Is it permissible to adjust a child's highchair on Shabbat, which often entails removing and then inserting a peg, or to assemble a child's playpen on Shabbat?
Chacham Bentzion Abba Shaul (Jerusalem, 1924-1998), in his work Or Le'tziyon, Helek 2, 27:1, writes that highchairs are made to be frequently adjusted, and one generally does not make a point of inserting the pegs tightly in their positions when adjusting a highchair. Therefore, highchairs fall under the category addressed by the Shulchan Aruch (313:6) of articles that are assembled through the loose connection of various components. The Shulchan Aruch writes that since the parts are assembled loosely, this assembly does not constitute "Boneh" (building) and is thus permissible on Shabbat. Hence, Chacham Bentzion rules, one may adjust a highchair on Shabbat, since the adjustment entails merely the loose, temporary assembly of the various parts. He applies this ruling also to playpens, which are intended for frequent assembly and disassembly.
By the same token, Chacham Bentzion rules that one may add or remove a leaf from a table on Shabbat. These leaves are made to be frequently inserted and removed, and people are generally not careful to insert the leaf forcefully and tightly. This therefore does not entail "building," and it is entirely permissible on Shabbat.
Summary: It is permissible on Shabbat to adjust a highchair, assemble or dissemble a playpen, and insert or remove a leaf of a table.