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I am trying to symbolically resolve the angle of rope that suspends a load (rectangle) between two pulleys given the length of rope that is let out over the pulleys. See attached image.

the load is not intended to move horizontally, only vertically. so you can imagine each pulley must have an equal length of line pulled or let out between them.

I can solve for this for any number of points for known lengths of rope with the assistance of CAD software and excel to generate a polynomial curve, but I would like to solve this only in terms of rope let out over the pulleys symbolically to achieve modularity and increased accuracy.

I am not sure this can be done, so I am seeking some insight and advice here.

Thank you

the load is not intended to move horizontally, only vertically. so you can imagine each pulley must have an equal length of line pulled or let out between them.

I can solve for this for any number of points for known lengths of rope with the assistance of CAD software and excel to generate a polynomial curve, but I would like to solve this only in terms of rope let out over the pulleys symbolically to achieve modularity and increased accuracy.

I am not sure this can be done, so I am seeking some insight and advice here.

Thank you