In this paper data are presented concerning the motion of limb segments during drawing movements executed in different planes in free space. The technique used allows the determination of the wrist and elbow positions in space as well as the measurement of the elbow angle of extension. Other kinematic variables are determined trigonometrically. Elbow and shoulder torque is also calculated. For circles and ellipses, it was found that the motion at the wrist is sinusoidal in two orthogonal directions in the plane of motion. Angular motion, when described by a set of angles previously identified psychophysically as constituting an appropriate coordinate system, is also sinusoidal. Although the number of degrees of freedom of the arm affords many possible ways of performing the task, there is a fixed phase relation between the angles of elevation of the upper arm and forearm for naturally executed movements in all planes of space. Also, the phase of the yaw angles of the upper arm and forearm relative to the angles of elevation are related to the plane of motion and to the slant of ellipses in a fixed manner. There is a simple mapping between angular motion and intended wrist trajectory. Because this mapping is not valid for all planes of space, the actual trajectory can deviate from the intended one. However, the subject has no cognizance of the distortion. The calculated torque deviates substantially from sinusoidal and does change significantly when the same movement is executed in different planes. Results of simulations and mathematical analysis indicate that the fixed phase relationship between angles of elevation leads to a minimal distortion from sinusoidal motion at the wrist in an average sense and that the characteristic distortions observed in the sagittal plane result inevitably from this constraint on the phase relations. The results support the assumption that the topology of the sensorimotor map used for the production of the movement and for its perception is the same. The problem of invariant relationships between kinematic parameters is discussed and the suggestion is made that they represent a general constraint, leading through learning and practice to an optimal solution in an average sense.
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