Table 1 Kinematic features and corresponding definitions for quantification

End-point speed

The instantaneous speed at which the endpoint is moving.

Reaching lime

The time duration from the initiation of movement until a reach is successfully completed. A reach is completed when the end-point reaches a specified distance from the target, the end-point velocity decreases below 5% of the maximum velocity, and the hand activates a sufficient number of sensors on the force-sensing target object (if a physical target is present).

Speed range

The maximum speed of the end-point (within a reach) while moving towards the target from the starting position.

Speed consistency measure

The average variation of the maximum speed (within a reach) over a set of ten reaches.

Reaching time consistency

The average variation of the maximum reaching time (within a reach) over a set of ten reaches.

Trajectory Profile

Real-time trajectory error

Real-time deviation of the end-point that is greater in magnitude than the maximum horizontal and vertical deviations within range of unimpaired variation, calculated as a function of the end-point's percentage completion of the reach.

Maximum trajectory errors

Largest magnitude values among the real-time trajectory errors within a single reach.

Trajectory consistency

Measurement of how trajectories vary over several reaches using a profile variation function [28].

Targeting

Target acquisition

The binary indicator of finishing the task, achieved when the end-point reaches a specified distance from the target, the end-point velocity decreases below 5% of the maximum velocity, and the hand activates a sufficient number of sensors on the force-sensing target object (if a physical target is present).

Initial spatial error approaching target

The Euclidian distance between the hand position (x, y, z)_hand and reference curve position (x, y, z)_ref measured at the first time the velocity decreases to 5% of the velocity peak, where (x, y, x)_ref is the reference of the hand position for grasping the target obtained from adjusted unimpaired reaching profiles.

Final spatial error approaching the target

The Euclidian distance between the hand position (x, y, z)_hand and reference curve position (x, y, z)_ref at the end of movement, where (x, y, z)_ref is the reference of the hand position for grasping the target that is obtained during calibration.

Final spatial consistency

Used to measure variation of final spatial error across several trials, and is computed as the square root of summation of the ending point variances along the x-y-z directions for a set of ten trials.

Velocity Profile

Additional phase number

The first phase is identified as the initiai prominent acceleration and deceleration by the end-point, and an additional phase is defined as a local minimum in the velocity profile beyond the initial phase. The additional phase number counts the number of phases that occurred beyond the first phase before reach completion.

Phase magnitude

Compares the size of separate phases within one reach, and is calculated as the ratio between distance traveled after the peak of first phase (during deceleration) and the distance over the entire deceleration of the reach [36]. Only the deceleration part of the first phase is examined because this portion of a reach is where the most adjustments tend to occur.

Bell curve fitting error

Compares the shape of the decelerating portion of the velocity profile to a Gaussian curve by measuring the total amount of area difference between the two curves.

Jerkiness

Measure of the velocity profile's smoothness, and is computed as the integral of the squared third derivative of end-point position [37].

Compensation

All compensation measures are computed as a function of the end-point's distance to target because the extent of allowable compensation varies throughout the reach [38].

Torso flexion

Compares the flexion of the torso relative to the non-impaired subjects' torso forward angular profile, adjusted to participant-specific start and end reference angles determined by a clinician during calibration.

Torso rotation

Compares the rotation of the torso relative to the non-impaired subjects' torso rotation angular profile, adjusted to participant-specific start and end reference angles determined by a clinician during calibration.

Shoulder elevation

Compares the elevation of the shoulder relative to the non-impaired subjects' shoulder elevation profile, adjusted to participant-specific start and end reference angles determined by a clinician during calibration.

Shoulder protraction

Compares the protraction of the shoulder relative to the non-impaired subjects' shoulder protraction profile, adjusted to participant-specific start and end reference angles determined by a clinician during calibration.

Pre-emptive elbow lift

Computed as the difference between current elbow position and the elbow position during rest calibration. Elbow lifting is only examined at the beginning of the reach as a predictive measure of initiation of the movement through compensatory strategies.

Joint Function

Joint angles of the shoulder, elbow and forearm are evaluated based on the following measures

Range of motion (ROM)

The difference in angle from the initiation to the completion of the movement.

ROM error

The difference between the ROM of an observed reach and the reference ROM obtained during the assisted calibration reach.

Real-time error

The maximum error between the observed joint angle curve during a reach and the reference curve derived from non-impaired reaching data that is scaled to the start and end reference angle of each participant.

Consistency of the angular profile

The average variation between angular profiles within a set often reaches.

Upper extremity joint correlation category

Measures synergy of two different joints moving in a linked manner, computed using the standard mathematical cross-correlation function of two angles over the duration of a reach for each pair listed below. May be compared to non-impaired upper extremity joint correlations for evaluation [39].

Shoulder flexion and elbow extension

Measured cross-correlation between shoulder flexion and elbow extension

Forearm rotation and shoulder flexion

Measured cross-correlation between forearm rotation and shoulder flexion

Forearm rotation and elbow extension

Measured cross-correlation between forearm rotation and elbow extension

Shoulder abduction and shoulder flexion

Measured cross-correlation shoulder abduction and shoulder flexion

Shoulder abduction and elbow extension

Measured cross-correlation between shoulder abduction and elbow extension