Interesting challenge, stepping into the realm of positive feedback.
Using the diagrams provided by MMC,
https://igkt.net/sm/index.php?action=dlattach;topic=6574.0;attach=26504;image
Assuming the red line is the riding cord and the small top circle is the ridden cord, I presume you are attempting to compute the normal (i.e clamping) force of the small circle against whatever is below it.
MMc’s diagram allows you to make an estimate of the tangential angle of the overriding cord and his second diagram allows you to compute an estimate of the tensions either side of the overriding contact
https://igkt.net/sm/index.php?action=dlattach;topic=6574.0;attach=26506;image
Using the parallelogram of forces you can then compute the diagonal which is the normal force using
c^2=a^2+b^2−2abcos(C)
where c is the diagonal and C is the included angle.
You can estimate the area of contact of the ridden cord and knowing its cf and the normal force, you can compute the load needed to move it against friction.
A little more about what you are trying to achieve would be very much appreciated.
Derek