What semantic notions underlie 'hem, margin; reason, cause; karma, fate' for 緣?
First, you seemed to have asked a lot of questions about etymology and you are always quoting Yellowbridge. Yellowbridge may have its merits, but it does not seem to provide enough information in this area. If you consulted a good dictionary, you would not need to ask so many questions and could save yourself a lot of time.
For instance, this site as suggested by other users is good enough. The result for 緣 is this. (I have consulted other dictionaries and they are more or less the same.)
As we can see from the link, its basic original meaning is &quot;edge of clothes&quot;, which is why it has the semantic radical 糸.
Hence the meaning &quot;edge&quot; in general.
Hence the meaning &quot;go around or along&quot; (as in &quot;go around or along the edge&quot;), and &quot;climb up&quot; (go along the edge upward).
Hence the meaning &quot;follow&quot; (follow this path) and &quot;depend on, utilize&quot; (use this way to achieve your goal).
Hence the meaning &quot;reason, cause, or link between two things&quot; (go from one point to another point following this path -- this path is the link, or the reason).
Hence the meaning &quot;fate&quot; (the link that links two people and make them meet). &quot;Karma&quot; is put here also for this reason, but note that the English word &quot;fate&quot; is already not a very accurate translation, and &quot;karma&quot; is even more prone to misunderstanding. In English &quot;karma&quot; has two senses: one is &quot;destiny, fate&quot;, and the other is more like &quot;law of consequences&quot;, which is irrelevant here. In Chinese, 緣 does not mean things are predetermined, as fate or destiny, but rather that things or people have links or connections, their lives are intertwined.