  Twisted links are obtained from a base link by starting with a $n$-braid
representation, choosing several ($m$) adjacent strands, and applying one or
more twists to the set. Various restrictions may be applied, e.g. the twists
may be required to be positive or full twists, or the base braid may be
required to have a certain form.
  The Jones polynomial of full $m$-twisted links have some interesting
properties. It is known that when sufficiently many full $m$-twists are added
that the coefficients break up into disjoint blocks which are independent of
the number of full twists. These blocks are separated by constants which
alternate in sign. Other features are known. This paper presents the value of
these constants when two strands of a three-braid are twisted. It also
discloses when this pattern emerges for either two or three strand twisting of
a three-braid, along with other properties.
  Lorenz links and the equivalent T-links are positively twisted links of a
special form. This paper presents the Jones polynomial for such links which
have braid index three. Some families of braid representations whose closures
are identical links are given.
