Synergies reciprocally relate end-effector and joint-angles in rhythmic pointing movements

Abstract

During rhythmic pointing movements, degrees of freedom (DOF) in the human action system—such as joint-angles in the arm—are assumed to covary to stabilise end-effector movement, e.g. index finger. In this paper, it is suggested that the end-effector movement and the coordination of DOF are reciprocally related in synergies that link DOF so as to produce the end-effector movement. The coordination of DOF in synergies and the relation between end-effector movement and DOF coordination received little attention, though essential to understand the principles of synergy formation. Therefore, the current study assessed how the end-effector movement related to the coordination of joint-angles during rhythmic pointing across target widths and distances. Results demonstrated that joint-angles were linked in different synergies when end-effector movements differed across conditions. Furthermore, in every condition, three joint-angles (shoulder plane of elevation, shoulder inward-outward rotation, elbow flexion-extension) largely drove the end-effector, and all joint-angles contributed to covariation that stabilised the end-effector. Together, results demonstrated synergies that produced the end-effector movement, constrained joint-angles so that they covaried to stabilise the end-effector, and differed when end-effector movement differed. Hence, end-effector and joint-angles were reciprocally related in synergies—indicating that the action system was organised as a complex dynamical system.

Adjustments in end-effector trajectory and underlying joint angle synergies after a target switch: Order of adjustment is flexible

“…Using all the trials in one condition we computed the mean projection lengths over stationary target trials and their 95% CI in the UCM (i.e., the null-space of the Jacobian) and the space orthogonal to it (CI-PL ucm and CI-PL ort , respectively, cf. [36]). Note that the mean projection lengths were not zero because absolute values were taken when the projection lengths were computed.…”

“…Then these joint deviation vectors were projected onto the null-space of the Jacobian of the stationary target condition and onto its orthogonal complement, resulting in the measures PL ucm_switch and PL ort_switch for each switch condition separately (cf. [36]). Again all projection lengths were normalized by the square root of its number of DOF.…”

“…Self-organization implies that the macroscopic order emerges from the DOF, but at the same time the macroscopic order constraints these DOF, often referred to as circular causality [ 34 , 35 ]. This implies that for understanding properties of the synergy from this framework, the focus should not just be on the emergent synergy, but also on the involved DOF [ 36 ].…”

Robotic rehabilitation for end-effector device and botulinum toxin in upper limb rehabilitation in chronic post-stroke patients: an integrated rehabilitative approach

“…We can consider three main functional consequences of impairments on UL function after stroke: (1) learned nonuse, (2) learned bad use, and (3) forgetting use [6], where robotic rehabilitation with both the endeffector system (EE) and the exoskeleton (ES) can be effective in the recovery alone or in association with conventional therapy. For example, during rhythmic pointing movements of the UL and the hand, end-effector and joint angles are reciprocally related in synergies and the action system is organized as a complex dynamical system [7][8][9]; then, robotic training exercises could improve the fine and purposeful motor organization of the UL as in acute as in chronic phase after stroke. Moreover, recovery of the UL function recognizes a recovery time of over 1 year that is likely mediated by a complex combination of spontaneous and learning-dependent processes, including restitution, substitution, and compensation.…”

Task constraints act at the level of synergies and at the level of end-effector kinematics in manual reaching and manual lateral interception.

“…Clusters of joint angle configurations. The goal of the current analyses was to establish whether different tasks and different conditions were performed with different synergies (see also Valk, Mouton, Otten, & Bongers, 2019b). It is important to realize that the main variables in this analysis were the lengths of projection vectors, whereas in the UCM analysis the variances of these vectors were computed.…”