A Simple Model for Handwriting

An understanding of the human motor system, though interesting as a facet of intelligence, would also have application for computer controlled manipulat ion. To enhance this understanding, handwriting is appropriate for study because of its commonality, its susceptibil i ty to measurement, and the possibility of its simulation with a manipulator. A theory of handwriting has been developed and implemented on a 6-joint manipulator, the M IT VIC ARM The theory views handwriting as a constrained modulation of an underlying oscillation pattern. This pattern, chosen from a repertoire of carrier waves such as sawteeth or garland chains, is established by programming of horizontal and vertical actuators. The two actuators assume different roles: the vertical actuator drives the movement with rhythmic down-up movements. The horizontal actuator, acting within time constraints imposed by the vertical rhythm, produces letter shapes. The choice of underlying oscillation pattern restricts the shapes the horizontal actuator can produce, and is the primary factor influencing writing style. A simple set of constraints on actuator force patterns, derived in part f rom an analysis of some handwriting measurements, imposes a certain structure on the handwriting programs: 1. a basic time quantum in which force is constant 2. synchronous joint activation 3. force magnitude restriced to a few levels The basic time quantum for the V ICARM, representing a compromise among such factors as speed of response and jerkiness, was chosen as 24 msec. A cycle of the carrier is a down-up movement comprised of several time quanta. The fastest cycle consists of one quantum acceleration-deceleration bursts by the vertical actuator, resulting in a four quantum down-up cycle of 96 msec. When coupled with a horizontal pattern that rounds the bottoms of the oscillation, a smoothed sawtooth results (la below). Horizontal (H) and vertical (V) The constraints on force patterns lead to a small set of allowable horizontal rounding patterns Coupled with restrictions on how these rounding patterns overlap with the down-up motion, there arises a vocabulary of corner shapes that range from rounded to sharp, symmetric to asymmetric. With this vocabulary an oscillation train is readily shaped, subject of course to time and stylistic limitations imposed by the choice of oscillation. As an illustration of the ability to manufacture different letter shapes, four a's drawn by d i f fe ren t human subjects (taken f rom [Koster and Vredenbregt]) appear below paired with their V I C A R M facsimiles, the former on the left and the VICARM writing on the right. The first two a's are derived from an 8quantum cycle, the last two a's from a 12-quantum cycle.