C.A. Terzuolo

THE LAW RELATING THE KINEMATIC AND FIGURAL ASPECTS OF DRAWING MOVEMENTS

Considerable evidence exists that the velocity of execution of handwriting and drawing movements depends on some global metric properties of the movement (size, linear extent etc.). Recent experiments have demonstrated that the instantaneous velocity also depends on the local curvature of the trajectory, that is, on the differential geometrical properties of the movement. In this paper we investigate further the role of the differential factors. Experiments are described in which drawing movements of simple geometrical forms and scribbles are performed either freely and extemporaneously, or in the presence of external constraints. It is shown that, at any time during the movement, the velocity component related to differential factors only depends on the value of the curvature of the trajectory at the same time (no dynamics). The relation can be described quantitatively as a specific Power Law and applies to all movements considered here, including those which are performed by following the edge of a template. The fact that the velocity of execution increases with the radius of curvature implies a built-in tendency of the motor control system to keep angular velocity relatively constant and qualifies the Isogony Principle proposed previously. The specific exponent of the Power Law suggests a possible interpretation of this empirical relation.

32 Space-Time Invariance in Learned Motor Skills

The data presented here generalizes the notion of homotetic behavior in the time domain for learned motor sequences, that is, the presence of an invariant structure in such sequences, from typing to handwriting. Furthermore, it extends the principle to the space-time domain for unrestricted, continuous movements. An interpretation of the teleological value of this behavior is provided.

An algorithm for the generation of curvilinear wrist motion in an arbitrary plane in three-dimensional space

The elements of an algorithm are presented which predicts for some simple forms (circles and ellipses) the kinematic and figural aspects of the trajectories of the human wrist when these are drawn in any arbitrary plane of free, three-dimensional space. The algorithm is based on theoretical considerations and experimental data and specifies in a unique way the angular motion at the shoulder and elbow joints by utilizing a coordinate transformation, which is only approximate, between the chosen extrinsic (trajectory) and intrinsic (joint angles) parameters. A way to extend the use of this algorithm to generate any arbitrary complex movement in all possible planes of space is also suggested.

Determinants and characteristics of motor patterns used for typing

Abstract In the course of a study directed to investigate whether or not a relationship exists between changes in typing rate throughout a sentence and the syntactic structure, we found that the motor patterns used by professional typists are highly characteristic of individual words. The following main points were demonstrated: (1) First order interactions for letter-to-letter transitions, as determined by keyboard designing, digrams frequency in the language and individual ‘habits’ cannot account for the specific structure of the motor sequences used for typing individual words. (2) This structure is invariant and independent of the absolute time used for typing the word. It is the same whether the word is part of a meaningful sentence, a list of unrelated words, or it is typed from memory. The structure consists of a set of ratios of the time intervals between each successive pairs of key pressings. Time is instead a free parameter, which is independently regulated. (3) These patterns are characteristic of the word and the subject, and represent well-defined units of motor action. However, in the case of long polysyllabic words, it was possible to prove that subunits are present in the pattern (which sometimes coincided with the syllables, but at other times did not). The uniqueness of the pattern for the entire word then arises, in these cases, from the fact that the subunits are either typed at different speeds or some discontinuity is present between two adjacent subunits. (4) For the pattern to be correctly implemented, sensory input data generated by touching and/or pressing the keys are necessary. However, the motor commands and the proprioceptive inputs generated by the movements of the fingers are insufficient alone to insure such implementation. Also, the force necessary to accomplish the task can be regulated by the subject without affecting the structure of the pattern. When a disturbance in the implementation of the pattern is obtained, using a very large and asymmetric load (loading of only one finger), such disturbance is spatially localized to the loaded fingers, and it consists of a jump discontinuity which resets the implementation of the pattern, without causing any further disruption. On the basis of these and other data, it has been concluded that an anatomico-functional representation of the pattern is likely to be permanently available in the nervous system which consists of: (1) a set of basic motor engrams for the most common words and groups of letters; (2) a set of rules for combining basic motor engrams into larger units. It has also been argued that, functionally, a parallel arrangement of the events included in each engram is likely, since the variability of each of these events does not increase with its rank order. Time would then intervene as a free parameter during the implementation of the pattern, being responsible for modulating uniformly the rate of the motor commands pertinent to each engram. The internal process responsible for such modulation apparently is accessible to sensory inputs and perceptual events.

Coordination of arm movements in three-dimensional space. Sensorimotor mapping during drawing movement

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.

Some factors pertinent to the organization and control of arm movements

Trajectories of arm movement during a pointing task were shown to be unaffected by large loads. Moreover, when the effective arm length was changed, the target was still approached along a direct trajectory. It is concluded that: (1) compensation for load occurs automatically without affecting those constraints on the basis of which movements are organized; (2) that the effective lengths of body segments as well as joint angles constitute variables utilized in the organization of trajectories.

SEPARATION OF TRANSDUCER AND IMPULSE-GENERATING PROCESSES IN SENSORY RECEPTORS.

New evidence is presented that spike and transducer processes in sensory receptors are independent events; impulse activity in tile crustacean stretch receptor neuron and the mammalian pacinian corpuscle was selectively blocked by a compound (tetrodotoxin) without affecting any of the parameters of the generator potential.

Organization of arm movements in three-dimensional space. Wrist motion is piecewise planar

It is shown that human subjects are incapable of producing with the arm, in free space, planned or extemporaneously drawn trajectories in which the plane of wrist motion changes smoothly or continuously. The three-dimensional nature of these movements results from the fact that the plane of motion changes abruptly from one segment of the trajectory to the next, being confined to one plane during each segment (i.e. piecewise planar).

Modulation of the myotatic reflex gain in man during intentional movements

Human subjects were asked to perform sinusoidal tracking movements (0.5--3.0 Hz) with their forearms while external torque disturbances were applied at the elbow. The changes in angular position, velocity, and acceleration produced by these disturbances were found to be represented in the reflex changes in EMG activity of both biceps and triceps muscles. The gain of each of these reflex components varied during the tracking task, their maximal being about the same as those measured when the torque disturbances were applied in the absence of movements and the subjects attempted to maintain a constant forearm position. Such changes in gain were found to be centrally regulated since they were shown not to depend on the movement itself, being also present during force tracking, i.e. under nearly isometric conditions. Also their minima and maxima did not coincide with those of the EMG activity. These results suggest that an internal plan (or model) of the learned task is present, whereby reflex gains can be regulated independently from the motion and alpha-motoneuron activity. Such regulation effectively uncouples the reflex motor output from the intentionally controlled motion and maintains spindle sensitivity to external disturbances independent of large changes in muscle length. These conclusions are discussed in the context of the functional role of gamma-motoneurons in the control of movements.

Myotatic Reflex: Its Input-Output Relation

The dynamic properties of the myotatic reflex and of its components were determined by a systems-analysis approach. The gain and phase relations between an applied stretch, whiclh initiates the reflex, and the output of the primary mulscle spindles, which impinge upon α-motoneurons, are not further changed by the properties of the motoneurons. The dynamic relation between motoneuron activity and the resultant muscle tension balances these changes in gain and phase; the result is a flat gain and nearly zero phase difference between stretch and tension produced by the myotatic reflex. Moreover, the distribution of activity in multiple channels extends the range in which the overall reflex is linear.