Yes, it is related to some movement of hands most of the time. People wrote it as "攴" before we change the radical "攴" into "攵". (There are still some words using "攴" ). We can get the original meaning of "攵" from "攴". For "攴", its upper looks like the branch of tree in accent character, the rest part looks like a hand. So it means a hand holding a instrument to rap or tap something. “收”= 丩(using ropes to tie bad guys) + 攵= to arrest. eg, 收监.Then peole make further meaning like " to receive....." "攻“ = “工”（ a instrument looks like a ladder which help people to climb rampart during wars) + " 攵"= to attack "教” =“孝”（ a child is doing math + " 攵" ( instrument here is something that teacher using to punish students in accent time)= to teach It seems that it is realted to violence sometimes. What do you think ? :)

攵在古代同“攴”。1、轻轻地击打,2、同“扑”，戒尺。 所以，确实和手有关。 攵是简体汉字的部首，它来自繁体字的“攴”（简体字是由繁体字简化而来的）。“攴”有轻轻击打的意思，古时候的教师经常手持教鞭。所以和手部动作有关的字里有“攴”这个部首。 至于为什么“攴”有轻轻击打的意思，在汉语里有“象形字”一说，是古人根据人用手击打的样子画出图画，然后慢慢演变成“攴”这个模样。

hey,there! I m sorry,i dont agree with that! when i was a little girl.my chinese teacher told me,if we wanted to remember them easy,at first,you have to know the meaning from one word group，like 攻，攻击~ and some words look like 攻，then u can distinguish them ~like 攻，收，玫... the 玫，It means jade, or pearls, and plant names，for example,玫瑰means rose~

you wrote "Many times, the radicals <...> tend to make sense" many but not all a big amount of them is meaninless including 攵