I saw your previous answer to the person looking to travel to shul using a bicycle on Shabbat which you said is prohibited. Is the use of a bicycle prohibited in general on Shabbat? Is it Muktsa ONLY because we are worried one might come to adjust some part of the "works"? Does this hold true for a child? Any difference if the child is riding the bicycle in the house or within an Eruv?
Rav Waldenberg (Tzitz Eliezer 7; 30) brings three reasons to prohibit bicycle riding on Shabbat: 1. One might ride out of the Eruv 2. One might come to repair or fix if broken 3. It's a daily activity not in the spirit of Shabbat In the book Shmirat Shabbat Kehilchatah p. 185 Rav Noivirt permits a little kid to ride his tricycle within the Eruv borders.