The question arises about striking in koryu jujutsu and specifically Shibukawa Ichi Ryu. Depending on the style, striking may be taught as stand-alone techniques or they may be integrated as a part of a larger technique or both. This is the case with our koryu style, Shibukawa Ichi Ryu jujutsu. Several of the kata incorporate strikes as part of a bigger sequence of moves eg. a throw followed by a kick. Other kata focus soley on teaching individual striking techniques against vital points. In this instance the term atari is often used, similar to the term atemi.
Where some koryu styles may teach atemi quite early on, in Shibukawa Ichi Ryu stand-alone atari is not formally taught until the student is more advanced. This allows the beginner to rely less on striking and to focus more on developing other skills such as timing, distancing, balance, posture and so on. In Shibukawa Ichi Ryu there is also the term yawara which is used to describe attacks to painful points or 'pressure points'. This term is used in a similar way to the Japanese word 'kyusho'.
Striking and pressure point attacking techniques in Shibukawa Ichi Ryu include various finger grabbing and gouging methods against different targets on the body. There are also single-knuckle punching techniques, knife-hand strikes, big toe kicks and stomping kicks.
NO KARATE PUNCHING!
Many so-called jujitsu styles created outside of japan incorporate punching techniques that actually have no origins in japanese jujutsu. They employ a clenched fist that is rotated as it strikes out. This type of punching did not originate from jujutsu of feudal japan but from different martial arts in other regions such as karate in Okinawa, and in various Chinese martial arts.
The earliest jujutsu styles involved grappling with swords and daggers. In these circumstances samurai wore armour to protect them from blades. This armour also meant that the effectiveness of punching and striking techniques was greatly limited. Later in the Edo period, especially in the 1800s jujutsu was used more and more by normal people (non-bushi) and samurai not wearing armour. As a result striking techniques grew in usefulness and popularity. Even without armour however, koryu jujutsu styles have a tendency to focus strikes against very specific organs and arteries in the body rather than striking towards general areas like the head and torso (jodan, chudan, gedan). This in essence is the difference between atari/atemi of jujutsu and the strikes of other martial arts such as karate.
It is worth noting that the knowledge about which vital points were good targets was in many cases related to cutting techniques in iaijutsu and kenjutsu, japanese swordsmanship.