C-402 Captain reported during taxi the aircraft began to shimmy. After stopping it was discovered the right main landing gear was turned 90 degrees to the fuselage.

Narrative

Following an approach (ILS XXR) I completed a safe and normal landing on Runway XXR. I rolled the airplane out to the end of the runway while slowing and exited on taxiway. While rolling off the runway the aircraft start a strange shaking while taxing at approximately 10 knots. I slowed the aircraft and the shaking stopped and I slowly taxied the aircraft to a safe parking area in front of the terminal building. I shutdown; exited the aircraft and called our maintenance department to inform them of the situation. I was requested to inspect the nose wheel and main landing gear and found no clearly visible issues. After not noting anything; I was asked to assist in troubleshooting the problem on a short test taxi; with no intent to fly; to describe the issue in further detail as I did not know specifics as to what was causing the problem. I started both engines; made a left hand turn away from the terminal building and proceeded south west down the taxiway. The shake began again at approx the same ground speed and informed maintenance that I was not sure the cause but I was grounding the aircraft. As I proceeded with a left turn to park the aircraft in front of the FBO that was adjacent to me; the aircraft began an uncommanded right turn and the aircraft came to a halt. I shutdown; exited the aircraft and found the right main gear was at approx a 90 degree angle to the fuselage and some of the landing gear hardware had separated from its normal connection. The aircraft was still positioned partially on the taxiway and I had company employee get in contact with the airport manager on duty that morning and requested that they come out and mark the aircraft and release a NOTAM for the taxiway closure until someone could come and relocate the airplane. After the aircraft was safely marked; I was instructed by my company to relocate on a charter back to ZZZ and that maintenance would be handling the relocation and repair from there.