Example of a single constraint force doing virtual work despite the sum of work done by constraints being zero

Question

When deriving d'Alembert's Principle it must be assumed, that the total virtual work done by constraint forces vanishes. $$\sum_{j=1}^N\mathbf{C}_j\cdot\delta \mathbf{r}_j=0.$$ In the books I've read, the authors have made it a point to state, that the virtual work being done by individual constraints forces doesn't have to be zero. It isn't quite clear to me how that would be possible. I can't think of a single example where any constraint force does any virtual work.

So I'm searching for a system where: $\exists j\in\{1,\ldots,N\}:\quad\mathbf{C}_j\cdot\delta \mathbf{r}_j\neq0.$

Answer 1

Example. Consider two point-masses at positions ${\bf r}_1$ and ${\bf r}_2$ connected by a rigid massless rod, which is a constraint. If we (virtually) move the point-masses, the internal forces (=constraint forces) acting on the two point-masses will separately produce (virtual) work, but their sum will vanish due to Newton's 3rd law.

See also this related Phys.SE post.