The 'Begg appliance' is a modification of
Raymond Begg had been taught use of the ribbon arch appliance at the Angle school before his return to Australia in the 1920s.  Working independently in Adelaide, Begg also concluded that  extraction of teeth was often necessary, and set out to adapt the ribbon arch appliance so that it could be used for better control of root position.
Begg’s adaptation took three forms:

He replaced the precious metal ribbon arch with high-strength 16-mil round stainless steel wire when this became available from an Australian company in the late 1930s;
He retained the original ribbon arch bracket, but turned it upside down so that the bracket slot pointed gingivally rather than occlusally; and 
He added auxiliary springs to the appliance for control of root position. 

In the resulting Begg appliance friction was minimized because the area of contact between the narrow ribbon arch bracket and the archwire was very small and the force of the wire against the bracket was also small. 
Binding was minimized because Begg’s strategy for anchorage control was tipping and uprighting , and tipping minimizes the angle of contact between the wire and corner of the bracket.
Ribbon arch appliance
E-arch appliance
Edgewise appliance
Pin and tube appliance