Include; Cat Rig, Cutter Rig, Gaff Rig, Jibhead Rig, Ketch Rig, Lanteen Rig, Sloop Rig, Sprit Rig
Cat Rig - Having a single mast and a single sail.
Cutter Rig - One mast, one sail aft of mast, two or more forward. Similar to a sloop except that there are at least two triangular sails forward of the mast. The mast is stepped farther aft than a sloop, creating a larger foretriangle. Because of the large area, multiple, smaller sails, are easier to handle than one large sail. The rig allows more versatility than a single large sail but is less powerful in light airs.
Gaff Rig - Has a lower boom and an upper "mast" or boom that attaches to the mainmast. The sail is a quadrangle. This is an older style rig currently used to give a boat a traditional look. Does not come to windward as well as "modern" rigs, requires more hardware, including separate halyards, one for the main and one for the upper boom. Generally less efficient for top performance, but does have less windage aloft when sail is reduced.
Jibhead Rig - In a jibhead rig the forestay does not attach to the masthead but at a point lower on the mast where the top of the jib meets the mast.
Ketch Rig - Two masts, three sails. The ketch is very similar to the yawl. Both rigs have a main, foretriangle, and a mizzen. The ketch generally has its mizzenmast (aft mast) farther forward than a yawl allowing for a larger mizzen. There are various definitions of what constitutes the difference between the two rigs: That a ketch's mizzen must be at least 2/3 of her main, that a yawl's mizzenmast is less than half the height of her mainmast. At the extremes, these rigs are easy to distinguish but there is a mid "gray" area where identification is open to interpretation.
Lanteen Rig - One mast, one sail, two booms.
Sloop Rig - One mast, two sails. Has a main aft of the mast and a triangular sail (jib) forward of the mast, usually attached to the forestay. A sloop is more maneuverable than a cat rig, and more versatile for reducing sail in a blow.
Sprit Rig - A sprit is a boom that extends upward from the mast to the topmost corner of a quadrangle sail. A sprit rig allows more sail area on a short mast.