Need an expert well versed in Matlab and/or Mathematica to determine, and demonstrate using Matlab and/or Mathmatica what are the dimensions of X and Y in the following examples of two movable strings where a sliding mechanism is prevented from altogether sliding off the two movable strings.
Example 1: Two parallel strings (each 0.1 inches diameter) are each 1 inch long and spaced apart 0.3 inch. A movable flat plate, one at each end of the strings, fixes the respective ends of the two strings. The two strings are moved by manipulating the two plates. Then a sliding mechanism is inserted between the two parallel strings and overlaps but does not fully enclose each of the two strings by at least X.
Example 2. The above two parallel strings that originally were spaced apart 0.3 inch are subsequently criss-crossed once in the middle so that their ends are still spaced apart 0.3 inch. The two strings are criss-crossed by rotating (180 degrees) one of the movable flat plates at one end of the two strings. Then to the left of the criss-cross, and to the right of the criss-cross, two sliding mechanisms are inserted between the two strings so as to overlap but not fully enclose the two strings by at least Y.