Beginsel van Virtueel Werk: Probleemoplossing

Consider a scissors linkage system connected to a spring, which is unstretched at a certain angle.

In the presence of an external force, the spring stretches and the system undergoes a virtual displacement. In this condition, only the spring force and the external force contribute to work.

To determine the deflection angle to maintain the system's equilibrium, the position coordinates of the two forces with respect to a fixed point are determined.

Then, the amount by which the spring is compressed and the corresponding spring force are evaluated.

Differentiating position coordinates gives the virtual displacements corresponding to the two forces.

The external force acts in the direction of virtual displacement, so it does positive work. Meanwhile, the spring force acts opposite to the virtual displacement and does negative work.

Next, the principle of virtual work is used to write down the virtual-work equation for the system.

Solving the virtual-work equation for the given force, the angle needed to maintain the equilibrium of the scissors linkage system can be obtained.