take one's place的意思是“就位”,take sb's place的意思是坐某人的座位；代替某人的职务.那

one's 一般 是指形容词性物主代词my,our,your,his,her, its,their,后接名词.
例：Linda is washing her clothes.
sb's一般是指具体某人的,如：Tom's,可作形容词性或名词性使用,也可表某一住所.
例：This is Tom's pen.
Let's go to Tom's （home).
祝学习进步!~