I think this is a polyline / polygon dataset? One way to do this is to chop the features to lines with two vertexes using a Chopper and calculate the line lenght using a LengthCalculator.

I think we need more specifics to give an exact answer, but I wanted to give the solution a shot because I thought it was interesting challenge. I'm assuming when you say previous point that you mean there is a consecutively numbered attribute such as ObjectID in the example below. If so:

• Use an AttributeManager to extract the previous ObjectID in a copy of the points in a new attribute previous_ObjectID
• Use an AttributeRenamer to rename previous_ObjectID to ObjectID
• Feed these features along with the original features into a LineBuilder
• In the LineBuilder, set the Group By processing to ObjectID
• Use LengthCalculator to get the distance between consecutive points
• From there you could use a Tester or TestFilter to find those lines (distances) less than your tolerance.

@travis34​ "a picture is worth a thousand words" (F. Barnard). A small sample dataset is worth a thousand pictures (annon.) If you can attach a small sample dataset someone might be able to piece together a proof-of-concept