Three-dimensional drawings in isometric conditions: relation between geometry and kinematics

Normal human subjects grasped a 3-D isometric handle with an otherwise unrestrained, pronated hand and exerted forces continuously to draw circles, ellipses and lemniscates (figure-eights) in specified planes in the presence or absence of a 3-D visual force-feedback cursor and a visual template. Under any of these conditions and in all subjects, a significant positive correlation was observed between the instantaneous curvature and angular velocity, and between the instantaneous radius of curvature and tangential velocity; that is, when the force trajectory was most curved, the tangential velocity was lowest. This finding is similar to that obtained by Viviani and Terzuolo (1982) for 2-D drawing arm movements and supports the notion that central constraints give rise to the relation between geometric and kinematic parameters of the trajectory.