Why the degree of freedom in double Atwood machine (one block on one side and a pulley with one block in its each side on other side) is 2 and not 1?
According to the formula $s=3*n-m$; where $n=$number of particles and $m$ is number of constraint equations,it should be 1 as for here there would be 3 particles and for and 2 constraint equation for length of ropes and 6 for not allowing each particle for moving in $x$ and $y$ directions?
Can somebody explain where is fault in my interpretation?
Best Answer
The answer is two, as can be seen by considering the angular positions of the pulleys: each pulley can be set independently.
I think your error is that the length of rope of the "lone" mass (call it mass number 1) is not a constraint. The position of mass 1 can be set independently of masses 2 and 3. On the other hand, the position of mass 2 cannot be set independently of mass 3, and vice versa.