Transformation from arm joint coordinates to hand external coordinates explains non-uniform precision of hand position sense in horizontal workspace.

People perceive hand position in horizontal workspace more precisely in radial than in azimuth directions and closer to the body than farther away. Current explanations for this position sense non-uniformity include spatial asymmetry in arm proprioceptive activities and/or cortex maps, experience-dependent learning, arm posture, and others. Here we investigated contributions to this non-uniformity of a posture-dependent transformation from arm joint angles, sensed by arm proprioceptors, to hand position. We measured precision of hand position sense in a bimanual hand mirror-position matching task at four horizontal targets forming a square in front of the body in 11 blindfolded individuals. We found lower hand precision in azimuth than in radial direction, higher azimuth precision at close targets, and higher radial precision at distant targets. We then theoretically analyzed the transformation of random angle errors at shoulder and elbow into hand position random errors in a horizontal plane and obtained similar distributions of hand position errors. The predicted and experimental hand-precision ellipse orientations, but not ellipse shapes or sizes, were highly correlated and were nearly orthogonal to arm stiffness ellipse orientations reported in the literature. We concluded that the joint-to-hand coordinate transformation is responsible for the non-uniform precision of hand position sense.