  We use magnetic force microscopy to both image and manipulate individual
vortex lines threading single crystalline YBa$_2$Cu$_3$O$_{6.4}$, a layered
superconductor. We find that when we pull the top of a pinned vortex, it may
not tilt smoothly. Sometimes, we observe a vortex to break into discrete
segments that can be described as short stacks of pancake vortices, similar to
the "kinked" structure proposed by Benkraouda and Clem. Quantitative analysis
gives an estimate of the pinning force and the coupling between the stacks. Our
measurements highlight the discrete nature of stacks of pancake vortices in
layered superconductors.
