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Inverse Kinematics is defined as the problem of determining a set of appropriate joint configurations for which the end effectors move to desired positions as smoothly, rapidly, and as accurately as possible. However, many of the currently available methods suffer from high computational cost and production of unrealistic poses. In this paper, a novel heuristic method, called Forward And Backward Reaching Inverse Kinematics (FABRIK), is described and compared with some of the most popular existing methods regarding reliability, computational cost and conversion criteria. FABRIK avoids the use of rotational angles or matrices, and instead finds each joint position via locating a point on a line. Thus, it converges in few iterations, has low computational cost and produces visually realistic poses. Constraints can easily be incorporated within FABRIK and multiple chains with multiple end effectors are also supported.