Underactuated compliant arms are a promising technology to outperform traditional rigid robots in interaction tasks, thanks to their adaptability and shock-absorbing prop- erties. However, the control problem is yet to be solved. In this paper, we study the controllability for a class of planar underactuated compliant arms under gravity. We prove the Kalman rank condition for a system with one actuated elastic joint, i.e., base joint, and a generic number of unactuated elastic ones. The proof relies on the induction principle on the dimension of the reachability matrix. Finally, we generalize the result for a generic number of actuated elastic joints in the chain.