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Start with just one moving link with a revolute joint to a fixed link. Choose a link that has the fewest bends in the wires. There should be two wires, one to move the link up and the other wire to move the link down. Suppress all other links and all other wires.
The idea of using springs is that they replace a wire, they are not added to the end of the wire. Springs do not wrap around corners, two springs are used to go around a corner, one spring attaches at the tangent to the input side of the corner and the other spring attaches at the tangent to the output side of the corner. A roller body with a revolute joint is used to model the corner and transfers the tension in one spring to the other spring that exits at a different angle. If you have one corner the up wire wraps around and another corner the down wire wraps around, then you will have four springs and two rollers to represent the two wires wrapping around two corners.
In my example model, I demonstated one “wire” wrapped around one “corner” by using two springs attached to a roller on a revolute joint. This is a revolute joint at the corner and is different from the revolute joint the link is rotating around.