The Force Generation in a Two-Joint Arm Model: Analysis of the Joint Torques in the Working Space

Abstract

The two-segment model of the human arm is considered; the shoulder and elbow joint torques (JTs) are simulated, providing a slow, steady rotation of the force vector at any end-point of the horizontal working space. The sinusoidal waves describe the JTs, their periods coincide with that of the rotation, and phases are defined by the slopes of the correspondent lines from the joint axes to the end-point. Analysis of the JTs includes an application of the same discrete changes in one joint angle under fixation of the other one and vice versa; the JT pairs are compared for the “shoulder” and “elbow” end-point traces that pass under fixation of the elbow and shoulder angles, respectively. Both shifts between the sinusoids and their amplitudes are unchanged along the “shoulder” traces, whereas these parameters change along the “elbow” ones. Therefore, if we consider a combined action of both JTs acting at the proximal and distal joints, we can assume that for the end-point transitions along the “shoulder,” and “elbow” traces this action possesses isotropic and anisotropic properties, respectively. The model also determines the patterns of the torques of coinciding and opposing directions (TCD, TOD), which would evoke a simultaneous loading of the elbow and shoulder muscles with the coinciding or opposing function (flexors, extensors). For a complete force vector turn, the relationship between the TCD and TOD remains fixed in transitions at the “shoulder” end-point traces, whereas it is changing at the “elbow” ones.

Hysteresis and Synergy of the Central Commands to Muscles Participating in Parafrontal Upper Limb Movements

“…Earlier, we suggested that the synergy of activation, reflecting the simultaneous activation of muscles belonging to different joints, might be closely related to the patterns of coincidence/opposition in the directions of the torques around the corresponding joints (Kostyukov, 2016; Tomiak et al, 2016; Gorkovenko, 2018; Kostyukov and Tomiak, 2018). Therefore, the existence might be proposed of a close relationship between the activation and force synergies.…”

“…The coinciding synergy relates to the similar modalities of the activated muscles at the joints (flexors and flexors; extensors and extensors), the opposing synergy matches combination of the different modalities (flexors and extensors; extensors and flexors). It has been shown theoretically that there is a strict prevalence of the coinciding synergy for isometric two-joint muscle contractions with complete circle turning of the end-point force vector within the working space (see Figure 6 in Kostyukov and Tomiak, 2018). The present study demonstrates experimentally the strong predominance of coincident synergy in real parafrontal movements produced in different parts of the working space.…”

“…Despite essential positional influences on the EMGs in the muscles providing two-joint movements, the spatial distributions of the forces acting on different muscles and their synergic characteristics could play a predominant role in forming the synergies of the related central processes. In our previous theoretical study (Kostyukov and Tomiak, 2018), we classified two types of the force synergy in accordance with simultaneous excitation of the muscles belonging to different joints. The coinciding synergy relates to the similar modalities of the activated muscles at the joints (flexors and flexors; extensors and extensors), the opposing synergy matches combination of the different modalities (flexors and extensors; extensors and flexors).…”

“…It is likely that the simplest type of synergy can belong to the single-joint movements, in which it is possible to consider the synergic interactions between agonists and to evaluate the role of cocontractions of the antagonists (Gorkovenko et al, 2012). The two-joint movements (Tomiak et al, 2015, 2016; Kostyukov and Tomiak, 2018) constitute the next level of synergic interaction of the muscles during fulfillment of more complex movement tasks with arbitrary planar transitions of the end-points produced under the loading action of externally applied forces. The synergy effects in the above simplest types of arbitrary movements cannot be treated in terms of reduction in the number of degrees of freedom (Tresch and Jarc, 2009).…”

“…In both types of movements, the intensities of EMG activity in the shoulder and elbow muscles are correlated with the respective joint torques, consisting of the positive and negative components, each of which corresponds to the predominant activation of the flexor and extensor muscles, respectively. The methods allowing to evaluate the forces acting on the arm muscles and to define character of the muscle contractions (eccentric vs. concentric) along trajectories of the two-joint movements can be found in earlier studies by our group (Kostyukov, 2016; Lehedza et al, 2016; Lehedza, 2017; Gorkovenko, 2018; Kostyukov and Tomiak, 2018; Vereshchaka et al, 2018a). To distinguish various combinations of activity in muscles acting at different joints, we proposed extracting along the movement paths the segments of coinciding and opposing synergies, with active muscles of different joints belonging to the same (flexor and flexor, extensor and extensor) or opposite (flexor and extensor, extensor and flexor) functionalities, respectively (Tomiak et al, 2015, 2016; Kostyukov and Tomiak, 2018).…”