì)存在的問題解和多解的出現(xiàn)。顯然，如果機(jī)器人用純粹的模式記錄和關(guān)節(jié)的位置和運(yùn)動(dòng)的播放，沒有算法有關(guān)的關(guān)節(jié)空間的笛卡爾空間是必要的。在某些方面，這個(gè)問題的解決方案是在操作系統(tǒng)中最重要的元素。在一個(gè)案例像一個(gè)機(jī)器人仿真系統(tǒng)，我們需要?jiǎng)?chuàng)建的控制算法計(jì)算機(jī)可以使這個(gè)計(jì)算。這個(gè)問題提出了如下：給出了末端執(zhí)行器的位置和方向機(jī)械手，計(jì)算所有可能的關(guān)節(jié)角度，可以用來(lái)實(shí)現(xiàn)這個(gè)給定的位置和方向。具體而言，給定一組關(guān)節(jié)角，正向運(yùn)動(dòng)學(xué)問題是計(jì)算位置和方向工具架相對(duì)于底座。根據(jù)機(jī)器人的應(yīng)用，末端執(zhí)行器可以是一個(gè)抓手，焊槍，電磁鐵，或其他裝置。這是一個(gè)總稱，任何機(jī)制。這些節(jié)點(diǎn)通常儀表有位置傳感器，使鄰近的鏈接是相對(duì)位置測(cè)量。運(yùn)動(dòng)學(xué)是科學(xué)的運(yùn)動(dòng)，對(duì)運(yùn)動(dòng)不考慮力這導(dǎo)致它。然后我們繼續(xù)相對(duì)于一些參考描述該幀的位置和方向坐標(biāo)系統(tǒng)。這些對(duì)象是機(jī)械手的鏈接，零件和工具，它的交易，并在機(jī)器人的環(huán)境的其他對(duì)象。數(shù)學(xué)描述空間供應(yīng)工具機(jī)械手的運(yùn)動(dòng)和其他屬性。這是最機(jī)部分有限的一類的任務(wù)被認(rèn)為是固定的自動(dòng)化。這本書著重于力學(xué)和最重要的形式控制的工業(yè)機(jī)器人，機(jī)械手。這是最重要的趨勢(shì)推動(dòng)了工業(yè)機(jī)器人的市場(chǎng)增長(zhǎng)。在上世紀(jì)90年代的十年中，機(jī)器人的價(jià)格下降了雖然人類的勞動(dòng)成本增加。自那時(shí)起，市場(chǎng)越來(lái)越多的（），雖然它是受經(jīng)濟(jì)波動(dòng)，是所有市場(chǎng)。無(wú)論是作為一個(gè)原因或一個(gè)效果，這種變化的時(shí)期自動(dòng)化技術(shù)是緊密聯(lián)系在一起的世界經(jīng)濟(jì)。具體地說(shuō)，觀眾不需要嚴(yán)格的機(jī)械工程師，雖然大部分材料是從那場(chǎng)。這本書是適合高年級(jí)本科生一年級(jí)的課程。這本書是從課堂筆記用來(lái)教機(jī)器人學(xué)導(dǎo)論，斯坦福大學(xué)在1983的秋天到1985。這一分支學(xué)科的機(jī)器人已經(jīng)在幾個(gè)經(jīng)典的領(lǐng)域?yàn)榛A(chǔ)的。s a coarse and important level, these objects are described by two attributes: the position and course, a direct interest in the topic is the attitude in which we represent these quantities and manipulate their order to describe the human body position in space and direction, we will always highly coordinate system, or frame, rigid we continue to describe the position and orientation of the reference frame of the coordinate framework can be used as a reference system in the expression of a body position and direction, so we often think of conversion or transformation of the body of these properties from one frame to another 2 chapter discusses the Convention methods of dealing with job descriptions discussed method of treating and post convention described positioning and manipulation of coordinate system the quantity and mathematics developed skills relevant to the position and rotation of the description and is very useful in the field of rigid is the science of sports, the movement does not consider the force which resulted in the scientific research of kinematics, a position, velocity, acceleration, and the location variable high order derivative(with respect to time of all or any of the other variables(S)).Therefore, the kinematics of manipulator is refers to the geometric and temporal characteristics of all manipulator prises nearly rigid connection, which is the relative movement of the joint connection of adjacent nodes are usually instrument position sensor, so that adjacent link is a relative position the case of rotating or rotary joint, the displacement is called the joint robots including sliding(or prism)connection, in which the connection between the relative displacement is a translation, sometimes called the joint manipulator has a number of independent position variables are specified as the mechanism to all parts of is a very general term, any example, a four connecting rod mechanism has only one degree of freedom(even with three members of the movement).In the case of the typical industrial robots, because the robots is usually an open kinematic chain, because each joint position usually define a variable, the node is equal to the number of degrees of free end of the link chain consisting of the manipulator end to the application of robot, the end effector can be a starting point, the torch, electromagnet, or other usually by mechanical hand position description framework description tool, which is connected to the end effector, relative to the base, the base of the mobile the study of mechanical operation of a very basic problem is the is to pute the position of mechanical static geometric problems in hand terminal , given a set of joint angles, the forward kinematics problem is to pute the position and orientation relative to the base of the tool , we think this is a change from the joint space is described as a manipulator position that Cartesian space description.“This problem will be discussed in the 3 the 4 chapter, we will consider the inverse kinematics problems are as follows: the end effector position and direction of the manipulator, puting all possible joint angle, can be used to achieve the position and direction of a given.(see Figure .)This is a practical problem of manipulator is is quite a plex geometry problem, the conventional solution in tens of thousands of humans and other biological systems time every a case like a robot simulation system, we need to create puter control algorithm can make the some ways, the solution to this problem is the most important element in the operating is quite a plex geometry problem, the conventional solution in tens of thousands of humans and other biological systems time every a case like a robot simulation system, we need to create puter control algorithm can make the some ways, the solution to this problem is the most important element in the operating can use this problem as a mapping on 3D Descartes ”position“ space ”position“ in the robot joint need will occur when the 3D spatial objects outside the specified of this kind of algorithm some early robot, they just transfer(sometimes by hand)required for the position, and then be recorded as a mon set of values(., as a position in joint space for later playback).Obviously, if the playback position and motion pattern recording and joint of the purely robot in Cartesian space, no algorithm for the joint space is , the industrial robot is rare, the lack of basic inverse kinematics inverse kinematics problem is not a simple forward kinematics of equation of motion is nonlinear, their solution is not always easy(or even possible in a closed form).At the same time, the existing problems of solutions and multiple solutions study of these problems provides an appreciation of what the human mind nervous system is achieved when we, there seems to be no conscious thought, object movement and our arms and hands is a solution of the presence or absence of a given definition of work solution for the lack of means of mechanical hands can not reach the desired position and orientation, because it is in the manipulator working addition to static p