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By Moshe Shoham (auth.)

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_ ' . . . " ~/ " ...... 31B: The work volume of a horizontal articulated robot Let us designate the extent of motion of the prismatic joint by A, and the lengths of the links as L1 and L2. In spite of the assumptions and comparisons made above, in which all links were taken as equal, the present section discusses cases where L1 and L2 are not equal, in order to present all possible work volume shapes for this type of robot. Assuming that the revolute joints are capable of 360P rqtation, the work envelope will be in the shape of a cylinder - hollow if L2 is smaller than Ll , and solid if L2 is equal to or greater than L1• The equations describing cylinders, respectively are: the hollow and solid VHA = TIA{(L 1 + L2)2 - (L1 - L2)2} VHA = TIA(L 1 + L2)2 52 The mechanical arm In these formulas, VHA is the work volume of a horizontal articulated robot.

As the number of revolute joints increases, so does the difficulty of controlling the robot. Thus, vertical articulated robots are the most difficult to control. Vertical articulated robots can provide the largest work volume. By contrast, the smallest work volume is that of Cartesian robots. 33: The work volume of a robot manufactured by Unimation 57 Structure, Control and Operation Open and Closed Kinematic Structures In order to complete the description of robot kinematic structures, we will now consider a type of structure which differs in one important respect from all the structures described above.

For example, almost all revolute joints of most robots are incapable of 3600 rotation. Being able to move the end effector to every point in the work envelope is not enough; the end effector must be able to reach the desired points 55 Structure, Control and Operation with the proper orientation or direction. While the change of position of the end effector is enabled by the first three joints, a change in orientation in the same position is permitted by additional joints. Thus the extremes of the work envelope are accessible to the end effector only from one particular angle - which may be the wrong one - and the effective work envelope is reduced even further.

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