Make the constraint relation between `a_(1),a_(2)` and `a_(3)`

Explanation

Point `1,2,3` and `4` are movable .Let that displacement , from the fixed dotted line be`x_(1),x_(2),x_(3)` and `x_(4)`(ignoring the length over the pulley)

We have,
`x_(1) + x_(4) = l_(1)` (length of first string)
and `(x_(2) - x_(4)) + (x_(3) - x_(4)) = l_(2)` (length of second string)
or `x_(2) - x_(3) - 2x_(4)) = l_(2)` ...(ii)
On double different with respect to time, we get
`a_(1) + a_(4) = 0`...(iii)
and `a_(2) + a_(3) - 2a_(4) = 0` ...(iv)
but `a_(4) = - a_(1)` [From Eq. (iii)]
We have `a_(2) + a_(3) + 2a_(1) = 0`
This is the required constraint relation between `a_(1),a_(2)` and`a_(3)`