Detection of Stretching And Folding (SAF) traits in a time series is still controversial and of great interest. Also, visuo-manual tracking studies did not pay attention to SAF in hand motion trajectories. This research aims to find out the relevance of SAF to the discontinuities in chaotic dynamics of hand motion through target tracking tasks. Specifically, a new method is constructed based on this relation in which SAF can extract accurately trajectories in both time domain and phase space. Consequently, we designed experiments to track sinusoidal and trapezoidal target movements shown on a monitor. In these experiments, fourteen participants were instructed to move the joystick handle by wrist flexion-extension movements. Results confirm intermittency in significant human motor control behavior which results in discontinuities in hand motion trajectories. The relation between SAF and these discontinuities is realized by chaotic and intermittent behaviors of tracking dynamics. Verification of the method’s accuracy is also carried out by taking advantage of the Poincaré section. Our method can provide insight into the dynamical behaviors of chaotic and intermittent systems involving mechanisms in human motor control. It can be applied to general systems with intermittent behavior and other systems with modification.

The specification of stretching and folding properties, particularly in time series, is of substantial interest. This study is sought to perceive the relationship between stretching and folding and irregular discontinuities in hand motion trajectories during target tracking tasks. In this regard, a new method is proposed based on compiling physiological characteristics and hand motion dynamics' geometrical traits. Thus, five tracking conditions are designed in which participants are instructed to track different target motion patterns. In these experiments, sinusoidal and trapezoidal target movements with frequencies of 0.1 and 0.3 Hz, as well as pseudo-periodic target motion created by summing two sinusoids with frequencies of 0.117 and 0.278 Hz, are used as visual targets. The results illustrate that nonuniform discontinuities are noticeable properties of the hand motion trajectory. Also, the largest Lyapunov exponent, correlation dimension, and fractal dimension corroborate that the tracking attractor is low-dimensional and chaotic. Moreover, the results are compared with the curvature-based method, and its modified version is presented by taking advantage of the proposed method. As a result, through the suggested method, stretching and folding points are well discerned regardless of discontinuities. This method can deal with the systems with intermittency in both times-and state space.