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
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.
If we know the value of L, we can calculate the angles A
and B (which, remember, are always equal) using the
following trigonometric equation:
Figure 5. A little math can find the angles needed for
positioning the arm.