【正文】 ection, 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 positioning problem, we can analyze the robot , the analysis in the actuator velocity, it is convenient to define a matrix called the Jacobi matrix of the speed of Jacobi matrix specified in Descartes from the velocity mapping space and joint space.(see Figure .)This mapping configuration of the manipulator changes the natural some point, called a singularity, this mapping is not to make the phenomenon are important to the understanding of the mechanical hand designers and ：FIGURE : Coordinate systems or ”frames“ are attached to the manipulator and toobjects in the : Kinematic equations describe the tool frame relative to the base frameas a function of the joint : For a given position and orientation of the tool frame, values for the joint variables can be calculated via the inverse : The geometrical relationship between joint rates and velocity of the endeffector can be described in a matrix called the 、Symbol Symbol is always the problems in science and this book, we use the following convention: First: Usually, uppercase variables vector or lowercase ：Tail buoy use(such as the widely accepted)indicating inverse or transposed ：Tail buoy not subject to strict conventions, but may be that the vector ponents(for example, X, Y, Z)or can be used to describe the PBO / P in a position of the ：We will use a lot of trigonometric function, we as a cosine symbol angle E1 can adopt the following methods: because the E1 = CE1 = the vector sign note general: many mechanics textbook treatment number of vector at a very abstract level and often used vector is defined relative to expression in different coordinate most obvious example is, in addition to vector is relative to a given or known a different frame of is usually very convenient, resulting in pact structure, elegant example, consider the angular velocity, connected in series with the last body 176。s ten years, robot prices dropped although human labor the same time, the robot is not only cheaper, they bee more effective and faster, more accurate, more we factor these quality adjusted to the number, the use of robots to decrease the cost of even than their price tag costeffective in