Principle: For an inextensible string, the total length remains constant. Differentiate the length equation twice to get acceleration constraints.

Method 1: String Length Method Write total string length L = sum of segments. Since dL/dt = 0 and $d^{2L}$/$dt^2$ = 0, get velocity and acceleration constraints.

Method 2: Virtual Work Method Sum of T*v for all connected bodies = 0 (for massless string).

Common Constraints:

1. Simple Atwood: $a_1$ = -$a_2$ (if one goes up, other comes down)
2. Fixed pulley, one end fixed: If one end moves with a, the block on the other end moves at a/2 (movable pulley halves acceleration)
3. Multiple pulleys: Count string segments on each side

Movable Pulley Rule: If a pulley is attached to a block and has n string segments supporting it, the block's acceleration = $\frac{sum of string accelerations}{n}$.