外文翻譯--坐標(biāo)系變換和速度分解控制方法 英文版

1、<p>　　Coordinate Transformation and. Resolved Motion Rate Control</p><p>　　A robot is made up of links connected by joints. In kinematic analysis, it is considered to be a chain of links and joints. At

2、one end of the chain is the supporting base;at the other end is the end effector or hand. Controlling a robot requires that the end effector or hand be moved to a specific point in space to carry out a task. In perfo

3、rming the task, the robot¡¯s end effector must move through a particular designated path. This section discusses a simplified mathematical method that is</p><p>　　Joint-to-World Transformations &l

4、t;/p><p>　　World coordinates are defined as the base reference coordinates of the robot. These coordinates are taken through the base joint of the robot or at a known distance from it. Base coordinates, by conv

5、ention, are defined asx0,y0, and z0 in the 0 coordinate frame. Joint coordinates are defined as the set of coordinates centered on a particular j¨¤int. In a sliding or prismatic joint, one coordinate of the

6、 coordinate set is along the direction of motion. In a rotary or revolute joint, one coordi</p><p>　　2. Coordinate Frame Parameters </p><p>　　Each coordinate set is also called a frame. Every fr

7、ame is determined by four parameters that describe how it relates to a previous frame. This mathematical approach was first developed by Denavit and Hartenberg in 1955. It provides the necessary parameters in homogeneous

8、 matrices to perform the transformations between coordinate systems in a remarkably simple way (Denavit and Hartenberg [10] , as described in Section 6.6.2. There are two distances and two angles in each set of four par

9、ameters.</p><p>　　In a cartesian coordinate system,the x axis is always normal(perpendicular) to the z axis. Thus, rule 2 above means that the x1 axis is normal to both the z, axis and the Z axis and goes fr

10、om the zi_1 axis to the Z1 axis. Trace out this relationship in figure 6.23 to make sure that this point is clear. Note that the coordinate system is attached to the corresponding link even though its z axis directio

11、n is determined by the direction of the joint. The ith frame moves with the ith link; the n</p><p>　　Any point in the ith coordinate frame ( x , y, , z1 ) can be transformed to the ( i-1)th system by using t

12、he homogeneous matrix defined by the parameters previously determined in the matrix equation </p><p>　　where A(,_1) iS the 4 X 4 homogeneous matrix derived from the values of the four joint parameters. Mult

13、iplying the coordinate vector of the ( I -1)th frame by the A(l_ 1) matrix generates the coordinate vector of the ith frame. The value of the generalized A matrix is given by Paul [321 as </p><p>　　Transf

14、ormation of hand coordinates to world coordinates can be done by successively multiplying together the individual homogeneous matrices, the A matrices, representing the transformations between coordinate frame. These A m

15、atrices are obtained by substituting in the preceding matrix the values found for the four parameters in Table 6.5. The T matrix is the total transformation matrix and is defined by where the subscripts for the A mat

16、rices indicate the initial and final coordinate system</p><p>　　This matrix was first applied to the Stanford Arm, designed by V. Sheinman in 1969. The Stanford Arm is shown in Figure 6.24. Nodesin the schem

17、atic diagram represent the six joints of the arm. Five of the joints are rotary (hinge joints) with angles of rotation O 02 04 05 , and 06 The remaining joint, at position 3, has a prismatic (sliding) joint with a length

18、, s3 , that is variable. Note that three of the rotary joints coincide, so that S4 and S5 are zero. These three joints act as a ball-and-</p><p>　　By inserting the parameter values from Table 6.5 into the A(

19、1_ 1)1 matrix of Equation (61) for each joint we obtain the D-H matrices for the Stanford Arm. It has become customary to substitute C, for cos and S1 for sin O in these matrices in order to reduce the space required and

20、 improve the readability of the matrix equations. Those substitutions have been made in the following matrices for the Stanford Arm.</p><p>　　Multiplying these matrices together in the reverse sequence gives

21、 us the T matrix described by Equation (62). We start by multiplying A45 by A56 to obtain A46 , multiply A34 by A46, , and continue this process to finally obtain the T matrix. The first result is：</p><p>　　

22、Repeating this process, we obtain the T06 matrix, which relates the position of the end of the arm to the base as </p><p>　　In the preceding equations, the values for s1 and s6 have been set to zero, so the

23、effective base is at the center of the cylinder and the end of the arm is taken as the end of the wrist. This arrangement simplifies and clarifies the equations. The reverse problem, determining the joint angles req