barcode printing using vb.net Degrees of rotation in Software

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Degrees of rotation
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The term degrees of rotation refers to the extent to which a robot joint, or a set of robot joints, can turn clockwise or counterclockwise about a prescribed axis. Some reference point is always used, and the angles are given in degrees with respect to that joint. Rotation in one direction (usually clockwise) is represented by positive angles; rotation in the opposite direction is specified by negative angles. Thus, if angle X 58 degrees, it refers to a rotation of 58 degrees clockwise with respect to the reference axis. If angle Y 274 degrees, it refers to a rotation of 74 degrees counterclockwise. Figure 34-2 shows a robot arm with three joints. The reference axes are J1, J2, and J3, for rotation angles X, Y, and Z. The individual angles add together. To move this robot arm to a certain position within its work envelope, or the region in space that the arm can reach, the operator enters data into a computer. This data includes the measures of angles X, Y, and Z. The operator has specified X 39, Y 75, and Z 51. In this example, no other parameters are shown. (This is to keep the illustration simple.) But there would probably be variables such as the length of the arm sections, the base rotation angle, and the position of the robot gripper (hand).
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The word articulated means broken into sections by joints. A robot arm with articulated geometry bears some resemblance to the arm of a human. The versatility is defined in terms of the number of degrees of freedom. For example, an arm might
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Z = 51 degrees
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Y = 75 degrees
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X= 39 degrees
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J1 X + Y + Z = 165 degrees
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34-2 Degrees of rotation. Angles X, Y, and Z are measured relative to axes J1, J2, and J3. This robot arm employs articulated geometry.
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have three degrees of freedom: base rotation (the equivalent of azimuth), elevation angle, and reach (the equivalent of radius). If you re a mathematician, you might recognize this as a spherical coordinate scheme. There are several different articulated geometries for any given number of degrees of freedom. Figure 34-2 is a simplified drawing of a robot arm that uses articulated geometry.
Cartesian coordinate geometry
Another mode of robot arm movement is known as cartesian coordinate geometry or rectangular coordinate geometry. This term comes from the cartesian system often used for graphing mathematical functions. The axes are always perpendicular to each other. Variables are assigned the letters x and y in a two-dimensional cartesian plane, or x, y, and z in cartesian three-space. The dimensions are called reach for the x variable, elevation for the y variable, and depth for the z variable. Figure 34-3 depicts a robot arm capable of moving in two dimensions using cartesian coordinate geometry.
AM FL Y
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34-3 Cartesian coordinate geometry in two dimensions. Variable x represents reach; y represents elevation.
Sliding movement
Cylindrical coordinate geometry
A robot arm can be guided by means of a plane polar coordinate system with an elevation dimension added (Fig. 34-4). This is known as cylindrical coordinate geometry. In the cylindrical system, a reference plane is used. An origin point is chosen in this plane. A reference axis is defined, running away from the origin in the reference plane. In the reference plane, the position of any point can be specified in terms of reach x, elevation y, and rotation z, the angle that the reach arm subtends relative to the reference axis. Note that this is just like the situation for two-dimensional cartesian coordinate geometry shown in Fig. 34-3, except that the sliding movement is also capable of rotation. The rotation angle z can range from 0 to 360 degrees counterclockwise from the reference axis. In some systems, the range is specified as 0 to 180 degrees (up to a half circle counterclockwise from the reference axis), and 0 to 180 degrees (up to a half circle clockwise from the reference axis).
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