The reachable 3-D workspace volume is a measure of payload and body-mass-index: A quasi-static kinetic assessment

A compact 3-DOF shoulder mechanism constructed with scissors linkages for exoskeleton applications

“…This spherical triangle ACM allows defining the real mechanism's angular limits in its most stretched configuration by the spherical law of cosines as in Equation (2). Since the cosine of the right angle at the vertex M is zero, the spherical law of cosines is simplified to Equation (24).…”

“…As it may not be feasible to test such device for every ADL, an alternative is to use the reachable 3-D workspace that gives a global approximation of the working ranges of the mechanism and can account for extreme cases too. Thus, the full anatomical reachable 3-D workspace was estimated based on the five-tasks protocol created in our previous work, Castro et al [24]. These five tasks are capable of capturing the close-to-torso (through the 'shower', 'curls' and 'free-motion' tasks) and far-from-torso (through the 'vertical' and 'horizontal' tasks) regions of the reachable 3-D workspace, allowing estimation of its envelope shape and volume.…”

“…To experimentally evaluate the reachable 3-D workspace, the test-subject was instrumented with reflective markers, according to the marker-set presented in [24] as exemplified in Figure 12. Firstly, all segments' length and hand breadth in the model were geometrically scaled to one test-subject (male, age 27, body mass 80 kg, height 1.75 m, upper-extremity length 0.642 m) from a static calibration trial using the method by Andersen et al [29].…”

“…Firstly, all segments' length and hand breadth in the model were geometrically scaled to one test-subject (male, age 27, body mass 80 kg, height 1.75 m, upper-extremity length 0.642 m) from a static calibration trial using the method by Andersen et al [29]. Afterwards, the participant was instructed to perform the five-tasks protocol for the kinematic assessment of the reachable workspace [24] three times: the first time consisted on recording the full active reachable workspace; keeping in mind the exoskeleton's mechanical constraint preventing shoulder protraction/retraction motion, the participant was instructed to perform the protocol a second time without protracting or retracting the shoulder (null angle); lastly, the protocol was performed while wearing the exoskeleton prototype. The recorded kinematic data was then used to drive the skeletal model by optimizing all model's marker trajectories as formulated by Andersen et al [30].…”

“…Later, a point cloud set including all hand palm points (the end-effector of the upper extremity), for each of the two five-tasks protocols performed, was recorded relative to a thorax reference frame located on top of the sternum bone. The non-convex shaped envelopes of each of the three reachable workspaces were obtained resorting to the alphashape algorithm [31] according to the processing steps described on our previous work [24]. This algorithm works on a mesh of the point cloud as a "carving" sphere shaping its envelope and enables to capture its non-convex nature.…”