tangential force we need to overcome,
which is Mass cos( 82. 8), or about
3. 75 kg of force, at half the body height
from the servo. This conveniently is 3. 75
kilogram meters. (Refer to Figure 2.)
Multiply by 35.274 to convert kg to
ounces and by 39. 37 to convert meters to
inches, and we can convert this to about
5,208 oz-in. Using the Hitec servo
previously mentioned, we would need
79 of them just to hold this position. From
this one simple calculation, we can see why
12” tall robots weighing only a few pounds
are so popular!
Most servos just don’t deliver that much torque, so we
need to gear them down with pulleys.
Referring to Figure 3, if we have a servo on the left
attached to a pulley with radius R1, turning the pulley on
the right with radius R2, the shaft at the center of the
second pulley will turn slower but with more torque. The
speed will be reduced by a factor of R1/R2, but will
increase the torque by R2/R1. For example, using the Hitec
HS-645MG servo with a 1” pulley on the left and a 79”
pulley on the right, we could make it work. (Let’s ignore the
fact that our simple robot happens to be about 79” tall.)
To further lessen the torque requirements of the servos,
we can employ springs. When we attach a weight with
mass m as in Figure 4, the spring stretches by the amount
h. This relation is linear: Twice the weight will stretch twice
In the previous example, we needed a 1: 79 ratio pulley
to overcome the torque on the ankle servo to stand up.
Adding a simple spring allows us to offload most of the
force from the servo.
Instead of the force as a function of lean angle
being [Weight cos(angle)], adding a spring makes it
[Weight cos(angle) - (K sin(angle))]. By choosing the
right spring constant K, we can now have the robot
standing with little to no force needed from the servos.
Take a look at Figure 5.
Next time, we will present the last rebuild before the
competition. It will include the new servos, and the
improved feet and hips. We will also install the vision
system for testing. SV
SERVO 10.2013 59