Got a reply on another forum
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Assume that the frame is a square, with pulleys at a=(0,0), b=(0,1), c=(1,0), 
and d=(1,1). Given a path function x(t), y(t):

a(t) = sqrt(x(t)^2 + y(t)^2)
b(t) = sqrt(x(t)^2 + (1 - y(t)^2))
c(t) = sqrt((1 - x(t)^2) + y(t)^2)
d(t) = sqrt((1 - x(t)^2) + (1 - y(t)^2))

Error analysis might come later, if I can spare the time. You will almost 
certainly want to keep the lines that aren't supposed to be 'pulling' -- 
pulling means f'(t) is negative -- somewhat slack, as keeping them tensioned 
will increase strain on the system and increase error. Put those pullies in 
neutral or something.
--

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