Final answer:
To determine the couple M that must be applied to the crank AB to hold the Whitworth mechanism in equilibrium, one would need to calculate the sum of all torques around the pivot point, ensuring that the sum is zero for equilibrium. This involves considering the forces acting on the crank and using the equation for static equilibrium.
Step-by-step explanation:
The Whitworth mechanism in question involves analyzing the forces on the crank AB to maintain equilibrium. When analyzing such mechanisms, it's common to use principles such as torque and equilibrium.
At a given angle α, the couple M that must be applied to the crank AB can be calculated by considering the sum of all torques around the pivot point. This sum must be zero for the system to be in equilibrium. The torques include the applied couple M, the weight of the block, any friction force, and any reaction force of the block within the slot.
To solve for M, we would take the perpendicular distance from the line of action of each force to the pivot point and multiply it by the magnitude of the force. This process is an application of the equation for static equilibrium, Ττ = 0, where Ττ is the sum of all torques.