A new type of AFM is presented which allows for direct measurements of nanomechanical properties in ultra-high vacuum and liquid environments. The AFM is also capable to atomic-scale imaging of force gradients. This is achieved by vibrating a stiff lever at very small amplitudes of less than 1 Å (peak-to-peak) at a sub-resonance amplitude. This linearizes the measurement and makes the interpretation of the data straight-forward. At the atomic scale, interaction force gradients are measured which are consistent with the observation of single atomic bonds. Also, atomic scale damping is observed which rapidly rises with the tip-sample separation. A mechanism is proposed to explain this damping in terms of atomic relaxation in the tip. We also present recent results in water where we were able to measure the mechanical response due to the molecular ordering of water close to an atomically flat surface.