On representations for joint moments using a 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.

Continuous models for peristaltic locomotion with application to worms and soft robots.

A continuous model for the peristaltic locomotion of compressible and incompressible rod-like bodies is presented. Using Green and Naghdi's theory of a directed rod, incompressibility is enforced as an internal constraint. A discussion on muscle actuation models for a single continuum is included. The resulting theory is demonstrated in a simulation of a soft-robotic device. In addition, a calibration of parameters is performed and the incompressible rod is validated against a biomimetic model of earthworm locomotion.

Interclinician and intraclinician variability in the mechanics of the pivot shift test for posterolateral rotatory instability (PLRI) of the elbow.

HYPOTHESIS: Posterolateral rotatory instability (PLRI) of the elbow results from injury to the lateral collateral ligament complex from trauma or iatrogenic injury. The lateral pivot-shift test (PST) is standard for diagnosing PLRI, but its subjectivity affects diagnosis and makes it difficult to train young surgeons. A well-controlled investigation has not been done to quantify interclinician and intraclinician variability in PST mechanics in the intact and unstable elbow. The authors predict that there exist differences in PST mechanics between clinicians. MATERIALS AND METHODS: Five unpaired elbow specimens underwent PST intact and after sequential sectioning of lateral stabilizing ligaments. Multiple PST trials were performed on each specimen by 3 clinicians (1 expert, 2 in-training) while 3-dimensional motion and loads were recorded. Intraclinician and interclinician variability were analyzed. RESULTS: Mean supination torque, valgus torque, and axial force were 3.6 ± 1.9 Nm, 5.6 ± 3.1 Nm, and -8.3 ± 15.7 N, respectively. Mean radial head displacement was 13.7 ± 4.6 mm. There were no significant differences in these measures after sequential ligament sectioning. One surgeon (in-training 2) applied significantly greater axial compressive forces across the elbow joint (5-9 N difference). Variability of axial force (380% ± 473%) was greater than that of supination torque (20% ± 11%), valgus torque (14% ± 4%), and radial head displacement (8% ± 6%; P < .05 for analysis of variance). DISCUSSION: The clinicians performed the PST consistently and with comparable loads, with the exception of axial compressive force across the radiohumeral joint, which varied across clinicians by 1 to 2 pounds (5-9 N). CONCLUSION: This study suggests that the PST is a mechanically reproducible clinical examination, despite differing levels of training in performing the maneuver. With the exception of axial force, PST mechanics are highly repeatable for a given surgeon applying the test on a single specimen.

Mechanics-based model for the cooking-induced deformation of spaghetti.

In this article, we propose a minimal model for the cooking-induced deformation of spaghetti and related food products. Our approach has parallels to the use of rod theories for the mechanics of slender bodies undergoing growth and is inspired by a wealth of experimental data from the food science literature. We use our model to investigate the cooking of a single strand of spaghetti confined to a pot and reproduce a curious three-stage deformation sequence that arises in the cooking process.

On Planar Discrete Elastic Rod Models for the Locomotion of Soft Robots.

Modeling soft robots that move on surfaces is challenging from a variety of perspectives. A recent formulation by Bergou et al. of a rod theory that exploits new developments in discrete differential geometry offers an attractive, numerically efficient avenue to help overcome some of these challenges. Their formulation is an example of a discrete elastic rod theory. In this article, we consider a planar version of Bergou et al.'s theory and, with the help of recent works on Lagrange's equations of motion for constrained systems of particles, show how it can be used to model soft robots that are composed of segments of soft material folded and bonded together. We then use our formulation to examine the dynamics of a caterpillar-inspired soft robot that is actuated using shape memory alloys and exploits stick-slip friction to achieve locomotion. After developing and implementing procedures to prescribe the parameters for components of the soft robot, we compare our calibrated model to the experimental behavior of the caterpillar-inspired soft robot.

Verifying the equivalence of representations of the knee joint moment vector from a drop vertical jump task.

Biomechanics software programs, such as Visual3D, Nexus, Cortex, and OpenSim, have the capability of generating several distinct component representations for joint moments and forces from motion capture data. These representations include those for orthonormal proximal and distal coordinate systems and a non-orthogonal joint coordinate system. In this article, a method is presented to address the challenging problem of evaluating and verifying the equivalence of these representations. The method accommodates the difficulty that there are two possible sets of non-orthogonal basis vectors that can be used to express a vector in the joint coordinate system and is illuminated using motion capture data from a drop vertical jump task.

The roles of impact and inertia in the failure of a shoelace knot.

The accidental untying of a shoelace while walking often occurs without warning. In this paper, we discuss the series of events that lead to a shoelace knot becoming untied. First, the repeated impact of the shoe on the floor during walking serves to loosen the knot. Then, the whipping motions of the free ends of the laces caused by the leg swing produce slipping of the laces. This leads to eventual runaway untangling of the knot. As demonstrated using slow-motion video footage and a series of experiments, the failure of the knot happens in a matter of seconds, often without warning, and is catastrophic. The controlled experiments showed that increasing inertial effects of the swinging laces leads to increased rate of knot untying, that the directions of the impact and swing influence the rate of failure, and that the knot structure has a profound influence on a knot's tendency to untie under cyclic impact loading.

Dynamical analysis and development of a biologically inspired SMA caterpillar robot.

With the goal of robustly designing and fabricating a soft robot based on a caterpillar featuring shape memory alloy (SMA) actuators, analytical and numerical models for a soft robot were created based on the forward crawling motion of the Manduca sexta caterpillar. The analytical model features a rod theory and the mechanics of undulation were analyzed using a motion pattern based on the 'Witch of Agnesi' curve. Complementing these models, experiments on a SMA actuator sample were performed in order to determine its flexural rigidity and curvature as a function of the actuation voltage. A series of these actuators can be modeled as a system of rigid bodies connected by torsional springs. As these bodies are actuated according to the motion pattern based on the individual caterpillar segments, ground contact forces are calculated and analyzed to determine the requirements of successful forward locomotion. The energetics of the analytical and numerical models are then compared and discussed.

A Kinect-based movement assessment system: marker position comparison to Vicon.

Accurate movement analysis systems are prohibitive in cost and size to be accessible to the general population, while commercially available, affordable systems lack the accuracy needed for clinical relevance. To address these limitations, we developed a Depth Camera Movement Assessment System (DCMAS) featuring an affordable, widely available depth camera (e.g. Microsoft Kinect). After examining 3D position data for markers adhered to participants and a flat surface, captured with both DCMAS and the industry standard Vicon system, we demonstrated DCMAS obtained measurements comparable, within soft tissue artifact, to the Vicon system, paving the way for a breakthrough technology in preventative medicine.

A musculoskeletal model for the lumbar spine.

A new musculoskeletal model for the lumbar spine is described in this paper. This model features a rigid pelvis and sacrum, the five lumbar vertebrae, and a rigid torso consisting of a lumped thoracic spine and ribcage. The motion of the individual lumbar vertebrae was defined as a fraction of the net lumbar movement about the three rotational degrees of freedom: flexion-extension lateral bending, and axial rotation. Additionally, the eight main muscle groups of the lumbar spine were incorporated using 238 muscle fascicles with prescriptions for the parameters in the Hill-type muscle models obtained with the help of an extensive literature survey. The features of the model include the abilities to predict joint reactions, muscle forces, and muscle activation patterns. To illustrate the capabilities of the model and validate its physiological similarity, the model's predictions for the moment arms of the muscles are shown for a range of flexion-extension motions of the lower back. The model uses the OpenSim platform and is freely available on https://www.simtk.org/home/lumbarspine to other spinal researchers interested in analyzing the kinematics of the spine. The model can also be integrated with existing OpenSim models to build more comprehensive models of the human body.

On the stiffness matrix of the intervertebral joint: application to total disk replacement.

The traditional method of establishing the stiffness matrix associated with an intervertebral joint is valid only for infinitesimal rotations, whereas the rotations featured in spinal motion are often finite. In the present paper, a new formulation of this stiffness matrix is presented, which is valid for finite rotations. This formulation uses Euler angles to parametrize the rotation, an associated basis, which is known as the dual Euler basis, to describe the moments, and it enables a characterization of the nonconservative nature of the joint caused by energy loss in the poroviscoelastic disk and ligamentous support structure. As an application of the formulation, the stiffness matrix of a motion segment is experimentally determined for the case of an intact intervertebral disk and compared with the matrices associated with the same segment after the insertion of a total disk replacement system. In this manner, the matrix is used to quantify the changes in the intervertebral kinetics associated with total disk replacements. As a result, this paper presents the first such characterization of the kinetics of a total disk replacement.

Curve encirclement and protein structure.

A method of measuring the extent to which space curves encircle one another is introduced. The method provides a family of sets which characterize encircling curves, allowing curve pairs that engage (and also single curves that self-engage) to be distinguished. The method is applied to the backbone chains of protein molecules.