Expression of Joint Moment in the Joint Coordinate System

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Guillaume Desroches ◽  
Laurence Chèze ◽  
Raphaël Dumas
Keyword(s):  
Coordinate System ◽  
Orthogonal Projection ◽  
Mechanical Action ◽  
Joint Moment ◽  
Joint Moments ◽  
Orthogonal Projections ◽  
Motor Torque ◽  
Moment Vector ◽  
Nonorthogonal Projections ◽  
Joint Coordinate System

The question of using the nonorthogonal joint coordinate system (JCS) to report joint moments has risen in the literature. However, the expression of joint moments in a nonorthogonal system is still confusing. The purpose of this paper is to present a method to express any 3D vector in a nonorthogonal coordinate system. The interpretation of these expressions in the JCS is clarified and an example for the 3D joint moment vector at the shoulder and the knee is given. A nonorthogonal projection method is proposed based on the mixed product. These nonorthogonal projections represent, for a 3D joint moment vector, the net mechanical action on the JCS axes. Considering the net mechanical action on each axis seems important in order to assess joint resistance in the JCS. The orthogonal projections of the same 3D joint moment vector on the JCS axes can be characterized as “motor torque.” However, this interpretation is dependent on the chosen kinematic model. The nonorthogonal and orthogonal projections of shoulder joint moment during wheelchair propulsion and knee joint moment during walking were compared using root mean squares (rmss). rmss showed differences ranging from 6 N m to 22.3 N m between both projections at the shoulder, while differences ranged from 0.8 N m to 3.0 N m at the knee. Generally, orthogonal projections were of lower amplitudes than nonorthogonal projections at both joints. The orthogonal projection on the proximal or distal coordinates systems represents the net mechanical actions on each axis, which is not the case for the orthogonal projection (i.e., motor torque) on JCS axes. In order to represent the net action at the joint in a JCS, the nonorthogonal projection should be used.

scholarly journals On Representations for Joint Moments Using a Joint Coordinate System

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Oliver M. O'Reilly ◽  
Mark P. Sena ◽  
Brian T. Feeley ◽  
Jeffrey C. Lotz
Keyword(s):  
Knee Joint ◽  
Coordinate System ◽  
Three Dimensional ◽  
Human Knee ◽  
Human Knee Joint ◽  
Six Dof ◽  
Clinical Description ◽  
Definition Of ◽  
Nonorthogonal Projections ◽  
Joint Coordinate System

In studies of the biomechanics of joints, the representation of moments using the joint coordinate system has been discussed by several authors. The primary purpose of this technical brief is to emphasize that there are two distinct, albeit related, representations for moment vectors using the joint coordinate system. These distinct representations are illuminated by exploring connections between the Euler and dual Euler bases, the “nonorthogonal projections” presented in a recent paper by Desroches et al. (2010, “Expression of Joint Moment in the Joint Coordinate System,” ASME J. Biomech. Eng., 132(11), p. 11450) and seminal works by Grood and Suntay (Grood and Suntay, 1983, “A Joint Coordinate System for the Clinical Description of Three-Dimensional Motions: Application to the Knee,” ASME J. Biomech. Eng., 105(2), pp. 136–144) and Fujie et al. (1996, “Forces and Moment in Six-DOF at the Human Knee Joint: Mathematical Description for Control,” Journal of Biomechanics, 29(12), pp. 1577–1585) on the knee joint. It is also shown how the representation using the dual Euler basis leads to straightforward definition of joint stiffnesses.

Using Reinforcement Learning to Estimate Human Joint Moments via EMG Signals or Joint Kinematics: An Alternative Solution to Musculoskeletal-Based Biomechanics

2020 ◽  
Author(s):  
Wen Wu ◽  
Kate Saul ◽  
He (Helen) Huang
Keyword(s):  
Reinforcement Learning ◽  
Correlation Coefficients ◽  
Metacarpophalangeal Joint ◽  
Joint Moment ◽  
Biomechanical Analysis ◽  
Model Parameters ◽  
Optimization Approach ◽  
Joint Moments ◽  
Moment Estimation ◽  
Policy Optimization

Abstract Reinforcement learning (RL) has potential to provide innovative solutions to existing challenges in estimating joint moments in motion analysis, such as kinematic or electromyography (EMG) noise and unknown model parameters. Here we explore feasibility of RL to assist joint moment estimation for biomechanical applications. Forearm and hand kinematics and forearm EMGs from 4 muscles during free finger and wrist movement were collected from six healthy subjects. Using the Proximal Policy Optimization approach, we trained and tested two types of RL agents that estimated joint moment based on measured kinematics or measured EMGs, respectively. To quantify the performance of RL agents, the estimated joint moment was used to drive a forward dynamic model for estimating kinematics, which were then compared with measured kinematics. The results demonstrated that both RL agents can accurately reproduce wrist and metacarpophalangeal joint motion. The correlation coefficients between estimated and measured kinematics, derived from the kinematics-driven agent and subject-specific EMG-driven agents, were 0.98±0.01 and 0.94±0.03 for the wrist, respectively, and were 0.95±0.02 and 0.84±0.06 for the metacarpophalangeal joint, respectively. In addition, a biomechanically reasonable joint moment-angle-EMG relationship (i.e. dependence of joint moment on joint angle and EMG) was predicted using only 15 seconds of collected data. In conclusion, this study serves as a proof of concept that an RL approach can assist in biomechanical analysis and human-machine interface applications by deriving joint moments from kinematic or EMG data.

scholarly journals Marstrand-type Theorems for the Counting and Mass Dimensions in ℤ

2016 ◽  
Vol 25 (5) ◽  
pp. 700-743 ◽  
Author(s):  
DANIEL GLASSCOCK
Keyword(s):  
Recent Work ◽  
Orthogonal Projection ◽  
Side Length ◽  
Orthogonal Projections ◽  
Mass Dimension ◽  
Image Position ◽  
Almost All

The counting and (upper) mass dimensions of a set A ⊆ $\mathbb{R}^d$ are $$D(A) = \limsup_{\|C\| \to \infty} \frac{\log | \lfloor A \rfloor \cap C |}{\log \|C\|}, \quad \smash{\overline{D}}\vphantom{D}(A) = \limsup_{\ell \to \infty} \frac{\log | \lfloor A \rfloor \cap [-\ell,\ell)^d |}{\log (2 \ell)},$$ where ⌊A⌋ denotes the set of elements of A rounded down in each coordinate and where the limit supremum in the counting dimension is taken over cubes C ⊆ $\mathbb{R}^d$ with side length ‖C‖ → ∞. We give a characterization of the counting dimension via coverings: $$D(A) = \text{inf} \{ \alpha \geq 0 \mid {d_{H}^{\alpha}}(A) = 0 \},$$ where $${d_{H}^{\alpha}}(A) = \lim_{r \rightarrow 0} \limsup_{\|C\| \rightarrow \infty} \inf \biggl\{ \sum_i \biggl(\frac{\|C_i\|}{\|C\|} \biggr)^\alpha \ \bigg| \ 1 \leq \|C_i\| \leq r \|C\| \biggr\}$$ in which the infimum is taken over cubic coverings {Ci} of A ∩ C. Then we prove Marstrand-type theorems for both dimensions. For example, almost all images of A ⊆ $\mathbb{R}^d$ under orthogonal projections with range of dimension k have counting dimension at least min(k, D(A)); if we assume D(A) = D(A), then the mass dimension of A under the typical orthogonal projection is equal to min(k, D(A)). This work extends recent work of Y. Lima and C. G. Moreira.

Interpretation of Ankle Joint Moments during the Stance Phase of Walking: A Comparison of Two Orthogonal Axes Systems

2001 ◽  
Vol 17 (2) ◽  
pp. 173-180 ◽  
Author(s):  
Adrienne E. Hunt ◽  
Richard M. Smith
Keyword(s):  
Coordinate System ◽  
Ankle Joint ◽  
Stance Phase ◽  
Reaction Force ◽  
Frontal Plane ◽  
Transverse Plane ◽  
The Body ◽  
Global Coordinate System ◽  
Coordinate Systems ◽  
Joint Moments

Three-dimensional ankle joint moments were calculated in two separate coordinate systems, from 18 healthy men during the stance phase of walking, and were then compared. The objective was to determine the extent of differences in the calculated moments between these two commonly used systems and their impact on interpretation. Video motion data were obtained using skin surface markers, and ground reaction force data were recorded from a force platform. Moments acting on the foot were calculated about three orthogonal axes, in a global coordinate system (GCS) and also in a segmental coordinate system (SCS). No differences were found for the sagittal moments. However, compared to the SCS, the GCS significantly (p < .001) overestimated the predominant invertor moment at midstance and until after heel rise. It also significantly (p < .05) underestimated the late stance evertor moment. This frontal plane discrepancy was attributed to sensitivity of the GCS to the degree of abduction of the foot. For the transverse plane, the abductor moment peaked earlier (p < .01) and was relatively smaller (p < .01) in the GCS. Variability in the transverse plane was greater for the SCS, and attributed to its sensitivity to the degree of rearfoot inversion. We conclude that the two coordinate systems result in different calculations of nonsagittal moments at the ankle joint during walking. We propose that the body-based SCS provides a more meaningful interpretation of function than the GCS and would be the preferred method in clinical research, for example where there is marked abduction of the foot.

scholarly journals The effect of stride length on lower extremity joint kinetics at various gait speeds

2018 ◽  
Author(s):  
Robert L. McGrath ◽  
Melissa L. Ziegler ◽  
Margaret Pires-Fernandes ◽  
Brian A. Knarr ◽  
Jill S. Higginson ◽  
...  
Keyword(s):  
Lower Extremity ◽  
Gait Speed ◽  
Stride Length ◽  
Inverse Dynamics ◽  
Sagittal Plane ◽  
Gait Training ◽  
Joint Moment ◽  
Joint Moments ◽  
Joint Kinetics ◽  
Trailing Limb Angle

AbstractRobot-assisted training is a promising tool under development for improving walking function based on repetitive goal-oriented task practice. The challenges in developing the controllers for gait training devices that promote desired changes in gait is complicated by the limited understanding of the human response to robotic input. A possible method of controller formulation can be based on the principle of bio-inspiration, where a robot is controlled to apply the change in joint moment applied by human subjects when they achieve a gait feature of interest. However, it is currently unclear how lower extremity joint moments are modulated by even basic gaitspatio-temporal parameters.In this study, we investigated how sagittal plane joint moments are affected by a factorial modulation of two important gait parameters: gait speed and stride length. We present the findings obtained from 20 healthy control subjects walking at various treadmill-imposed speeds and instructed to modulate stride length utilizing real-time visual feedback. Implementing a continuum analysis of inverse-dynamics derived joint moment profiles, we extracted the effects of gait speed and stride length on joint moment throughout the gait cycle. Moreover, we utilized a torque pulse approximation analysis to determine the timing and amplitude of torque pulses that approximate the difference in joint moment profiles between stride length conditions, at all gait speed conditions.Our results show that gait speed has a significant effect on the moment profiles in all joints considered, while stride length has more localized effects, with the main effect observed on the knee moment during stance, and smaller effects observed for the hip joint moment during swing and ankle moment during the loading response. Moreover, our study demonstrated that trailing limb angle, a parameter of interest in programs targeting propulsion at push-off, was significantly correlated with stride length. As such, our study has generated assistance strategies based on pulses of torque suitable for implementation via a wearable exoskeleton with the objective of modulating stride length, and other correlated variables such as trailing limb angle.

ISB recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motion—part I: ankle, hip, and spine

2002 ◽  
Vol 35 (4) ◽  
pp. 543-548 ◽  
Author(s):  
Ge Wu ◽  
Sorin Siegler ◽  
Paul Allard ◽  
Chris Kirtley ◽  
Alberto Leardini ◽  
...  
Keyword(s):  
Coordinate System ◽  
Joint Motion ◽  
Joint Coordinate System ◽  
Human Joint
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