Why did Naruto and Sasuke hit Tobi with Rasenshuriken directly? When Naruto first mastered Rasenshuriken and used it against Kakuzu, his arm was also injured due to multiple wind blades that also damage the user and had to recover for a while.

But in a recent chapter, combined with Sasuke's Amaterasu, both of them were holding the Rasenshuriken and they hit Tobi without throwing it. So how come it seems like they did not take any damage when they hit Tobi without throwing it?
The first time Naruto was shown using the Rasenshuriken, it was during the fight with Kakuzu. At the time, Naruto had not mastered the Rasen Shuriken completely. He had to hit the target in point blank range. Since he was in the blast range of the jutsu he was heavily impacted by the corrosive power of the jutsu.

But during his training in Mount Myoboku he mastered the Rasen Shuriken in a secretive manner, enabling him to throw the Rasen Shuriken over a distance. This allowed Naruto to stay off the blast range and also control the area covered by the blast from the Rasen Shuriken. But, even in his Sage mode, Naruto could use only two Rasen Shurikens, but he no longer sustained damage from his own jutsu.

Later, when he took control of the Kyuubi he had access to a huge amount of chakra previously unavailable to him, giving him the capability to use Rasen Shurikens more than two times. 

Sasuke's Amaterasu is a fire technique, and Naruto's Rasenshuriken is a Wind technique, it is known that wind techniques increase the effectiveness of a fire technique. Thus Naruto and Sasuke combined their jutsus to make a far powerful jutsu. And since both of them were out of the blast radius, none of them were hurt from it.



Image taken from Manga chapter 634.

Regarding the recent usage of the combination of Rasenshuriken and Amaterasu, I can only assume as to why it did not affect Naruto and Sasuke. The second hokage swapped Minato and Obito just before the attack landed, so similarly with the same jutsu he may redirect the aftershock of the attack away from Naruto and Sasuke. 

The second possibility is, since Naruto can himself control the area of effect of the Rasen Shuriken, as we have seen him perform earlier (mainly during the fight with Pain where he increases the area covered by the rasen shuriken as Pain was escaping). Due to which he himself may be able to minimize the are of impact of the jutsu and concentrate it only on Obito thereby saving both sasuke and himself.