Background: The ability to measure joint kinematics in natural environments over long durations using inertial measurement units (IMUs) could enable at-home monitoring and personalized treatment of neurological and musculoskeletal disorders. However, drift, or the accumulation of error over time, inhibits the accurate measurement of movement over long durations. We sought to develop an open-source workflow to estimate lower extremity joint kinematics from IMU data that was accurate and capable of assessing and mitigating drift. Methods: We computed IMU-based estimates of kinematics using sensor fusion and an inverse kinematics approach with a constrained biomechanical model. We measured kinematics for 11 subjects as they performed two 10-min trials: walking and a repeated sequence of varied lower-extremity movements. To validate the approach, we compared the joint angles computed with IMU orientations to the joint angles computed from optical motion capture using root mean square (RMS) difference and Pearson correlations, and estimated drift using a linear regression on each subject’s RMS differences over time. Results: IMU-based kinematic estimates agreed with optical motion capture; median RMS differences over all subjects and all minutes were between 3 and 6 degrees for all joint angles except hip rotation and correlation coefficients were moderate to strong (r = 0.60–0.87). We observed minimal drift in the RMS differences over 10 min; the average slopes of the linear fits to these data were near zero (− 0.14–0.17 deg/min). Conclusions: Our workflow produced joint kinematics consistent with those estimated by optical motion capture, and could mitigate kinematic drift even in the trials of continuous walking without rest, which may obviate the need for explicit sensor recalibration (e.g. sitting or standing still for a few seconds or zero-velocity updates) used in current drift-mitigation approaches when studying similar activities. This could enable long-duration measurements, bringing the field one step closer to estimating kinematics in natural environments.

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Humans typically coordinate their muscles to meet movement objectives like minimizing energy expenditure. In the presence of pathology, new objectives gain importance, like reducing loading in an osteoarthritic joint, but people often do not change their muscle coordination patterns to meet these new objectives. Here we use musculoskeletal simulations to identify simple changes in coordination that can be taught using electromyographic biofeedback, achieving the therapeutic goal of reducing joint loading. Our simulations predicted that changing the relative activation of two redundant ankle plantarflexor muscles-the gastrocnemius and soleus-could reduce knee contact force during walking, but it was unclear whether humans could re-coordinate redundant muscles during a complex task like walking. Our experiments showed that after a single session of walking with biofeedback of summary measures of plantarflexor muscle activation, healthy individuals reduced the ratio of gastrocnemius-to-soleus muscle activation by 25 ± 15% (p = 0.004, paired t test, n = 10). Participants who walked with this "gastrocnemius avoidance" gait pattern reduced late-stance knee contact force by 12 ± 12% (p = 0.029, paired t test, n = 8). Simulation-informed coordination retraining could be a promising treatment for knee osteoarthritis and a powerful tool for optimizing coordination for a variety of rehabilitation and performance applications.

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Accurate computation of joint angles from optical marker data using inverse kinematics methods requires that the locations of markers on a model match the locations of experimental markers on participants. Marker registration is the process of positioning the model markers so that they match the locations of the experimental markers. Markers are typically registered using a graphical user interface (GUI), but this method is subjective and may introduce errors and uncertainty to the calculated joint angles and moments. In this investigation, we use OpenSim to isolate and quantify marker registration–based error from other sources of error by analyzing the gait of a bipedal humanoid robot for which segment geometry, mass properties, and joint angles are known. We then propose a marker registration method that is informed by the orientation of anatomical reference frames derived from surface-mounted optical markers as an alternative to user registration using a GUI. The proposed orientation registration method reduced the average root-mean-square error in both joint angles and joint moments by 67% compared to the user registration method, and eliminated variability among users. Our results show that a systematic method for marker registration that reduces subjective user input can make marker registration more accurate and repeatable.

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Musculoskeletal models enable movement scientists to examine muscle function by computing the mechanical work done by muscles during motor tasks. To estimate muscle work accurately requires a model that is physiologically plausible. Previous models of the human shoulder have coupled scapula movement to humeral movement. While coupled movement produces a stereotypical scapulohumeral rhythm, it cannot model shrugging or independent movement of the scapula and humerus. The artificial coupling of humeral elevation to scapular rotation permits muscles that cross the glenohumeral joint, such as the rotator-cuff muscles and deltoids, to do implausible work to elevate and rotate the scapula. In reality, the motion of the scapula is controlled by thoracoscapular muscles, yet the roles of these muscles in shoulder function remains unclear. To elucidate the roles of the thoracoscapular muscles, we developed a shoulder model with an accurate scapulothoracic joint and includes scapular muscles to drive its motion. We used the model to compute the work done by the thoracoscapular muscles during shrugging and arm elevation. We found that the bulk of the work done in upper-extremity tasks is performed by the largest muscles of the shoulder: Trapezius, deltoids, pectoralis major, and serratus-anterior. Trapezius and serratus anterior prove to be important synergists in performing upward-rotation of the scapula. We show that the large thoracoscapular muscles do more work than glenohumeral muscles during arm-elevation tasks. The model, experimental data and simulation results are freely available on SimTK.org to enable anyone to explore our results and to perform further studies in OpenSim 4.0.

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Deficits in the ankle plantarflexor muscles, such as weakness and contracture, occur commonly in conditions such as cerebral palsy, stroke, muscular dystrophy, Charcot-Marie-Tooth disease, and sarcopenia. While these deficits likely contribute to observed gait pathologies, determining cause-effect relationships is difficult due to the often co-occurring biomechanical and neural deficits. To elucidate the effects of weakness and contracture, we systematically introduced isolated deficits into a musculoskeletal model and generated simulations of walking to predict gait adaptations due to these deficits. We trained a planar model containing 9 degrees of freedom and 18 musculotendon actuators to walk using a custom optimization framework through which we imposed simple objectives, such as minimizing cost of transport while avoiding falling and injury, and maintaining head stability. We first generated gaits at prescribed speeds between 0.50 m/s and 2.00 m/s that reproduced experimentally observed kinematic, kinetic, and metabolic trends for walking. We then generated a gait at self-selected walking speed; quantitative comparisons between our simulation and experimental data for joint angles, joint moments, and ground reaction forces showed root-mean-squared errors of less than 1.6 standard deviations and normalized cross-correlations above 0.8 except for knee joint moment trajectories. Finally, we applied mild, moderate, and severe levels of muscle weakness or contracture to either the soleus (SOL) or gastrocnemius (GAS) or both of these major plantarflexors (PF) and retrained the model to walk at a self-selected speed. The model was robust to all deficits, finding a stable gait in all cases. Severe PF weakness caused the model to adopt a slower, "heel-walking" gait. Severe contracture of only SOL or both PF yielded similar results: the model adopted a "toe-walking" gait with excessive hip and knee flexion during stance. These results highlight how plantarflexor weakness and contracture may contribute to observed gait patterns.@en

Movement is fundamental to human and animal life, emerging through interaction of complex neural, muscular, and skeletal systems. Study of movement draws from and contributes to diverse fields, including biology, neuroscience, mechanics, and robotics. OpenSim unites methods from these fields to create fast and accurate simulations of movement, enabling two fundamental tasks. First, the software can calculate variables that are difficult to measure experimentally, such as the forces generated by muscles and the stretch and recoil of tendons during movement. Second, OpenSim can predict novel movements from models of motor control, such as kinematic adaptations of human gait during loaded or inclined walking. Changes in musculoskeletal dynamics following surgery or due to human–device interaction can also be simulated; these simulations have played a vital role in several applications, including the design of implantable mechanical devices to improve human grasping in individuals with paralysis. OpenSim is an extensible and user-friendly software package built on decades of knowledge about computational modeling and simulation of biomechanical systems. OpenSim’s design enables computational scientists to create new state-of-the-art software tools and empowers others to use these tools in research and clinical applications. OpenSim supports a large and growing community of biomechanics and rehabilitation researchers, facilitating exchange of models and simulations for reproducing and extending discoveries. Examples, tutorials, documentation, and an active user forum support this community. The OpenSim software is covered by the Apache License 2.0, which permits its use for any purpose including both nonprofit and commercial applications. The source code is freely and anonymously accessible on GitHub, where the community is welcomed to make contributions. Platform-specific installers of OpenSim include a GUI and are available on simtk.org.

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Predictive simulations of human walking have great potential to expand our understanding of locomotion. For instance, they can isolate the effect of specific impairments on observed gait pathologies or aid in designing assistive devices by modeling human-device interactions. Introducing simulated impairments or adding augmentation devices to a model may change kinematics, including preferred walking speed. Experimental studies have characterized cost of transport over a wide range of walking speeds, and have shown that humans prefer walking at a speed that minimizes their cost of transport [1]. The purpose of this study was to use a predictive simulation framework to reproduce experimental energetic cost of transport. We trained a model to walk at speeds between 0.5 and 2.0 m/s and compared our simulated cost of transport to experimental data.@en

Tools have been used for millions of years to augment the capabilities of the human body, allowing us to accomplish tasks that would otherwise be difficult or impossible. Powered exoskeletons and other assistive devices are sophisticated modern tools that have restored bipedal locomotion in individuals with paraplegia and have endowed unimpaired individuals with superhuman strength. Despite these successes, designing assistive devices that reduce energy consumption during running remains a substantial challenge, in part because these devices disrupt the dynamics of a complex, finely tuned biological system. Furthermore, designers have hitherto relied primarily on experiments, which cannot report muscle-level energy consumption and are fraught with practical challenges. In this study, we use OpenSim to generate muscle-driven simulations of 10 human subjects running at 2 and 5 m/s. We then add ideal, massless assistive devices to our simulations and examine the predicted changes in muscle recruitment patterns and metabolic power consumption. Our simulations suggest that an assistive device should not necessarily apply the net joint moment generated by muscles during unassisted running, and an assistive device can reduce the activity of muscles that do not cross the assisted joint. Our results corroborate and suggest biomechanical explanations for similar effects observed by experimentalists, and can be used to form hypotheses for future experimental studies. The models, simulations, and software used in this study are freely available at simtk.org and can provide insight into assistive device design that complements experimental approaches.

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Subject-specific musculoskeletal modeling can be applied to study musculoskeletal disorders, allowing inclusion of personalized anatomy and properties. Independent of the tools used for model creation, there are unavoidable uncertainties associated with parameter identification, whose effect on model predictions is still not fully understood. The aim of the present study was to analyze the sensitivity of subject-specific model predictions (i.e., joint angles, joint moments, muscle and joint contact forces) during walking to the uncertainties in the identification of body landmark positions, maximum muscle tension and musculotendon geometry. To this aim, we created an MRI-based musculoskeletal model of the lower limbs, defined as a 7-segment, 10-degree-of-freedom articulated linkage, actuated by 84 musculotendon units. We then performed a Monte-Carlo probabilistic analysis perturbing model parameters according to their uncertainty, and solving a typical inverse dynamics and static optimization problem using 500 models that included the different sets of perturbed variable values. Model creation and gait simulations were performed by using freely available software that we developed to standardize the process of model creation, integrate with OpenSim and create probabilistic simulations of movement. The uncertainties in input variables had a moderate effect on model predictions, as muscle and joint contact forces showed maximum standard deviation of 0.3 times body-weight and maximum range of 2.1 times body-weight. In addition, the output variables significantly correlated with few input variables (up to 7 out of 312) across the gait cycle, including the geometry definition of larger muscles and the maximum muscle tension in limited gait portions. Although we found subject-specific models not markedly sensitive to parameter identification, researchers should be aware of the model precision in relation to the intended application. In fact, force predictions could be affected by an uncertainty in the same order of magnitude of its value, although this condition has low probability to occur.@en

Muscle-driven simulations of human and animal motion are widely used to complement physical experiments for studying movement dynamics. Musculotendon models are an essential component of muscle-driven simulations, yet neither the computational speed nor the biological accuracy of the simulated forces has been adequately evaluated. Here we compare the speed and accuracy of three musculotendon models: two with an elastic tendon (an equilibrium model and a damped equilibrium model) and one with a rigid tendon. Our simulation benchmarks demonstrate that the equilibrium and damped equilibrium models produce similar force profiles but have different computational speeds. At low activation, the damped equilibrium model is 29 times faster than the equilibrium model when using an explicit integrator and 3 times faster when using an implicit integrator; at high activation, the two models have similar simulation speeds. In the special case of simulating a muscle with a short tendon, the rigid-tendon model produces forces that match those generated by the elastic-tendon models, but simulates 2-54 times faster when an explicit integrator is used and 6-31 times faster when an implicit integrator is used. The equilibrium, damped equilibrium, and rigid-tendon models reproduce forces generated by maximally-activated biological muscle with mean absolute errors less than 8.9%, 8.9%, and 20.9% of the maximum isometric muscle force, respectively. When compared to forces generated by submaximally-activated biological muscle, the forces produced by the equilibrium, damped equilibrium, and rigid-tendon models have mean absolute errors less than 16.2%, 16.4%, and 18.5%, respectively. To encourage further development of musculotendon models, we provide implementations of each of these models in OpenSim version 3.1 and benchmark data online, enabling others to reproduce our results and test their models of musculotendon dynamics.

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The lengths and velocities of muscle fibers have a dramatic effect on muscle force generation. It is unknown, however, whether the lengths and velocities of lower limb muscle fibers substantially affect the ability of muscles to generate force during walking and running. We examined this issue by developing simulations of muscle-tendon dynamics to calculate the lengths and velocities of muscle fibers from electromyographic recordings of 11 lower limb muscles and kinematic measurements of the hip, knee and ankle made as five subjects walked at speeds of 1.0-1.75?m?s-1 and ran at speeds of 2.0-5.0 m s^-1. We analyzed the simulated fiber lengths, fiber velocities and forces to evaluate the influence of force-length and force-velocity properties on force generation at different walking and running speeds. The simulations revealed that force generation ability (i.e. the force generated per unit of activation) of eight of the 11 muscles was significantly affected by walking or running speed. Soleus force generation ability decreased with increasing walking speed, but the transition from walking to running increased the force generation ability by reducing fiber velocities. Our results demonstrate the influence of soleus muscle architecture on the walk-to-run transition and the effects of muscle-tendon compliance on the plantarflexors' ability to generate ankle moment and power. The study presents data that permit lower limb muscles to be studied in unprecedented detail by relating muscle fiber dynamics and force generation to the mechanical demands of walking and running.

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The goals of this study were to determine if the muscle contributions to vertical and fore-aft acceleration of the mass center differ between crouch gait and unimpaired gait and if these muscle contributions change with crouch severity. Examining muscle contributions to mass center acceleration provides insight into the roles of individual muscles during gait and can provide guidance for treatment planning. We calculated vertical and fore-aft accelerations using musculoskeletal simulations of typically developing children and children with cerebral palsy and crouch gait. Analysis of these simulations revealed that during unimpaired gait the quadriceps produce large upward and backward accelerations during early stance, whereas the ankle plantarflexors produce large upward and forward accelerations later in stance. In contrast, during crouch gait, the quadriceps and ankle plantarflexors produce large, opposing fore-aft accelerations throughout stance. The quadriceps force required to accelerate the mass center upward was significantly larger in crouch gait than in unimpaired gait and increased with crouch severity. The gluteus medius accelerated the mass center upward during midstance in unimpaired gait; however, during crouch gait the upward acceleration produced by the gluteus medius was significantly reduced. During unimpaired gait the quadriceps and ankle plantarflexors accelerate the mass center at different times, efficiently modulating fore-aft accelerations. However, during crouch gait, the quadriceps and ankle plantarflexors produce fore-aft accelerations at the same time and the opposing fore-aft accelerations generated by these muscles contribute to the inefficiency of crouch gait.@en

Recent advances in computational technology have dramatically increased the use of muscle-driven simulation to study accelerations produced by muscles during gait. Accelerations computed from muscle-driven simulations are sensitive to the model used to represent contact between the foot and ground. A foot-ground contact model must be able to calculate ground reaction forces and moments that are consistent with experimentally measured ground reaction forces and moments. We show here that a rolling constraint can model foot-ground contact and reproduce measured ground reaction forces and moments in an induced acceleration analysis of muscle-driven simulations of walking, running, and crouch gait. We also illustrate that a point constraint and a weld constraint used to model foot-ground contact in previous studies produce inaccurate reaction moments and lead to contradictory interpretations of muscle function. To enable others to use and test these different constraint types (i.e., rolling, point, and weld constraints) we have included them as part of an induced acceleration analysis in OpenSim, a freely-available biomechanics simulation package.

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Impaired control of mediolateral body motion during walking is an important health concern. Developing treatments to improve mediolateral control is challenging, partly because the mechanisms by which muscles modulate mediolateral ground reaction force (and thereby modulate mediolateral acceleration of the body mass center) during unimpaired walking are poorly understood. To investigate this, we examined mediolateral ground reaction forces in eight unimpaired subjects walking at four speeds and determined the contributions of muscles, gravity, and velocity-related forces to the mediolateral ground reaction force by analyzing muscle-driven simulations of these subjects. During early stance (0-6% gait cycle), peak ground reaction force on the leading foot was directed laterally and increased significantly (p<0.05) with walking speed. During early single support (14-30% gait cycle), peak ground reaction force on the stance foot was directed medially and increased significantly (p<0.01) with speed. Muscles accounted for more than 92% of the mediolateral ground reaction force over all walking speeds, whereas gravity and velocity-related forces made relatively small contributions. Muscles coordinate mediolateral acceleration via an interplay between the medial ground reaction force contributed by the abductors and the lateral ground reaction forces contributed by the knee extensors, plantarflexors, and adductors. Our findings show how muscles that contribute to forward progression and body-weight support also modulate mediolateral acceleration of the body mass center while weight is transferred from one leg to another during double support.

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Multibody software designed for mechanical engineering has been successfully employed in biomedical research for many years. For real time operation some biomedical researchers have also adapted game physics engines. However, these tools were built for other purposes and do not fully address the needs of biomedical researchers using them to analyze the dynamics of biological structures and make clinically meaningful recommendations. We are addressing this problem through the development of an open source, extensible, high performance toolkit including a multibody mechanics library aimed at the needs of biomedical researchers. The resulting code, Simbody, supports research in a variety of fields including neuromuscular, prosthetic, and biomolecular simulation, and related research such as biologically-inspired design and control of humanoid robots and avatars. Simbody is the dynamics engine behind OpenSim, a widely used biomechanics simulation application. This article reviews issues that arise uniquely in biomedical research, and reports on the architecture, theory, and computational methods Simbody uses to address them. By addressing these needs explicitly Simbody provides a better match to the needs of researchers than can be obtained by adaptation of mechanical engineering or gaming codes. Simbody is a community resource, free for any purpose. We encourage wide adoption and invite contributions to the code base at https://simtk.org/home/simbody.

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Computer simulations are playing an increasingly important role in solving complex engineering problems, and have the potential to revolutionize experimentally-based medical decision making and treatment design. Experiments alone provide important but limited understanding of movement dynamics. Although we can measure some quantities, such as muscle activities and ground reaction forces, responsible for a movement, simulations complement these measurements with estimates of other important variables, such as muscle and joint forces. Simulations also allow us to establish cause-and-effect relationships giving insights into muscle function. Perhaps the most exciting feature of simulations is the potential to perform "what if" studies to test hypotheses, predict functional outcomes, and identify emergent behaviors. This paper highlights applications using OpenSim, including projects which: minimize measures of an unreasonable simulation; identify new movements as an athletic training tool to reduce injury risk, and establish relationships among posture, muscle forces, and ground reaction forces.@en

Movement science is driven by observation, but observation alone cannot elucidate principles of human and animal movement. Biomechanical modeling and computer simulation complement observations and inform experimental design. Biological models are complex and specialized software is required for building, validating, and studying them. Furthermore, common access is needed so that investigators can contribute models to a broader community and leverage past work. We are developing OpenSim, a freely available musculoskeletal modeling and simulation application and libraries specialized for these purposes, by providing: musculoskeletal modeling elements, such as biomechanical joints, muscle actuators, ligament forces, compliant contact, and controllers; and tools for fitting generic models to subject-specific data, performing inverse kinematics and forward dynamic simulations. OpenSim performs an array of physics-based analyses to delve into the behavior of musculoskeletal models by employing Simbody, an efficient and accurate multibody system dynamics code. Models are publicly available and are often reused for multiple investigations because they provide a rich set of behaviors that enables different lines of inquiry. This report will discuss one model developed to study walking and applied to gain deeper insights into muscle function in pathological gait and during running. We then illustrate how simulations can test fundamental hypotheses and focus the aims of in vivo experiments, with a postural stability platform and human model that provide a research environment for performing human posture experiments in silico. We encourage wide adoption of OpenSim for community exchange of biomechanical models and methods and welcome new contributors.

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Muscles actuate running by developing forces that propel the body forward while supporting the body's weight. To understand how muscles contribute to propulsion (i.e., forward acceleration of the mass center) and support (i.e., upward acceleration of the mass center) during running we developed a three-dimensional muscle-actuated simulation of the running gait cycle. The simulation is driven by 92 musculotendon actuators of the lower extremities and torso and includes the dynamics of arm motion. We analyzed the simulation to determine how each muscle contributed to the acceleration of the body mass center. During the early part of the stance phase, the quadriceps muscle group was the largest contributor to braking (i.e., backward acceleration of the mass center) and support. During the second half of the stance phase, the soleus and gastrocnemius muscles were the greatest contributors to propulsion and support. The arms did not contribute substantially to either propulsion or support, generating less than 1% of the peak mass center acceleration. However, the arms effectively counterbalanced the vertical angular momentum of the lower extremities. Our analysis reveals that the quadriceps and plantarflexors are the major contributors to acceleration of the body mass center during running.

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Pathological movement patterns like crouch gait are characterized by abnormal kinematics and muscle activations that alter how muscles support the body weight during walking. Individual muscles are often the target of interventions to improve crouch gait, yet the roles of individual muscles during crouch gait remain unknown. The goal of this study was to examine how muscles contribute to mass center accelerations and joint angular accelerations during single-limb stance in crouch gait, and compare these contributions to unimpaired gait. Subject-specific dynamic simulations were created for ten children who walked in a mild crouch gait and had no previous surgeries. The simulations were analyzed to determine the acceleration of the mass center and angular accelerations of the hip, knee, and ankle generated by individual muscles. The results of this analysis indicate that children walking in crouch gait have less passive skeletal support of body weight and utilize substantially higher muscle forces to walk than unimpaired individuals. Crouch gait relies on the same muscles as unimpaired gait to accelerate the mass center upward, including the soleus, vasti, gastrocnemius, gluteus medius, rectus femoris, and gluteus maximus. However, during crouch gait, these muscles are active throughout single-limb stance, in contrast to the modulation of muscle forces seen during single-limb stance in an unimpaired gait. Subjects walking in crouch gait rely more on proximal muscles, including the gluteus medius and hamstrings, to accelerate the mass center forward during single-limb stance than subjects with an unimpaired gait.@en

Biomechanical systems share many properties with mechanically engineered systems, and researchers have successfully employed mechanical engineering simulation software to investigate the mechanical behavior of diverse biological mechanisms, ranging from biomolecules to human joints. Unlike their man-made counterparts, however, biomechanisms rarely exhibit the simple, uncoupled, pureaxial motion that is engineered into mechanical joints such as sliders, pins, and ball-and-socket joints. Current mechanical modeling software based on internal-coordinate multibody dynamics can formulate engineered joints directly in minimal coordinates, but requires additional coordinates restricted by constraints to model more complex motions. This approach can be inefficient, inaccurate, and difficult for biomechanists to customize. Since complex motion is the rule rather than the exception in biomechanisms, the benefits of minimal coordinate modeling are not fully realized in biomedical research. Here we introduce a practical implementation for empirically-defined internal-coordinate joints, which we call "mobilizers." A mobilizer encapsulates the observations, measurement frame, and modeling requirements into a hinge specification of the permissible-motion manifold for a minimal set of internal coordinates. Mobilizers support nonlinear mappings that are mathematically equivalent to constraint manifolds but have the advantages of fewer coordinates, no constraints, and exact representation of the biomechanical motion-space - the benefits long enjoyed for internal-coordinate models of mechanical joints. Hinge matrices within the mobilizer are easily specified by user-supplied functions, and provide a direct means of mapping permissible motion derived from empirical data. We present computational results showing substantial performance and accuracy gains for mobilizers versus equivalent joints implemented with constraints. Examples of mobilizers for joints from human biomechanics and molecular dynamics are given. All methods and examples were implemented in Simbody™ - an open source multibody-dynamics solver available at https://Simtk.org.@en