>>> I want to know how to generate, for each part, a
>>> rotation-translation matrix that brings its nodes
>>> nearer to their mates.
>
>> Do you really mean this? Or do you actually only want to find the
>> matrix that brings the nodes *nearest* to their mates?
>
> Sure I'd like to find the transforms that bring the system to its
> optimal state, but I'm assuming it won't get there in one step.

I think this incorrect assumption is why you keep asking about stepping 
by half, rotation stepping and getting "nearer" to the nodes each step, 
when it sounds now like you don't really want to do that.

If you don't need all the intermediate steps then it's just an 
optimisation problem to find the rotation/translation matrix that 
minimises the sum of the distances between each node pair (or another 
similar metric). You can use the MS Excel solver if you only have a 
finite number of bodies to "design", probably faster than trying to code 
a solver or find a library.

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