Non-coding ribonucleic acids (ncRNA) are functional RNA molecules that are not translated into protein. They are extremely dynamic, adopting diverse conformational substates, which enables them to modulate their interaction with a large number of other molecules. The flexibility of ncRNA provides a challenge for probing their complex 3D conformational landscape, both experimentally and computationally. As a result, despite their conformational diversity, ncRNAs mostly preserve their secondary structure throughout the dynamic ensemble. Here we present a kinematics-based procedure to morph an RNA molecule between conformational substates, while avoiding inter-atomic clashes. We represent an RNA as a kinematic linkage, with fixed groups of atoms as rigid bodies and rotatable bonds as degrees of freedom. Our procedure maintains RNA secondary structure by treating hydrogen bonds between base pairs as constraints. The constraints define a lower-dimensional, secondary-structure constraint manifold in conformation space, where motions are largely governed by molecular junctions of unpaired nucleotides. On a large benchmark set, we show that our morphing procedure compares favorably to peer algorithms, and can approach goal conformations to within a low all-atom RMSD by directing fewer than 1% of its atoms. Furthermore, our results suggest that molecular junctions can modulate 3D structural rearrangements, while secondary structure elements guide large parts of the molecule along the transition to the correct final conformation.