These maple files draw four-bar linkages that solve 
Problem 3 of Wampler, Morgan, and Sommese, 
"Complete Solution of the Nine-Point Path Synthesis 
Problem for Four-Bar Linkages", hereafter refered to 
as (WMS).

We computed and certified (with alphaCertified) 
6*1442 = 8652 solutions to their formulation 
of the synthesis problem (input data were the nine points 

P0 = (0.25, 0.00)
P1 = (0.52, 0.10)
P2 = (0.80, 0.70)
P3 = (1.20, 1.00)
P4 = (1.40, 1.30)
P5 = (1.10, 1.48)
P6 = (0.70, 1.40)
P7 = (0.20, 1.00)
P8 = (0.02, 0.40)

The file RealSols.maple contains the 384=6*64 real 
solutions that were computed and certified in a 
list of Points for Maple consumption.  Each solution 
Point is a list of 12 components 

x1,x2,a1,a2,n1,n2,y1,y2,b1,b2,m1,m2

where x = (x1,x2), a = (a1,a2), y = (y1,y2), b = (b1,b2) 
are drawn in Figure 1 of WMS, and n=(n1,n2) and m=(m1,m2)
are auxiliary variables such that, 
  n = a * conjugate(x)   and    m = b * conjugate(y),
as complex numbers.

If (x,a,n,y,b,m) is a solution, then so is (y,b,m,x,a,n)
as well as the four Robert's cognates which are given in 
Equation 17 of WMS.  Each of these 6 solutions are listed 
in RealSols.maple.

   Parametrizing a 4-bar linkage by points of P^1 x P^1 
(rotations of two parallel bars) where the endpoints 
have distance equal to the length of the third bar, gives
a bi-homogeneous curve of bi-degree (2,2) that parametrizes
the positions of the linkage.    For a given four-bar 
linkage, we compute this curve and then parameterize it
in two branches using the quadratic formula.  The real geometry
of the curve affects our method of parametrizing, so 
we first sorted all linkages by the geometry of their (2,2) 
curves, and then drew each one, looking for appropriate
pictures, which are reproduced (with animation) in the
maple files NUMBER.maple

Here are the enclosed files with a short description

README           This file
RealSols.maple   The maple list of real solutions
grab.perl        perl script for parsing the alphaCertified output file 
                   realDistinctSolns
                   
sort.maple       Sorts the solutions according to the number of critical points
                   under the coordinate projections of the 2,2-curve
rst.maple        r00.maple --- r44.maple.  These draw the (2,2) curve and 
                   crudely draw the workspace of the different mechanisms.

           These next files draw certain solutions, with the number 
               17,28,49,104,171 representing the index of the solution
               in the list points.  The first three are complete, and 
               were used to create the graphics in our paper, as well as
               the animations for our web page.
171.maple    - The only viable solution.  One component of its workspace curve
                 contains all 9 control points and is a simple closed curve.
104.maple    - The workspace is connected, but the curve is not simple closed.
28.maple     - The workspace is disconnected with the control points lying on
               different components.

17.maple     - These represent early attempts to draw mechanisms, ones which 
49.maple        were not sufficiently interesting to warrant further development
