We can write the equations of the system in the following way:
are the Euclidean equations between the three points that define the lower platform R,S, and T and the points of the upper moving platform A,B, and C. We can also write the Euclidean equations of the top platform. Here, we assume that it is an equilateral triangle, but we are not making any simplifications based on this assumption.
where b is the length of the equilateral triangle of the top platform. We create a new reference coordinate system on S (Figure 10) to simplify the expressions as follow:
Figure: New coordinate system and some definitions
As shown in Figure 10, we define:
By looking at Figure 10
and by using definitions (13)
through (15),
we can easily write a polar parametric equation of 
in the
following manner,
in a similar way, after some trigonometric transformations the equations for
and
:
Let's assume that we have chosen a 
in 
using equations
(16)
through (18)
which uniquely defines a point A in 
. We are
interested in finding the points in 
that are a
distance b away from A. We will present two methods for
accomplishing this.
Two methods where tested (both with positive results:
Alberto Lacaze
