Virtual work problem

saubhik

See the diagram:
The diagram is an ideal mechanical system of massless beams. The platform C holds a weight of "W". There are gear-motor mechanisms at connections A and B, which provide internal torques.

Suppose, the smaller (acute) angle between beam OA and horizontal is θ.
The mechanism at A provides an initernal torque to maintain the smaller angle BAO = 2θ.
The mechanism at B provides an initernal torque to maintain the smaller angle ABC = 3θ.

Using principle of virtual work (δU=0), find the minimum moment M which must be applied at O to raise the load W.

Please help in solving the above problem. I cannot find a way to calculate the virtual work done by W when the virtual work done by M is Mδθ. Also what will happen to the internal torques provided. Will they appear in the moment M expression?

Thanks for the help.