Despite the extensive studies of topological systems, the experimental characterizations of strongly nonlinear topological phases have been lagging. To address this shortcoming, we design and build elliptically geared isostatic metamaterials. Their nonlinear topological transitions can be realized by collective soliton motions, which stem from the transition of nonlinear Berry phase. Endowed by the intrinsic nonlinear topological mechanics, surface polar elasticity and dislocation-bound zero modes can be created or annihilated as the topological polarization reverses orientation. Our approach integrates topological physics with strongly nonlinear mechanics and promises multiphase structures at the micro- and macroscales.