Under what circumstances is it forbidden to move a 'k'li shemelachto leheter' (a utensil whose purpose is for a permitted use)?

Question

Shulchan Aruch Orach Chaim 308:4:

כלי שמלאכתו להיתר מותר לטלטלו אפי' אינו אלא לצורך הכלי שלא ישבר או יגנב אבל שלא לצורך כלל אסור לטלטלו: וכתבי הקדש ואוכלים מותר לטלטלם אפי' שלא לצורך כלל:‏

A utensil whose purpose is for a permitted use [on shabbat] is permitted to be moved, even if only for the sake of the utensil itself, so that it not break or be stolen, but for no purpose at all, it is forbidden to move it. Holy writings and food may be moved, even for no purpose at all.

I'm having a little trouble thinking of a scenario where this rule applies. How does one move something for no purpose at all? Even if someone is playing or fidgeting with an object, would that not be considered moving it for the purpose of keeping his hands busy?

Please present (sourced) definitions / parameters of what is considered 'moving something for no purpose at all'.

Answer 1

{This is not "definitions / parameters of what is considered 'moving something for no purpose at all'" but just an example. I will happily remove it if you feel it is totally inadequate as an answer.}

This site has a commentary on Shabbos 124 and gives an example of 'moving something for no purpose at all' as follows:

"למשל, יש שהורו להוציא מן הכיס או מן החגורה צרור מפתחות שאין כוונה להשתמש בו בשבת. אמנם, מפתחות אינם מוקצה ואף אינם כלי שמלאכתו לאיסור, ואף על פי כן, הם אינם נחוצים לשבת ולכן יש להימנע מטלטולם שלא (1) לצורך! “

(note 1: The original has the word “ של" which I have changed to “ שלא")

For example they are those who teach that one should remove from the pocket or the belt a bunch of keys which one does not intend to use on Shabbos. These keys are not muktza nor are they keilim whose use is prohibited; even so they are not needed for Shabbos and therefore it is right to refrain from moving them for no purpose.