An oscillation theory of handwriting

Hollerbach, John M.

doi:10.1007/bf00336740

Cited by 415 publications

(161 citation statements)

References 11 publications

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“…Endpoint trajectories in rhythmic arm movements can be approximated by continuous oscillatory movements at the level of the biomechanical degrees of freedom of the arm. These results confirm previous data of and and also relate to work of Hollerbach (1981).…”

Section: Goals and Research Strategysupporting

confidence: 93%

Segmentation of endpoint trajectories does not imply segmented control

Sternad¹,

Schaal²

1999

Experimental Brain Research

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Abstract:While it is generally assumed that complex movements consist of a sequence of simpler units, the quest to define these units of action, or movement primitives, still remains an open question. In this context, two hypotheses of movement segmentation of endpoint trajectories in 3D human drawing movements are re-examined: (1) the strokebased segmentation hypothesis based on the results that the proportionality coefficient of the 2/3 power law changes discontinuously with each new "stroke", and (2) the segmentation hypothesis inferred from the observation of piecewise planar endpoint trajectories of 3D drawing movements. In two experiments human subjects performed a set of elliptical and figure-8 patterns of different sizes and orientations using their whole arm in 3D. The kinematic characteristics of the endpoint trajectories and the seven joint angles of the arm were analyzed. While the endpoint trajectories produced similar segmentation features as reported in the literature, analyses of the joint angles show no obvious segmentation but rather continuous oscillatory patterns. By approximating the joint angle data of human subjects with sinusoidal trajectories, and by implementing this model on a 7-degree-of-freedom anthropomorphic robot arm, it is shown that such a continuous movement strategy can produce exactly the same features as observed by the above segmentation hypotheses. The origin of this apparent segmentation of endpoint trajectories is traced back to the nonlinear transformations of the forward kinematics of human arms. The presented results demonstrate that principles of discrete movement generation may not be reconciled with those of rhythmic movement as easily as has been previously suggested, while the generalization of nonlinear pattern generators to arm movements can offer an interesting alternative to approach the question of units of action.

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Section: Goals and Research Strategysupporting

confidence: 93%

Segmentation of endpoint trajectories does not imply segmented control

Sternad¹,

Schaal²

1999

Experimental Brain Research

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“…First, the temporal patterns of handwriting are well described (Hollerbach, 1981;Michel, 1971Michel, , 1976Viviani & Terzuelo, 1980). Second, these tasks are essentially accomplished by distal portions of limbs and can be attributed mostly to contralateral hemisphere motor control (Brinkman and Kuypers, 1973).…”

Section: Introductionmentioning

confidence: 99%

Comparative analysis of actual and mental movement times in two graphic tasks

Decety

François

1989

Brain and Cognition

294

132

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“…In this section, we will show that the 2/3 power law (Lacquaniti et al 1983), which states that the radius r(t) and velocity v(t) are related by r(t)/v(t)= C r(t)2/3 or in 1/3 equivalent notation v(t) = C r(t) , follows in a straightforward way for a simple model, in which an object moves along a trajectory that is described by two orthogonal sinusoids (see Hollerbach 1980). We will use this as a starting point to interpret deviations from the expected 0.33 value for the exponent.…”

Section: Interpreting Deviations From the 2/3 Power Lawmentioning

confidence: 99%

Planning and drawing complex shapes

2005

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Arm and hand movements are generally controlled using a combination of sensory-based and memory-based guidance mechanisms. This study examined similarities and differences in visually-guided and memory-guided arm movements, and sought to determine to what extent certain control principles apply to each type of movement. In particular, the 2/3 power law is a principle that appears to govern the formation o f complex, curved hand trajectories; it specifies that the tangential velocity should be proportional to the radius of curvature raised to an exponent o f 1/3. A virtual reality system was used to project complex target paths in three-dimensional (3D) space.Human subjects first tracked (with the tip of a hand-held pen) a single target moving along an unseen path. The entire target path then became visible and the subject traced the shape. Finally, the target shape disappeared and the subject was to draw it, in the same 3D space, from memory. Most aspects of the movements (speed, path size and shape, arm postures) were very similar across the three conditions. However, subjects adhered to the 2/3 power law most closely in the tracing condition, when the entire target path was visible. Also, only within the tracing condition, there were significant differences in the value of the exponent depending on the size and the spatial orientation of the trajectory. In the tracking and drawing conditions, the exponent was greater than 1/3, indicating that subjects spent more time in areas of tight curvature. This may represent a strategy for learning and remembering the complex shape.2

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An oscillation theory of handwriting

Cited by 415 publications

References 11 publications

Segmentation of endpoint trajectories does not imply segmented control

Segmentation of endpoint trajectories does not imply segmented control

Comparative analysis of actual and mental movement times in two graphic tasks

Planning and drawing complex shapes

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