Objective

Develop a stochastic model of the reachable workspace of the human finger. This is needed to allow a FHD design which can accommodate a wide range of user finger sizes and workspaces.

Work Status/Results

Mechanism reachable workspace is usually represented as a boundary contour which divides the mechanism operational space in to "inside" and "outside" of the reachable workspace. This inside/outside boolean representation may be extended to a stochastic representation with values at each operational space location ranging between 0.0 and 1.0; these values represent the probability of that particular location being contained in a mechanism whose kinematic parameters are themselves defined stochastically.
For the case of the human finger operational space (considering only flexion/extension motion), a stochastic kinematic model was used where the finger segment (phalanx) lengths were represented as gaussian distributions based upon published anthropometric data. An example plot of the stochastic reachable workspaces for the index finger is shown below:

Note that the (x,y) origin in the above graph is the location of the Metacarpophalangeal (MCP or knuckle) joint for the index finger.