Servo - May 2009

Robotic Arm Fundamentals

Figure 2. The elbow motor can be mounted on the shoulder assembly.

Figure 3. Moving the elbow motor to the base gives a weight advantage.

Figure 4. Pulleys or tie rods can maintain the orientation of the end-effector.

joint. The placement of the motor for the elbow joint, though, has at least two options. It is easy to imagine mounting the arm on the shoulder assembly itself (see Figure 2). If the motor is mounted this way, the angle of the elbow is measured from the shoulder assembly which means that any movement of the shoulder will alter the elbow angle relative to the base (but not to the shoulder).

As an alternative, we could mount the elbow motor on the base and use a pulley system (see Figure 3) to move the elbow assembly. This has an obvious weight advantage because the shoulder motor does not have to lift the elbow motor in this configuration. Notice that in this case, the elbow assembly does not move (relative to the base) when the shoulder is moved.

Give Me A Hand

At the end of the elbow assembly (essentially a forearm), our arm will need some form of end-effector to enable it to pick up objects. This could be some form of hand with finger-like grippers, but that complicates the programming problem immensely. In order for such an arm to perform useful tasks (stacking blocks, for example), the end-effector would need an additional three DOF so that the hand can be oriented in relationship to the arm itself. Since this complication is beyond the scope of this introductory article, we will use a simplified vacuum-based gripper.

The basis for our end-effector will be a small 12 volt vacuum cleaner used for shop work or small household spills. Since we won’t need much suction, you could even make one from a box and a small fan. In either case, a small flexible hose should be connected to the vacuum housing and run along the robot arm to the gripper point where it terminates in a brass or plastic tube connected to a wrist joint. As long as we keep the tube pointed downward, we could pick up small pieces of cardboard (by turning on the vacuum) serving as blocks to be manipulated.

Keeping the tube pointed downward could require another DOF as mentioned earlier, but not if we are creative. Remember how the elbow assembly can maintain its position relative to the base if the elbow motor is mounted on the

base? We can do the same thing with the end-effector by using pulleys or even tie rods as shown in Figure 4. With this configuration, the vacuum tube will always point downward regardless of the angles assumed by the elbow and shoulder.

The New Math

If we make the length of the vacuum nozzle the same as the height the arm is mounted above the base (H in Figure 4), then the mathematics for our arm become much easier. Many first time arm builders fail to think about such considerations and end up building an arm that is difficult to use. Let’s look at some of the mathematical implications for our arm. The first thing we have to realize is that if we wish to touch the end-effector to the floor, the angles A and B must always be the same (shown in Figure 5). If A and B are not the same, then the bottom of the end-effector will mathematically be either above or below the working surface.

Notice in Figure 5 that when the arm is positioned with the gripper tube on the work surface, the elbow and shoulder assemblies form an equilateral triangle with the length (L) of the base of that triangle being the distance from the center of the arm’s base to the center of the end-effector.