CHAPTER 27

BUILDING A REVOLUTE
COORDINATE ARM
The revolute coordinate arm design provides a great deal of flexibility, yet requires few components. The arm described in this chapter enjoys only two degrees of freedom. You’ll find, however, that even with two degrees of freedom, the arm can do many things. It can be used by itself as a stationary pick-and-place robot, or it can be attached to a mobile platform. The construction details given here are for a left hand; to build a right hand, simply make it a mirror image of the left.
You can use just about any type of gripper with this arm. In Fig. 27-1, the completed arm is shown with a simple gripper built on it. You can design the forearm so it accepts many different grippers interchangeably. See Chapter 27, “Experimenting with Gripper Designs,” for more information on robot hands.
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The design of the revolute coordinate arm is modeled after the human arm. A shaft-mounted shoulder joint provides shoulder rotation (degree of freedom #1). A simple swing-arm rotating joint provides the elbow flexion (degree of freedom #2).
You could add a third degree of freedom—shoulder flexion—by providing another joint immediately after the shoulder. Tests have proved that this basic two-degree-of-freedom arm is quite sufficient for most tasks. It is best used, however, on a mobile platform where the robot can move closer to or farther away from the object it’s grasping. That’s cheating, in a way, but it’s a lot simpler than adding another joint.
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1
10-in length -by--by--in aluminum channel stock
1
10-in length -by--by--in aluminum channel stock
1
8-in length -by--by--in aluminum channel stock
1
8-in length -by-by--in aluminum channel stock
1
7-in length -in 20 all-thread rod
2
1-in-by- stove bolt
2
1-by--in flat corner iron
1
3-by--in mending plate "T" (for motor mounting)
2
-in aluminum spacer
1
-in aluminum spacer
2
-in-diameter, 5-lugs-per-in timing belt sprocket
1
201.2-in-length timing belt (5 lugs per in)
2
Stepper motors (see text)
1
3:1 gear reduction system (such as one 20-tooth 24-pitch spur gear and one 60-tooth 24-pitch spur gear)
Misc.
, , and -in 20 nuts, washers, tooth lock washers, fishing tackle weights

 
For a shoulder joint, 22 r/min is a little on the fast side. A gear ratio of 3:1 was chosen to decrease the speed by a factor of three (and increase the torque of the motor roughly by a factor of three). With the gear system, the shoulder joint moves at about one revolution every 8 s. That may seem slow, but remember that the shoulder joint swings in an arc of a little less than 50°, or roughly one-seventh of a complete circle. Thus, the shoulder will go from one extreme to the other in under 2 s.
The upper arm is constructed from a 10-in length of -by--by--in aluminum channel stock and a matching 10-in length of -by--by--in aluminum channel stock Fig. 27-3 . Sandwich the two stocks together to make a bar. Drill a 1.4—in hole 1.2 in from the end of the channel stock pieces. Cut a piece of -in 20 all-thread rod to a length of 7 in (this measurement depends largely on the shoulder motor arrangement, but 7 in gives you room to make changes). Thread a 1.4-in 20 nut, flat washer, and locking washer onto one end of the rod. Leave a little extra—about to in—on the outside of the nut. You'll need the room in a bit.
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Drill a -in hole in the center of a 3-in-diameter metal electrical receptacle cover plate. Insert the rod through it and the hole of the larger channel aluminum. Next, thread two -in 20 nuts onto the rod to act as spacers, then attach the smaller channel aluminum. Lock the pieces together using a flat washer, tooth washer, and -in 20 nut.
The shoulder is now complete.
The forearm attaches to the end of the upper arm. The joint there serves as the elbow. The forearm is constructed much like the upper arm: cut the small and large pieces of channel aluminum to 8 in instead of 10 in. Construct the elbow joint as shown in Fig. 27-4 and Fig. 27-5, using two 1-by--in flat corner angles, -in spacers, and hardware. The -in timing belt sprocket (5 lugs per inch) is used to convey power from the elbow motor, which is mounted at the shoulder. The completed joint is shown in Fig. 27-6.
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You can actually use just about any size of timing belt or sprocket. When using the size of sprockets specified in Table 27-1, the timing belt is 201.2 in. If you use another size sprocket for the elbow or the motor, you may need to choose another length. You can adjust for some slack by mounting the elbow joint closer to or farther from the end of the upper arm.
You may also use #25 roller chain to power the elbow. Use a sprocket on the elbow and a sprocket on the motor shaft. Connect the two with a #25 roller chain. You’ll need to experiment based on the size of sprockets you use to come up with the exact length for the roller chain.
When the elbow and forearm are complete, mount the motor on the shoulder, directly on the plate cover. The motor we chose for the prototype revolute coordinate arm was a 1A medium-duty stepper motor. Predrilled holes on the face of the motor made it easier to mount the arm. A 3-by--in mending plate T was used to secure the motor to the plate, as illustrated in Fig. 27-7. New holes were drilled in the plate to match the holes in the motor (1-in spacing), and the T was bent at the cross.
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As it is, the arm is unbalanced, and the shoulder motor must work harder to position the arm. You can help to rebalance the arm by relocating the shoulder rotation shaft and by adding counterweights or springs. Before you do anything hasty, however, you may want to attach a gripper to the end of the forearm. Any attempts to balance the arm now will be severely thwarted when you add the gripper.
The center of gravity for the whole arm, with the elbow drive motor included, is approximately midway along the length of the upper arm (at least this is true of the prototype arm; your arm may be different). Remove the long shaft from the present shoulder joint, and replace it with a short 1- or 2-in-long -in 20 bolt. Drill a new -in hole through the upper arm at the approximate center of gravity, and thread the shoulder shaft through it. Attach it as before, using -in 20 nuts, flat washers, and toothed lock washers.
The forearm is also out of balance, and you can correct it in a similar manner, by attaching the shoulder joint nearer to the center of the arm. This has the unfortunate side effect, however, of shortening the reach of the forearm. One solution is to make the arm longer to compensate. In effect, you’ll be keeping the elbow joint where it is, just adding extra length behind it.
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The stepper motors used for the shoulder and elbow joints of the prototype provide a natural control over the position of the arm. Under electronic control, the motors can be commanded to rotate a specific number of steps, which in turn moves the upper arm and forearm a specified amount.
When using continuous DC motors, you need to provide some type of feedback to report the position of the arm. Otherwise, the control electronics (almost always a computer) will never know where the arm is or how far it has moved. There are several ways you can provide this feedback. The most popular methods are a potentiometer and an incremental shaft encoder.
Attach the shaft of a potentiometer to the shoulder or elbow joint or motor (see Fig. 27-9), and the varying resistance of the pot serves as an indication of the position of the arm. Just about any pot will do, as long as it has a travel rotation the same as or greater than the travel rotation of the joints in the arm. Otherwise, the arm will go past the internal stops of the potentiometer. Travel rotation is usually not a problem in arm systems, where joints seldom move more than 40° or 50°. If your arm design moves more than about 270°, use a multi turn pot. A three-turn pot should suffice.
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The incremental shaft encoder was first introduced in Chapter 20, “Working with DC Motors.” The shaft encoder is a disc that has many small holes or slots near its outside circumference. You attach the disc to a motor shaft or the shoulder or elbow joint. The shaft encoder circuit is typically composed of a circuit connected to the phototransistor (the latter of which is baffled to block off ambient light). The phototransistor counts the number of on/off flashes and then converts that number into distance traveled. For example, one on/off flash may equal a 2° movement of the joint. Two flashes may equal a 4° movement, and so forth.
The advantage of the incremental shaft encoder is that its output is inherently digital. You can use a computer, or even a simple counter circuit, to count the number of on/off flashes. The result, when the movement ends, is the new position of the arm.