materials we fabricate are cut with precision and
repeatability. We will be replacing most of the servos with
ones that have much higher torque.
For very high torque areas, we will be increasing the
pulley ratio. Some joints only require 45 degree movement.
This allows a servo with 180 degree rotation to be geared
down by a factor of four.
So, our new servos that are rated at about 1,600 oz-in
should provide true 3,000 oz-in of torque.
Before we begin talking about the specifics involved in
Watson, let’s start with a quick refresher on units, levers
and pulleys, and forces.
The fundamental units we need to work with are
distance, time, and mass. In the SI system, these are
respectively measured in meters, seconds, and kilograms.
You may be more familiar with feet (0.3048 meters) and
pounds (0.4536 Kg), but they are easily converted.
Derived from the fundamental units we have Speed
(meters / seconds), Acceleration (meters / seconds^ 2), and
Force (kg meters / seconds^ 2). Force can be a bit
confusing when it comes to acceleration due to gravity
because we often just give the mass and assume it is on
the surface of the Earth with its gravitational pull of 9. 8
M/S^ 2. If our robot weighs 100 pounds here on Earth, it
would only weigh about 16. 6 pounds on the Moon, with a
gravitational pull of only 1.622 M/S^ 2. In spite of weighing
16. 6 pounds (of force) on the Moon, it would still have a
mass of 100 pounds.
In the simple lever in Figure 1, the Fulcrum is fixed and
at rest; a mass M is pulling down with a force of 9. 8 M.
To keep everything balanced, we would need to lift the end
with a force of ( 9. 8 M A) / (A + B).
For example, if we had a 10 pound weight in the exact
center of a 2’ board, we would need to lift with ( 10 1) /
(1 + 1), or five pounds of force.
Torque is angular force rotating around a center point.
Servos provide torque to move our robot, and their specs
include how much torque they can exert. The units typically
given are in either oz-in or kilogram centimeters.
For example, a Hitec HS-645MG servo provides 133
oz-in of torque. This means if you attach a one inch lever to
this servo, it would be able to lift a 133 oz weight. In
practice, the specs given are under optimal conditions while
moving. For holding a static position (such as a standing
robot), it is rare to get more than half the rated spec from
Now, let’s do a simple calculation for a simplified robot,
standing up. It has a single servo at the ankle, one foot,
and a straight body. The mass is uniformly distributed along
the body. To keep the center of gravity in the center of the
foot for optimal stability, we need to lean forward a little
bit. Let’s give this robot the following parameters:
Height Two meters
Body Mass 30 kg
Foot Length . 25 meters
First, we need the angle at the ankle joint. Because we
want the center of mass in the middle of the foot, we
conveniently get the top directly above the toe, giving us a
nice right triangle.
We know Foot = Body cos(angle), so angle =
arccos(Foot/Body), or about 82. 8 degrees. The lateral force
is transferred through the rigid body to the ground, and the
servo does not need to deal with that. It is only the
58 SERVO 10.2013