The 24,355-hour airline transport pilot was conducting an instructional training flight with a 30,000-hour airline transport pilot performing touch and go landings to Runway 17 in a light twin-engine airplane. During the landing touchdown to the 7,000-feet long, by 100-feet wide asphalt runway, the right main landing gear collapsed. The flight instructor reported in the NTSB Form 6120.1 (Pilot/Operator Aircraft Accident/Incident Report) that immediately after touchdown on the runway, the "right side slowly lowered." The pilot receiving instruction was on the controls and announced "something is wrong" and both pilots immediately applied full left aileron and left brake to limit the right yaw. The aircraft departed the runway on the right side onto the grass and a shallow ditch before coming to a stop with the right gear collapsed and nose and left gear down and locked. The aircraft sustained structural damage to the right wing and right horizontal stabilizer and both occupants were able to egress the airplane unassisted. Neither pilot was injured. A post-accident inspection of the wreckage by a Federal Aviation Administration inspector revealed that the right landing gear over-center down link lock failed on touchdown. The weather at the accident site was reported as wind from 100 degrees at 9 knots, overcast skies at 2,000 feet, 10 miles visibility, and a barometric pressure setting of 29.70 inches of Mercury.