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The reachable space of the hand has received significant interests in the past from relevant medical researchers and health professionals. The reachable space was often computed from the joint angles acquired from a motion capture system such as gloves or markers attached to each bone of the finger. However, the contact between the hand and device can cause difficulties particularly for hand with injuries, burns or experiencing certain dermatological conditions. This paper introduces an approach to find the reachable space of the hand in a non-contact measurement form utilizing the Leap Motion Controller. The approach is based on the analysis of each position in the motion path of the fingertip acquired by the Leap Motion Controller. For each position of the fingertip, the inverse kinematic problem was solved under the physiological multiple constraints of the human hand to find a set of all possible configurations of three finger joints. Subsequently, all the sets are unified to form a set of all possible configurations specific for that motion. Finally, a reachable space is computed from the configuration corresponding to the complete extension and the complete flexion of the finger joint angles in this set.