The thick rafters which form part of the roof truss are called “principal-rafters” to distinguish them from the common-rafters that carry the battens that hold the thatch or roof-tiles. The principal rafters carry the purlins. These are the longitudinal members which run the length of the roof and support the common rafters.
The most common way of adding extra support to the purlins and thereby the rest of the roof is by “king-posts”, “crown-posts” or “queen-posts”. These were used in most timber framed barns from the thirteenth century to the eighteenth century.
However in an area of South Oxfordshire, Berkshire and Buckinghamshire from the mid-seventeenth century to the late eighteenth century there was a fashion for adding a curved or cranked member under the principal rafter. I have only managed to find and visit four examples so far. However there is an excellent article by David Clark (Cranked Inner Principals) -Vernacular Architecture, Vol. 35 (2004) 32-39, describing this type of structure.
I have plotted some of these barns onto Google maps. The icon on the right will take you to my map.