The Gemara (Succah 41b) says: תנו רבנן ולקחתם שתהא לקיחה ביד כל אחד ואחד – “The Rabbonon taught, ‘you shall take’ – there should be taking for each and every one”. I.e. there is an obligation for every single individual to take the arbah minim on Succos.
If one is weak and unable to hold the arbah minim on his own (i.e. a child or someone who is sick), is he able to fulfil the mitzvah, or do we say that since someone else is helping him it’s not considered a lekicha [a taking]?
The Shu”t HaEleph Lecha Shlomah (Orach Chaim 372) was asked: If someone gives his arbah minim to his friend to shake, but he kept hold of it, if the friend fulfils the mitzvah?
R’ Shlomah Kluger then brings that the answer to this question can be determined based on a sugya in Shabbos.
The Gemara in Shabbos (91) brings a dispute if two people together carry out a forbidden activity on Shabbos, if both of them have violated Shabbos, or if neither of them have violated Shabbos. The Gemara concludes: If each one could have done the melachah on his own, and they did it together they are both exempt. If neither could have done the melachah on their own, and they did it together they are both accountable. And if this one could do it, and this one couldn’t, and then they do it together, the one who could have done it on his own is accountable, and the second one is exempt, as מסייע ואין בו ממש – “merely helping, is insignificant”.
Extrapolating from this Gemara to our case, if each person could hold the arbah minim on their own and they did it together, then it would be a case of שנים שעשאוהו – “two people carrying out the act”, and the halachah is “that each and every person should take for himself”, therefore, it would be no good. If, however, the one holding it on the top isn’t holding it tight, and without the other person holding it lower down, it would fall, then the person holding it low down would fulfil his obligation, as we look at the one who is holding it on top as מסייע ואין בו ממש – “merely helping, is insignificant”.
Therefore, back to our case, if the weak person holds it on the bottom and someone else helps him by holding it on the top. If the one holding it from the top holds it loosely, and without the weak person on the bottom holding it, it would fall, it would seem that he fulfils his obligation.