Chapter 10 Manipulator Geometries Copyright © 2003 by The McGraw-Hill Companies, Inc. Click here for Terms of Use. This page intentionally left blank. M anipulator is a fancy name for a mechanical arm. A manipulator is an assembly of segments and joints that can be conveniently divided into three sections: the arm, consisting of one or more segments and joints; the wrist, usually consisting of one to three segments and joints; and a gripper or other means of attaching or grasping. Some texts on the subject divide manipulators into only two sections, arm and grip- per, but for clarity the wrist is separated out as its own section because it performs a unique function. Industrial robots are stationary manipulators whose base is perma- nently attached to the floor, a table, or a stand. In most cases, however, industrial manipulators are too big, use a geometry that is not effective on a mobile robot, or lack enough sensors -(indeed many have no envi- ronmental sensors at all) to be considered for use on a mobile robot. There is a section covering them as a group because they demonstrate a wide variety of sometimes complex manipulator geometries. The chap- ter’s main focus, however, will be on the three general layouts of the arm section of a generic manipulator, and wrist and gripper designs. A few unusual manipulator designs are also included. It should be pointed out that there are few truly autonomous manipu- lators in use except in research labs. The task of positioning, orienting, and doing something useful based solely on input from frequently inade- quate sensors is extremely difficult. In most cases, the manipulator is teleoperated. Nevertheless, it is theoretically possible to make a truly autonomous manipulator and their numbers are expected to increase dra- matically over the next several years. POSITIONING, ORIENTING, HOW MANY DEGREES OF FREEDOM? In a general sense, the arm and wrist of a basic manipulator perform two separate functions, positioning and orienting. There are layouts where the wrist or arm are not distinguishable, but for simplicity, they are treated as separate entities in this discussion. In the human arm, the 241 242 Chapter 10 Manipulator Geometries shoulder and elbow do the gross positioning and the wrist does the ori- enting. Each joint allows one degree of freedom of motion. The theoreti- cal minimum number of degrees of freedom to reach to any location in the work envelope and orient the gripper in any orientation is six; three for location, and three for orientation. In other words, there must be at least three bending or extending motions to get position, and three twist- ing or rotating motions to get orientation. Actually, the six or more joints of the manipulator can be in any order, and the arm and wrist segments can be any length, but there are only a few combinations of joint order and segment length that work effec- tively. They almost always end up being divided into arm and wrist. The three twisting motions that give orientation are commonly labeled pitch, roll, and yaw, for tilting up/down, twisting, and bending left/right respec- tively. Unfortunately, there is no easy labeling system for the arm itself since there are many ways to achieve gross positioning using extended segments and pivoted or twisted joints. A generally excepted generic description method follows. A good example of a manipulator is the human arm, consisting of a shoulder, upper arm, elbow, and wrist. The shoulder allows the upper arm to move up and down which is considered one DOF. It allows for- ward and backward motion, which is the second DOF, but it also allows rotation, which is the third DOF. The elbow joint gives the forth DOF. The wrist pitches up and down, yaws left and right, and rolls, giving three DOFs in one joint. The wrist joint is actually not a very well designed joint. Theoretically the best wrist joint geometry is a ball joint, but even in the biological world, there is only one example of a true full motion ball joint (one that allows motion in two planes, and twists 360°) because they are so difficult to power and control. The human hip joint is a limited motion ball joint. On a mobile robot, the chassis can often substitute for one or two of the degrees of freedom, usually fore/aft and sometimes to yaw the arm left/right, reducing the complexity of the manipulator significantly. Some special purpose manipulators do not need the ability to orient the gripper in all three axes, further reducing the DOF. At the other extreme, there are arms in the conceptual stage that have more than fifteen DOF. To be thorough, this chapter will include the geometries of all the basic three DOF manipulator arms, in addition to the simpler two DOF arms specifically for use on robots. Wrists are shown separately. It is left to you to pick and match an effective combination of wrist and arm geometries to solve your specific manipulation problem. First, let’s look at an unusual manipulator and a simple mechanism—perhaps the sim- plest mechanism for creating linear motion from rotary motion. Chapter 10 Manipulator Geometries 243 E-Chain 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. Slider Crank 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 effi- cient way to get linear motion from the rotary motion of a motor/gear- box. A connecting rod length to / crank radius ratio of four to one pro- duces nearly linear motion of the slider over most of its stroke and is, therefore, the most useful ratio. Several other methods exist for creating Figure 10-1 E-chain 244 Chapter 10 Manipulator Geometries 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. Figure 10-2 Slider Crank Chapter 10 Manipulator Geometries 245 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 Ø+ r cos Ø. ARM GEOMETRIES The three general layouts for three-DOF arms are called Cartesian, cylin- drical, and polar (or spherical). They are named for the shape of the vol- ume that the manipulator can reach and orient the gripper into any posi- tion—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 slid- ing 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 com- pactly. 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 246 Chapter 10 Manipulator Geometries 180°. This not only reduces the stowed volume, but also reduces any dead spaces. Many indus- trial 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 enve- lope, 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 rec- tangular 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 Figure 10-4 Gantry, simply supported using tracks or slides, working from outside the work envelope. Figure 10-5 Cantilevered manipulator geometry Chapter 10 Manipulator Geometries 247 arm segments are supported, gantry and can- tilevered. Mounted on the front of a robot, the first two DOF of a cantilevered Cartesian manipulator can move left/right and up/down; the Y-axis is not necessarily needed on a mobile robot because the robot can move back/forward. Figure 10-5 shows a cantilevered layout with three DOF. Though not the best solution to the problem of working off the front of a robot, it will work. It has the benefit of requiring a very simple control algorithm. CYLINDRICAL The second type of manipulator work envelope is cylindrical. Cylindrical types usually incorporate a rotating base with the first segment able to tele- scope or slide up and down, carrying a horizon- tally telescoping segment. While they are very simple to picture and the work envelope is fairly intuitive, they are hard to implement effectively because they require two linear motion segments, both of which have moment loads in them caused by the load at the end of the upper arm. In the basic layout, the control code is fairly simple, i.e., the angle of the base, height of the first segment, and extension of the second seg- ment. On a robot, the angle of the base can sim- ply be the angle of the chassis of the robot itself, leaving the height and extension of the second segment. Figure 10-6 shows the basic layout of a cylindrical three-DOF manipulator arm. A second geometry that still has a cylindrical work envelope is the SCARA design. SCARA means Selective Compliant Assembly Robot Arm. This design has good stiffness in the verti- cal direction, but some compliance in the hori- zontal. This makes it easier to get close to the right location and let the small compliance take up any misalignment. A SCARA manipulator replaces the second telescoping joint with two vertical axis-pivoting joints. Figure 10-7 shows a SCARA manipulator. Figure 10-6 Three-DOF cylindrical manipulator Figure 10-7 A SCARA manipulator 248 Chapter 10 Manipulator Geometries POLAR OR SPHERICAL The third, and most versatile, geometry is the spherical type. In this layout, the work envelope can be thought of as being all around. In real- ity, though, it is difficult to reach everywhere. There are several ways to layout an arm with this work envelope. The most basic has a rotat- ing base that carries an arm segment that can pitch up and down, and extend in and out (Figure 10-8). Raising the shoulder up (Figure 10-9) changes the envelope somewhat and is worth considering in some cases. Figures 10-10, 10-11, and 10-12 show variations of the spher- ical geometry manipulator. Figure 10-8 Basic polar coordinate manipulator Figure 10-9 High shoulder polar coordinate manipulator with offset joint at elbow [...]... be added externally by installing parts-handling equipment or mounting the industrial robot on tracks or rails so that it can move from place to place To be most effective, all axes should be servo-driven and controlled by the industrial robot s computer system Chapter 11 Proprioceptive and Environmental Sensing Mechanisms and Devices Copyright © 2003 by The McGraw-Hill Companies, Inc Click here for... robotics market today However, sales are now booming for less expensive industrial robots that are stronger, faster, and smarter than their predecessors Industrial robots are now spot-welding car bodies, installing windshields, and doing spray painting on automobile assembly lines They also place and remove parts from annealing furnaces and punch presses, and they assemble and test electrical and mechanical. .. joints in a wrist must twist up/down, clockwise/counter-clockwise, and left/right They must pitch, roll, and yaw respectively This can be done all-in-one using a ballin-socket joint like a human hip, but controlling and powering this type is difficult Most wrists consist of three separate joints Figures 1 0-1 3, 1 0-1 4, and 1 0-1 5 depict one, two, and three-DOF basic wrists each building on the previous design... move one or both jaws directly towards and away from each other These layouts are shown in Figures 1 0-2 1, 1 0-2 2, and 1 0-2 3 Figure 1 0-2 1 Parallel jaw on linear slides Chapter 10 Manipulator Geometries 255 Figure 1 0-2 2 Parallel jaw using four-bar linkage Figure 1 0-2 3 Parallel jaw using four-bar linkage and linear actuator PASSIVE PARALLEL JAW USING CROSS TIE Twin four-bar linkages are the key components... of the end-use tools that mount on the industrial robot s “hand” for the performance of specific tasks (e.g., parts handling, welding, painting) Industrial Robot Characteristics Load-handling capability is one of the most important factors in an industrial robot purchasing decision Some can now handle payloads of as much as 200 pounds However, most applications do not require the handling of parts that... of floor-standing industrial industrial robots today Hydraulic-drive industrial robots are generally assigned to heavy-duty lifting applications Some electric and hydraulic industrial robots are equipped with pneumatic-controlled tools or end effectors The number of degrees of freedom is equal to the number of axes of an industrial robot, and is an important indicator of its capability Limited-sequence... costs of more pow- Chapter 10 Manipulator Geometries erful microprocessors, solid-state and disk memory, and applications software However, overall system costs have not declined, and there have been no significant changes in the mechanical design of industrial robots during the industrial robot s twenty-year “learning curve” and maturation period The shakeout of American industrial robot manufacturers... industrial robot development include servomechanisms, hydraulics, and machine design The latest and most advanced industrial robots include dedicated digital computers The largest number of industrial robots in the world are limitedsequence machines, but the trend has been toward the electric-motor powered, servo-controlled industrial robots that typically are floorstanding machines Those industrial robots... on the wrist’s functionality and should be chosen carefully, especially for wrists with only one or two DOF Figure 1 0-1 3 Single-DOF wrist (yaw) Chapter 10 Manipulator Geometries 251 Figure 1 0-1 4 Two-DOF wrist (yaw and roll) Figure 1 0-1 5 Three-DOF wrist (yaw, roll, and pitch) 252 Chapter 10 Manipulator Geometries GRIPPERS The end of the manipulator is the part the user or robot uses to affect something... an important indicator of its capability Limited-sequence industrial robots typically have only two or three degrees of freedom, but point-to-point, continuous-path, and controlledpath industrial robots typically have five or six Two or three of those may be in the wrist or end effector Most heavy-duty industrial robots are floor-standing Others in the same size range are powered by hydraulic motors . floor-standing industrial industrial robots today. Hydraulic-drive industrial robots are generally assigned to heavy-duty lifting applica- tions. Some electric and hydraulic industrial robots. clockwise/counter-clockwise, and left/right. They must pitch, roll, and yaw respectively. This can be done all-in-one using a ball- in-socket joint like a human hip, but controlling and powering. considering in some cases. Figures 1 0-1 0, 1 0-1 1, and 1 0-1 2 show variations of the spher- ical geometry manipulator. Figure 1 0-8 Basic polar coordinate manipulator Figure 1 0-9 High shoulder polar coordinate