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Degrees of Freedom The term degrees of freedom refers to the number of different ways in which a robot manipulator can move Most manipulators move in three dimensions, but often they have more than three degrees of freedom You can use your own arm to get an idea of the degrees of freedom that a robot arm might have Extend your right arm straight out toward the horizon Extend your index finger so it is pointing Keep your arm straight, and move it from the shoulder You can move your shoulder joint in three ways Up-and-down movement is called pitch Movement to the right and left is called yaw You can rotate your whole arm from the shoulder (albeit to a limited extent); this motion is called roll Your shoulder therefore has three degrees of freedom: pitch, yaw, and roll Now move your arm from the elbow only Holding your shoulder in the same position constantly, you will see that your elbow joint has the equivalent of pitch in your shoulder joint But that is all Your elbow, therefore, has one degree of freedom Extend your arm toward the horizon again Now move only your arm below the elbow Your forearm and wrist can bend up and down, side to side, and it can also twist Your lower arm has three degrees of freedom

< xml version="10" > <document> <item>Raspberry</item> <item>Strawberry</item> <item>Blueberry</item> <item>Tomato</item> </document>

These XML <item> elements look like this in xmlphp:

degrees of rotation in articulated geometry Angles X, Y, and Z are measured relative to axes J1, J2, and J3, respectively

< php header('Content-Type: text/xml'); echo '< xml version="10" >'; echo '<document>'; echo '<item>'; echo 'Raspberry'; echo '</item>'; echo '<item>'; echo 'Strawberry'; echo '</item>'; echo '<item>'; echo 'Blueberry'; echo '</item>'; echo '<item>'; echo 'Tomato'; echo '</item>'; >

In total, your arm has seven degrees of freedom: three in the shoulder, one in the elbow, and three in the arm below the elbow It is tempting to suppose that a robot should never need more than three degrees of freedom, because, after all, space has only three dimensions But the extra possible motions, provided by multiple joints, give a robot arm (and a human arm) versatility that it could not have with only three degrees of freedom

We end by closing the <document> element:

Degrees of Rotation 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 with respect to a prescribed linear 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, for example, if angle X = 58 , it refers to a rotation of 58 clockwise with respect to the reference axis If angle Y = 74 , it refers to a rotation of 74 counterclockwise Figure 34-4 shows a robot arm with three joints The reference axes are J1, J2, and J3 for rotation angles X, Y, and Z, respectively The individual angles add together To move this robot arm to a certain position within its work envelope (the region in space that the arm can reach and actually manipulate things), 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

< php header('Content-Type: text/xml'); echo '< xml version="10" >'; echo '<document>'; echo '<item>'; echo 'Raspberry'; echo '</item>'; echo '<item>'; echo 'Strawberry'; echo '</item>'; echo '<item>'; echo 'Blueberry'; echo '</item>'; echo '<item>'; echo 'Tomato'; echo '</item>'; echo '</document>'; >

1 Quentin Hardy, Backstabbing Carly, Forbes (June 11, 2001): 54 55 2 Kim S Nash, Major-league CIOs, Computerworld (May 14, 2001): 43 3 Mark Hall, CIO on the Cutting Edge, Computerworld (February 12, 2001): 56 57 4 Gary H Anthes, The CIO/CTO Balancing Act, Computerworld (June 19, 2000): 50 51 5 Leaders Soup, Computerworld s Premier 100 IT Leaders (March 26, 2001): 50 6 Maryfran Johnson, The CIO Inside Brain Trust, Computerworldcom/ROI (May, June 2001): 25 28

Excellent now we ve created and returned XML from a PHP script (see Figure 9-3)