Page 292 - Concise Encyclopedia of Robotics

Scaling
to achieve data communication between two locations that are nearly at
opposite points on the surface of Earth. Station X can be considered the
location of the control operator, and station Y the location of a remotely
controlled robot.
One of the biggest challenges facing researchers in artificial intelligence
(AI) is how to link computers that are separated by vast distances. There
is no way to overcome the fact that the speed of light is slow on a large
scale, and when considered in terms of the time required for a computer
to execute a clock cycle.
See also MICROWAVE DATA TRANSMISSION.
SCALING
Scaling is a principle familiar to structural engineers and physicists. As
an object is made larger to an equal extent in all linear dimensions, its
structural integrity diminishes.
When things get larger but stay in the same relative proportions, me-
chanical strength increases as to the square (second power) of linear di-
mension—height, width, or depth. However, mass increases according to
the cube (third power) of the linear dimension.The illustration shows how
this works with cubes. The mass, and thus the weight in a constant gravita-
tional field, goes up faster than the linear dimension or cross-sectional
area increases. Eventually, if an object gets large enough, it becomes physi-
cally unstable or mechanically unworkable.
Consider a theoretical solid cube of variable size but perfectly homo-
geneous matter. In the illustration, the smaller cube has height = 1 unit,
width = 1 unit,and depth = 1 unit.The larger cube is double this size in each
linear dimension: height = 2 units, width = 2 units, and depth = 2 units.
The base (or cross-sectional) area of the smaller cube is 1 unit squared
(1 1); the volume of the smaller cube is 1 unit cubed (1 1 1). The
base (or cross-sectional) area of the larger cube is 4 units squared (2 2);
the volume is 8 units cubed (2 2 2). If the cubes are made of the
same homogeneous material, doubling the linear dimension also doubles
the weight per unit surface area at the base. As the cube keeps getting
larger, it will eventually fall through or sink into the surface, or collapse
under its own weight.
Imagine the situation with a humanoid robot. If its height suddenly
increases by a factor of 10, its cross-sectional structural area increases by
3
2
a factor of 10 = 100. However, its mass becomes 10 = 1000 times as
great. That is the equivalent of a 10-fold increase in gravitational acceler-
ation. A robot constructed of ordinary materials would have difficulty
maneuvering under these conditions, and would be unstable. Another

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