Functional range of movement of the hand : declination angles to reachable space

 The measurement of the range of hand joint movement is an essential part of clinical practice and rehabilitation. Current methods use three finger joint declination angles of the metacarpophalangeal, proximal interphalangeal and distal interphalangeal joints. In this paper we propose an alternate form of measurement for the finger movement. Using the notion of reachable space instead of declination angles has significant advantages. Firstly, it provides a visual and quantifiable method that therapists, insurance companies and patients can easily use to understand the functional capabilities of the hand. Secondly, it eliminates the redundant declination angle constraints. Finally, reachable space, defined by a set of reachable fingertip positions, can be measured and constructed by using a modern camera such as Creative Senz3D or built-in hand gesture sensors such as the Leap Motion Controller. Use of cameras or optical-type sensors for this purpose have considerable benefits such as eliminating and minimal involvement of therapist errors, non-contact measurement in addition to valuable time saving for the clinician. A comparison between using declination angles and reachable space were made based on Hume's experiment on functional range of movement to prove the efficiency of this new approach.

Deducing the reachable space from fingertip positions

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.

Quantification of the finger functional range via explicit descriptions of reachable subspaces

In recent times, the finger flexibility assessment by means of reachable space is considered as an effective tool to describe the range of motion of the hand. Existing approaches numerically compute the reachable space using forward kinematics such as exhaustive scanning or Monte Carlo methods. In this paper, we provide explicit formulas mathematically determining the reachable space boundary. Green's theorem is used to deduce the corresponding capacity formula for the size of the reachable space as opposed to an implicit numerical solution. Using this new mechanism, we accurately quantify and compare the reachable space of different subjects in order to effectively compare the functionality of the fingers. We evaluate the performance of our proposed method against the kinematic feed-forward (KFF) approach in calculating the reachable space. The execution time to capture the reachable space is significantly less than that for the standard KFF method. The computational cost for quantifying the reachable space capacity is significantly improved due to explicit capacity formulas resulting from the abstract form of boundary descriptions of the reachable space, unique to the proposed approach.

Describing human finger flexibility via reachable subspaces

In recent years, the reachable space concept has attracted the attention of many researchers as a mean of describing finger flexibility. Existing approaches such as exhaustive scanning or Monte Carlo methods to obtain the reachable space are resource-hungry techniques. In this paper, we introduce a novel approach to determine and quantify the reachable space of the finger. The approach was developed around a set of formulae determining the boundary of the reachable space. The Monte Carlo simulation is proposed to estimate the capacity of the reachable space. Using the new technique, reachable spaces can be visualised and quantified in order to effectively compare the functionality of different subjects and their therapeutic status. The performance of the proposed method was evaluated against the kinematic feed-forward approach. The computational cost to obtain the reachable space is significantly less than the standard kinematic feed-forward approach due to exclusive description of the reachable space boundary, unique to the proposed approach.