11.4 : Virtual Work for a System of Connected Rigid Bodies

Virtual work is a powerful method used to solve problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. When attempting to analyze such a system, first, use a free-body diagram, where an independent coordinate represents the configuration of the links, and mark its deflected position resulting from the positive virtual displacement.

Next, measure the position coordinates from a fixed point on the free-body diagram and direct them toward the forces that do the work. This allows for each virtual displacement to be expressed in terms of the independent coordinate. Next step is to write down the equation of the virtual work, which helps in the determination of the resultant forces and moments. It is also important to note here that if a force or couple moment acts along the direction of positive virtual displacement, then their work is determined as positive virtual work; otherwise, it's negative virtual work.

The main advantage of using this method is that it can be used to solve problems that involve a system of several connected rigid bodies Each of these systems is said to have only one degree of freedom since the arrangement of the links can be completely specified using only one coordinate. This greatly simplifies complex calculations and helps better understand how different variables are related to each other within complex systems.

All in all, analytically evaluating equilibrium problems involving multiple connected rigid bodies can be done effectively with virtual work, enabling not just accurate answers but also clear insight into their internal workings as well.