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Manipulator Geometries
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Figure 10-1 E-chain
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An unusual chain-like device can be used as a manipulator. It is based on a flexible cable bundle carrier called E-Chain and has unique properties. The chain can be bent in only one plane, and to only one side. This allows it to cantilever out flat creating a long arm, but stored rolled up like a tape measure. It can be used as a one-DOF extension arm to reach into small confined spaces like pipes and tubes. Figure 10-1 shows a simplified line drawing of E-chain s allowable motion.
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The slider-crank (Figure 10-2) is usually used to get rotary motion from linear motion, as in an internal combustion engine, but it is also an efficient way to get linear motion from the rotary motion of a motor/gearbox. A connecting rod length to / crank radius ratio of four to one produces nearly linear motion of the slider over most of its stroke and is, therefore, the most useful ratio. Several other methods exist for creating
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Figure 10-2 Slider Crank
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linear motion from rotary, but the slider crank is particularly effective for use in walking robots. The motion of the slider is not linear in velocity over its full range of motion. Near the ends of its stroke the slider slows down, but the force produced by the crank goes up. This effect can be put to good use as a clamp. It can also be used to move the legs of walkers. The slider crank should be considered if linear motion is needed in a design.
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In order to put the slider crank to good use, a method of calculating the position of the slider relative to the crank is helpful. The equation for calculating how far the slider travels as the crank arm rotates about the motor/gearbox shaft is: x = L cos + r cos .
ARM GEOMETRIES
The three general layouts for three-DOF arms are called Cartesian, cylindrical, and polar (or spherical). They are named for the shape of the volume that the manipulator can reach and orient the gripper into any position the work envelope. They all have their uses, but as will become apparent, some are better for use on robots than others. Some use all sliding motions, some use only pivoting joints, some use both. Pivoting joints are usually more robust than sliding joints but, with careful design, sliding or extending can be used effectively for some types of tasks. Pivoting joints have the drawback of preventing the manipulator from reaching every cubic centimeter in the work envelope because the elbow cannot fold back completely on itself. This creates dead spaces places where the arm cannot reach that are inside the gross work volume. On a robot, it is frequently required for the manipulator to fold very compactly. Several manipulator manufacturers use a clever offset joint design depicted in Figure 10-3 that allows the arm to fold back on itself
Figure 10-3 Offset joint increases working range of pivoting joints
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Figure 10-4 Gantry, simply supported using tracks or slides, working from outside the work envelope.
180 . This not only reduces the stowed volume, but also reduces any dead spaces. Many industrial robots and teleoperated vehicles use this or a similar design for their manipulators.
CARTESIAN OR RECTANGULAR
On a mobile robot, the manipulator almost always works beyond the edge of the chassis and must be able to reach from ground level to above the height of the robot s body. This means the manipulator arm works from inside or from one side of the work envelope. Some industrial gantry manipulators work from outside their work envelope, and it would be difficult indeed to use their layouts on a mobile robot. As shown in Figure 10-4, gantry manipulators are Cartesian or rectangular manipulators. This geometry looks like a three dimensional XYZ coordinate system. In fact, that is how it is controlled and how the working end moves around in the work envelope. There are two basic layouts based on how the
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