Separation of rotational and translational segmental momentum to assess movement coordination during walking

Abstract

This investigation presents an analysis of segmental angular momentum to describe segmental coordination during walking. Generating and arresting momentum is an intuitive concept, and also forms the foundation of Newton-Euler dynamics. Total segmental angular momentum is separated into separate components, translational angular momentum (TAM) and rotational angular momentum (RAM), which provide different but complementary perspectives of the segmental dynamics needed to achieve forward progression during walking. TAM was referenced to the stance foot, which provides insight into the mechanisms behind how forward progression is achieved through coordinated segmental motion relative to the foot. Translational and rotational segmental moments were calculated directly from TAM and RAM, via Euler’s 1st and 2nd laws in angular momentum form, respectively, and are composed of the effects of intersegmental forces and joint moments. Using data from 14 healthy participants, the effort required to generate and arrest momentum were assessed by linking the features of segmental angular momentum and the associated segmental moments to well-known spatiotemporal and kinetic features of the gait cycle. Segmental momentum provides an opportunity to explore and understand system-wide dynamics of coordination from an alternative perspective that is rooted in fundamentals of dynamics, and can be estimated using only segmental kinematic measurements.

Trunk kinetic effort during step ascent and descent in patients with transtibial amputation using angular momentum separation

“…The time derivative of trunk TAM is an expression of Euler’s 1 st Law in angular momentum form: $$\frac{{}^{I}d}{dt}\left({{}^I\mathrm{boldh}}_{\text{Trunk}/\text{Foot}}\right)={\mathrm{boldM}}_{\text{Trunk}/\text{Foot}}-\left({\mathrm{boldr}}_{\text{Trunk}/\text{Foot}}\times m_{\text{Trunk}}{{}^I\mathbf{a}}_{\text{Foot}}\right)$$ where r Trunk/Foot × m Trunk I a Foot is the corrective inertial moment of the trunk relative to the stance foot and is required to satisfy Euler’s laws when the foot accelerates during thetask. The translational trunk segmental moment about the foot, expressed as: $${\mathrm{boldM}}_{\text{Trunk}/\text{Foot}}={\mathrm{boldr}}_{\text{Trunk}/\text{Foot}}\times {\mathrm{boldF}}_{\text{Trunk}}^{\text{Ext}}$$ where ${\mathrm{boldF}}_{\text{Trunk}}^{\text{Ext}}$ is the net of all external forces applied to the trunk due to the force of gravity, intersegmental joint forces, and the forces applied to a segment due to muscle force actuators (Figure 1) (Gaffney et al, 2017). …”

“…M Trunk is the total trunk moment that is used to solve for the joint moments by adding the sum of the applied (external) proximal and distal moments and moments about the trunk COM due to intersegmental joint forces (Figure 1) (Gaffney et al, 2017). …”

“…Joint kinetics calculated from inverse dynamics are common clinical descriptors of joint demand or effort because they represent the total agonist and antagonist muscle activity spanning a joint (Carollo & Matthews, 2009). Therefore, a change in segmental translational or rotational moments represent a change in kinetic effort, in which the joint kinetics contribute (Gaffney et al, 2017)…”

Angular Moment and Corrective Forces in Human Walking Processes: Sensor and Actuator Analysis

“…This type of sensorization has been carried out on specific types of persons or through other types of sensors because such studies were focused on a specific problem [9]. In this paper, we studied a subject but, in order to extrapolate to anyone, we studied the dynamics [10,11]. In this case, it was about being able to extrapolate the obtained results to any person, since the moment of a force that a gyroscope generates is proportional to the generated force in an inflection.…”

Analytical model for computing translational and rotational angular momentum occurring in treadmill walking

“…A main direction in the human motion analysis is to describe the dynamic parameters associated to human gait. There are studies showing that dynamic parameters such as the reaction forces and moments were measured based on treadmill belts equipped with force sensors [8,[10][11][12][13][14] but only few are focused on computing dynamical parameters of the gait, starting from the kinematical measured parameters [9]. Some other authors applied nonlinear analysis to the flexion-extension movements of the human knee both on healthy and osteoarthritic individuals, observing the increasing of Largest Lyapunov Exponents for the OA patients with respect to healthy subjects [15,16].…”