Accelerator's crutch

Accelerator's crutch (一方通行の杖) is a tool used by Accelerator to support his body when not using the esper mode of his Calculation assistance device (the choker-type electrode), after being partly disabled from being shot in the head. It was first seen in the 8th light novel volume of Toaru Majutsu no Index, and is presumed to be a commercial one as on its second appearance Accelerator acquires another crutch after he breaks it in his fight with Musujime Awaki. Accelerator modifies the crutch extensively for his own purposes, making it unique from the previous one.

First incarnation
The first incarnation of the crutch appears as having a modernistic design, a long stick with a handle attached to it, similar to a. The crutch is a forearm crutch, having a cuff that goes around Accelerator's forearm. During his fight with Awaki, the crutch breaks into several pieces as he delivers the finishing blow on Awaki. In the anime adaptation, Accelerator still carries the crutch in flight but it mysteriously disappears just before he reaches Awaki. It is later revealed to have been discarded by Accelerator, and he later picks it up after defeating Awaki.

During his first fight with Kihara Amata, Accelerator loses the crutch and is forced to use a shotgun to support his body instead throughout the rest of the night. He later gains a crutch before his first mission with GROUP, presumably a different one, since it can be assumed that the Hound Dogs destroyed it to get rid of evidence after their Accelerator's first run in with them with Amata. Later, Accelerator tosses the crutch aside before battling Kakine Teitoku, and can be assumed he picked it up again afterwards.

Second incarnation
The second incarnation of his crutch occurs during the events of DRAGON Arc. From a tool, it becomes a complex device after Accelerator adds several components and features to it, which would allow Accelerator to stand up by himself even if his choker loses power completely. It contains a small motor and weight distribution sensors, allowing for it to determine the center of gravity. Instead of a single leg like a regular crutch, it ends with four legs attached to its end like a microphone stand, which according to the narration "holds the ground" helping Accelerator to get him up when he is down. The staff along with the four legs can be retracted in and out of the cuff, apparently in a swift enough motion that if added more power by Accelerator, he'd consider it as a weapon. Furthermore, the cuff, which has noticeably become wider and more stylized making it look like a shield, has a ring attached to it for Accelerator's forearm to go through, making it even more like a proper forearm crutch.

It is later revealed that the additional legs to aid in walking and the motor are just part of the disguise, as Accelerator added a component into that blocks other interference devices. The crutch allows for Accelerator to block specific wavelengths after successfully analyzing it and using the equipment of the crutch, an interference wavelength can be reverse-engineered to specifically block that wavelength. Accelerator specifically added this feature on the crutch in order to cover the weakness of his Calculation assistance device choker, which connects to the Misaka Network of the Sisters, allowing him to move at all in the first place.