Inverse Dynamics Optimization Research Articles

Human-Exoskeleton Coupling Simulation for Lifting Tasks with Shoulder, Spine, and Knee-Joint Powered Exoskeletons.

In this study, we introduce a two-dimensional (2D) human skeletal model coupled with knee, spine, and shoulder exoskeletons. The primary purpose of this model is to predict the optimal lifting motion and provide torque support from the exoskeleton through the utilization of inverse dynamics optimization. The kinematics and dynamics of the human model are expressed using the Denavit-Hartenberg (DH) representation. The lifting optimization formulation integrates the electromechanical dynamics of the DC motors in the exoskeletons of the knee, spine, and shoulder. The design variables for this study include human joint angle profiles and exoskeleton motor current profiles. The optimization objective is to minimize the squared normalized human joint torques, subject to physical and task-specific lifting constraints. We solve this optimization problem using the gradient-based optimizer SNOPT. Our results include a comparison of predicted human joint angle profiles, joint torque profiles, and ground reaction force (GRF) profiles between lifting tasks with and without exoskeleton assistance. We also explore various combinations of exoskeletons for the knee, spine, and shoulder. By resolving the lifting optimization problems, we designed the optimal torques for the exoskeletons located at the knee, spine, and shoulder. It was found that the support from the exoskeletons substantially lowers the torque levels in human joints. Additionally, we conducted experiments only on the knee exoskeleton. Experimental data indicated that using the knee exoskeleton decreases the muscle activation peaks by 35.00%, 10.03%, 22.12%, 30.14%, 16.77%, and 25.71% for muscles of the erector spinae, latissimus dorsi, vastus medialis, vastus lateralis, rectus femoris, and biceps femoris, respectively.

A Comparative Analysis of Optimal and Biomechanical Torque Control Strategies for Powered Knee Exoskeletons in Squat Lifting

Abstract Exoskeletons have the ability to aid humans in physically demanding and injury-prone activities, such as lifting loads while squatting. However, despite their immense potential, the control of powered exoskeletons remains a persistent challenge. In this study, we first predict the human lifting motion and knee joint torque using an inverse dynamics optimization formulation with a two-dimensional (2D) human skeletal model. The design variables are human joint angle profiles. The normalized human joint torque squared is minimized subject to physical and lifting task constraints. After that, the biomechanical assistive knee exoskeleton torque is obtained by scaling the predicted human knee joint torque. Second, we also present a 2D human skeletal model with a powered knee exoskeleton for predicting the optimal assistive torque and lifting motion. The design variables are human joint angle profiles and exoskeleton motor current profiles. Then, the biomechanical and optimal exoskeleton torques are implemented in a powered knee exoskeleton in real-time to provide external assistance in human lifting motion. Finally, the biomechanical and optimal assistive exoskeleton torque controls for lifting are compared. It is observed that both control methods have a significant impact on reducing muscle activations for the specific muscle groups compared to the cases without the exoskeleton. Especially, peak activations of erector spinae and rectus femoris muscles are reduced by 57.79% and 47.26% with biomechanical assistive torque. Likewise, vastus medialis and vastus lateralis activations drop by 46.82% and 52.24% with optimal assistive torque.

Subject specific optimal control of powered knee exoskeleton to assist human lifting tasks under controlled environment

AbstractWearable robots, sometimes known as exoskeletons, are incredible devices for improving human strength, reducing fatigue, and restoring impaired mobility. The control of powered exoskeletons, on the other hand, is still a challenge. This necessitates the development of a technique to simulate exoskeleton–wearer interaction. This study uses a two-dimensional human skeletal model with a powered knee exoskeleton to predict the optimal lifting motion and assistive torque. For lifting motion prediction, an inverse dynamics optimization formulation is utilized. In addition, the electromechanical dynamics of the exoskeleton DC motor are modeled in the lifting optimization formulation. The design variables are human joint angle profiles and exoskeleton motor current profiles. The human joint torque square is minimized subject to physical and lifting task constraints. Then, the lifting optimization problem is solved by the gradient-based sparse nonlinear optimizer (SNOPT). Furthermore, the optimal exoskeleton torque is implemented through a two-phase control strategy to provide optimal assistance in lifting. Experimental validations of the optimal control with 6 Nm and 16 Nm maximum assistive torque are presented. Both 6 Nm and 16 Nm maximum optimal assistance of the exoskeletons reduce the mean values of vastus lateralis, biceps femoris, and latissimus dorsi muscle activations compared to the lifting without the exoskeleton. However, the mean value of the vastus medialis activation is increased by a small amount for the exoskeleton case, although its peak value is reduced. Finally, the experimental results demonstrate that the proposed lifting optimization formulation and control strategy are promising for powered knee exoskeleton for lifting tasks.

Patellar Tendon Force Differs Depending on Jump-Landing Tasks and Estimation Methods

Patellar tendinopathy is a chronic overuse injury of the patellar tendon which is prevalent in jump-landing activities. Sports activities can require jumping not only with a vertical component but also in a forward direction. It is yet unknown how jumping in the forward direction may affect patellar tendon forces. The main purpose of this study was to compare PTF between landings preceded by a vertical jump and a forward jump in volleyball players. The second purpose was to compare two different estimation methods of the patellar tendon force. Fifteen male volleyball players performed vertical and forward jump-landing tasks at a controlled jump height, while kinetics and kinematics were recorded. Patellar tendon forces were calculated through two estimation methods based on inverse dynamic and static optimization procedures, using a musculoskeletal model. Results showed that forward jump-landing generated higher patellar tendon forces compared to vertical jump-landing for both estimation methods. Surprisingly, although the static optimization method considered muscle co-contraction, the inverse kinematic method provided statistically significant higher patellar tendon force values. These findings highlight that limiting the forward velocity component of the aerial phase appears to reduce the load on the patellar tendon during landing and may help to prevent patellar tendinopathy.

Musculoskeletal Load Analysis for the Design and Control of a Wearable Robot Bracing the Human Body While Crawling on a Floor

Wearable robots, such as exoskeletons, can potentially reduce the load at targeted muscles of the human body during fatiguing tasks. It is common, however, that use of a wearable robot causes increased load at untargeted muscles, leading to minimal net improvement. Here, musculoskeletal impacts of a wearable robotic device are examined to establish a foundation for the design and control of a robot based on a musculoskeletal model and experimental data. The model predicts the effect of the device, called Supernumerary Robotic Limbs (SuperLimbs), on the wearer’s whole body muscular effort. SuperLimbs brace the upper body of a human while they work near floor-level. Its effectiveness varies depending on how it is attached to the human (harness design), how it is coupled to the floor (wrist and hand design), and how it is controlled (actuation policy). These behaviors and their interplay are analyzed and used to inform the design and control of the robot. First, body movements are measured with a motion capture system while a human subject crawls on the floor. Their muscular activity and the floor reaction forces are then estimated based on a musculoskeletal model’s inverse dynamics optimization. The effect of the SuperLimbs is assessed by replacing both human arms in the model with robotic limbs. The analysis reveals that the human muscle load is minimized with a particular combination of SuperLimbs joint torques that can be used as feedforward commands to the SuperLimbs controller. Desirable harness and wrist properties are obtained by varying the parameters of the Human+Robot model, and tracking the effect of these changes on the distribution of muscles forces in the human’s back. It is found that a harness chest plate of the SuperLimbs attached at its anterior edge minimizes muscle activity in the back’s vulnerable lower lumbar region. The model is verified with ground reaction force experiments, and its validity is examined for every simulation experiment.

Single Task Optimization-Based Planar Box Delivery Motion Simulation and Experimental Validation

Abstract Box delivery is a complicated task and it is challenging to predict the box delivery motion associated with the box weight, delivering speed, and location. This paper presents a single task-based inverse dynamics optimization method for determining the planar symmetric optimal box delivery motion (multi-task jobs). The design variables are cubic B-spline control points of joint angle profiles. The objective function is dynamic effort, i.e., the time integral of the square of all normalized joint torques. The optimization problem includes various constraints. Joint angle profiles are validated through experimental results using root-mean-square-error (RMSE) and Pearson’s correlation coefficient. This research provides a practical guidance to prevent injury risks in joint torque space for workers who lift and deliver heavy objects in their daily jobs.

Two-Dimensional Versus Three-Dimensional Symmetric Lifting Motion Prediction Models: A Case Study

Abstract Symmetric lifting is a common manual material handling strategy in daily life and is the main cause of low back pain. In the literature, symmetric lifting is mainly simulated by using two-dimensional (2D) models because of their simplicity and low computational cost. In practice, however, symmetric lifting can generate asymmetric kinetics especially when the lifting weight is heavy and symmetric lifting based on 2D models misses this important asymmetric kinetics information. Therefore, three-dimensional (3D) models are necessary for symmetric lifting simulation to capture asymmetric kinetics. The purpose of this single-subject case study is to compare the optimization formulations and simulation results for symmetric lifting by using 2D and 3D human models and to identify their pros and cons. In this case study, a 10-degrees-of-freedom (DOFs) 2D skeletal model and a 40-DOFs 3D skeletal model are employed to predict the symmetric maximum weight lifting motion, respectively. The lifting problem is formulated as a multi-objective optimization (MOO) problem to minimize the dynamic effort and maximize the box weight. An inverse dynamic optimization approach is used to determine the optimal lifting motion and the maximum lifting weight considering dynamic joint strength. Lab experiments are carried out to validate the predicted motions. The predicted lifting motion, ground reaction forces (GRFs), and maximum box weight from the 2D and 3D human models for Subject #8 are compared with the experimental data. Recommendations are given.

Two-Dimensional Symmetric Box Delivery Motion Prediction and Validation: Subtask-Based Optimization Method

Box delivery is a complicated manual material handling task which needs to consider the box weight, delivering speed, stability, and location. This paper presents a subtask-based inverse dynamic optimization formulation for determining the two-dimensional (2D) symmetric optimal box delivery motion. For the subtask-based formulation, the delivery task is divided into five subtasks: lifting, the first transition step, carrying, the second transition step, and unloading. To render a complete delivering task, each subtask is formulated as a separate optimization problem with appropriate boundary conditions. For carrying and lifting subtasks, the cost function is the sum of joint torque squared. In contrast, for transition subtasks, the cost function is the combination of joint discomfort and joint torque squared. Joint angle profiles are validated through experimental results using Pearson’s correlation coefficient (r) and root-mean-square-error (RMSE). Results show that the subtask-based approach is computationally efficient for complex box delivery motion simulation. This research outcome provides a practical guidance to prevent injury risks in joint torque space for workers who deliver heavy objects in their daily jobs.

Investigation of lumbar spine biomechanics using global convergence optimization and constant loading path methods.

Computational models and inverse dynamic optimization methods are used to predict in-vivo spinal loading. Spinal force is conventionally predicted using the constant loading path method, which is based on the concept that the physiological directions of the spine loads follow the same path of the spinal curve. However, the global convergence optimization method, in which the instantaneous center of rotation of the joint should be also predicted, is necessary for accurate prediction of joint forces of the human body. In this study, we investigate the joint forces, instantaneous centers of rotation, and muscle forces of the human lumbar spine using both global convergence optimization method and constant loading path method during flexion, upright standing, and extension postures. The joint forces predicted using the constant loading path method were 130%, 234%, and 253% greater than those predicted using the global convergence optimization method for the three postures. The instantaneous centers of rotation predicted using the global convergence optimization method were segment level-dependent and moved anteriorly in the flexion and posteriorly in the extension, whereas those predicted using the constant loading path method moved posteriorly in both the flexion and extension. The data indicated that compared to the global convergence optimization method, the constant loading path method introduces additional constraints to the spinal joint model, and thus, it results in greater joint and muscle forces.

Learning inverse dynamics for human locomotion analysis

In this work, learning-based inverse dynamics algorithms are proposed for the analysis of human motion. Immeasurable joint torques and exterior contact forces are directly estimated from motions by machine learning techniques including deep neural networks, random forests and Ridge regression. A multistage subclass approach is introduced. The method recovers occluded motion data and generates meaningful features, as well as gait phase labels to restrict and facilitate the regression of forces and moments. In contrast to the state-of-the-art inverse dynamics optimization, the learning-based methods are independent of ground reaction force measurements and the global position and orientation of the human body. These properties make the application to reconstructed poses from videos or inertial measurements possible, creating fast and simple access to the underlying dynamics of recorded human motions. The performance of the proposed methods is evaluated on a self-recorded data set including walking and running motions and on a publicly available gait data set by Fukuchi et al. (PeerJ 6:e4640, 2018). Furthermore, the applicability to reconstructed gait sequences taken from the well-known CMU database (Human motion capture database, 2014. http://mocap.cs.cmu.edu/ ) is investigated. Finally, the method is tested as a tool to detect abnormal torque distributions in gait, based on a reconstructed 3D motion of a limping subject.

Design of the Cooperative Actuation in Hybrid Orthoses: A Theoretical Approach Based on Muscle Models.

Hybrid orthoses or rehabilitation exoskeletons have proven to be a powerful tool for subjects with gait disabilities due to their combined use of electromechanical actuation to provide motion and support, and functional electrical stimulation (FES) to contract muscle tissue so as to improve the rehabilitation process. In these devices, each degree of freedom is governed by two actuators. The main issue arises in the design of the two actuation profiles for there to be natural or normative gait motion in which the two actuators are transparent to each other. Hybrid exoskeleton control solutions proposed in the literature have been based on tracking the desired kinematics and applying FES to maintain the desired motion rather than to attain the values expected for physiological movement. This work proposes a muscle-model approach involving inverse dynamics optimization for the design of combined actuation in hybrid orthoses. The FES profile calculated in this way has the neurophysiological meaningfulness for the device to be able to fulfill its rehabilitative purpose. A general scheme is proposed for a hybrid hip-knee-ankle-foot orthosis. The actuation profiles, when muscle tissue is fatigued due to FES actuation are analyzed, and an integrated approach is presented for estimating the actuation profiles so as to overcome muscle peak force reduction during stimulation. The objective is to provide a stimulation profile for each muscle individually that is compatible with the desired kinematics and actuation of the orthosis. The hope is that the results may contribute to the design of subject-specific rehabilitation routines with hybrid exoskeletons, improving the exoskeleton's actuation while maintaining its rehabilitative function.

Changes of lumbosacral joint compression force profile when walking caused by backpack loads

Walking with backpack loads induces additional mechanical stress on the spine and has been identified as a risk factor of lower-back pain. This study evaluated the effects of walking with backpack loads on the lumbosacral joint compression force profile in both the magnitude and time domains. Ten male adults geared with anatomical markers and trunk surface electromyographic sensors walked along a walkway embedded with three force plates with no load and various backpack loads (5%, 10%, 15%, and 20% body weight). Lower-body movements, ground reaction forces, and trunk muscle activations were measured using a synchronized motion analysis, force plate, and surface electromyography system. The force profiles of identified gait cycles were predicted using an integrated inverse dynamic and electromyography-assisted optimization model and evaluated statistically. The results showed that as backpack load increased, the 10th, 50th, and 90th percentiles of force profiles escalated disproportionately. However, no significant changes were observed in the timing of the two peak force incidences. Such changes in the compression force might be an indication of the combined effects of the increase in both gravitational and mass moment of inertia of the system (body plus pack loads) when walking with a backpack. Pearson correlation coefficients of the force profiles between the five loading conditions were greater than 0.94. Strong associations between the force profiles at different backpack loads were confirmed.

An Inverse Dynamics Optimization Formulation With Recursive B-Spline Derivatives and Partition of Unity Contacts: Demonstration Using Two-Dimensional Musculoskeletal Arm and Gait.

In this study, an inverse dynamics optimization formulation and solution procedure is developed for musculoskeletal simulations. The proposed method has three main features: high order recursive B-spline interpolation, partition of unity, and inverse dynamics formulation. First, joint angle and muscle force profiles are represented by recursive B-splines. The formula for high order recursive B-spline derivatives is derived for state variables calculation. Second, partition of unity is used to handle the multicontact indeterminacy between human and environment during the motion. The global forces and moments are distributed to each contacting point through the corresponding partition ratio. Third, joint torques are inversely calculated from equations of motion (EOM) based on state variables and contacts to avoid numerical integration of EOM. Therefore, the design variables for the optimization problem are joint angle control points, muscle force control points, knot vector, and partition ratios for contacting points. The sum of muscle stress/activity squared is minimized as the cost function. The constraints are imposed for human physical constraints and task-based constraints. The proposed formulation is demonstrated by simulating a trajectory planning problem of a planar musculoskeletal arm with six muscles. In addition, the gait motion of a two-dimensional musculoskeletal model with sixteen muscles is also optimized by using the approach developed in this paper. The gait optimal solution is obtained in about 1 min central processing unit (CPU) time. The predicted kinematics, kinetics, and muscle forces have general trends that are similar to those reported in the literature.

Subject-specific strength percentile determination for two-dimensional symmetric lifting considering dynamic joint strength

This paper describes an efficient optimization method for determining the subject-specific strength percentile and predicting the maximum weight lifting motion by considering dynamic joint strength in symmetric box lifting. Dynamic strength is modeled as a three-dimensional function of joint angle and joint angular velocity based on experimentally obtained joint strength data from the literature. The function is further formulated as the joint torque limit constraint in an inverse dynamics optimization formulation to predict the maximum weight lifting motion. The initial, mid-time, and final postures are obtained from experiments and imposed as tracking constraints in the optimization formulation. In addition, the box weight and time duration are given as inputs for the lifting optimization problem. The normalized joint torque squared is used as the objective function. Subject-specific strength percentile ( $z\_\mathrm{score}$ ) is enumerated until the optimal solution is achieved. The determined strength percentile is a global score considering interactions of all joints for the two-dimensional symmetric lifting task. Results show that incorporating dynamic strength is critical in predicting lifting motion in extreme lifting conditions. The proposed algorithm can determine the subject-specific strength percentile based on experimental box lifting data. The accurate strength percentile is critical to predict strength related tasks to protect workers from injury.

PID Controller as a Platform for Implementation of the Adaptive Laws of the Electric Drive Control

Innovations in designing of the algorithmic supply of the moving control systems, based on the ideas of the inverse dynamic problem and local optimization, lead to analytic expressions for the automatic control laws of the dynamic objects with an incomplete description or with the parameters, which may be essentially changed during operation. The controllers, which implement such control laws, provide a closed loop system of the adaptive properties, and their structural interpretation allows us to see a familiar outline of a traditional PID controller. This gives us a chance to realize the new adaptive control laws for the existing DC electric drives equipped with the traditional PID controllers. Thus, the procedure of changing of the control law results in new parameters of setting of PID controller in the electric drive. In this paper the authors adhere to the concept of a direct adaptation, current numerical optimization for the local criterion of the main loop of the control system. The main problem of such an approach is to summarize the control error containing the data about all the uncontrolled changes of the object characteristics and environment included into the chosen optimization criterion. This problem is solved by introduction of a generalized control error as a difference between the derivative controlled coordinate and the respective derivative variable of the model reference, and by the use of the local quadratic criterion. Application of the new technology is demonstrated by construction of the control law for the adaptive controller of the electric drive designed to control the speed of DC motor with an independent excitation in the conditions of the uncontrollable change of its parameters and shaft load. Therefore, the aim is construction and investigation of the adaptive control laws, and designing on its basis of an appropriate structure available for use of the traditional PID controller platform, and also the synthesis of its parameters determining the desired static and dynamic properties of the projected electric drive. The authors present a statement and a solution to this problem. They demonstrate that the designed adaptive control law can be implemented on a conventional PID controller platform. At the same time, a traditional PID controller is converted into an adaptive one simply by changing of the parameter of its tuning with a constant element structure including integrator, differentiator and amplifiers. The results are presented using the construction of the adaptive electric drive with the use of the virtual units of the power electronic elements and electric DC motors included into SIMULINK library.

A window moving inverse dynamics optimization for biomechanics of motion

The application of musculoskeletal models to estimate muscle and joint reaction forces usually requires optimization strategies, regardless of using inverse or forward dynamics approaches. Most studies combined inverse dynamics and Static Optimization (SO) to solve the redundant muscle force distribution problem. However, the SO does not allow the simulation of time-dependent physiological criteria or of the time-dependent physiological nature of muscles. The Extended Inverse Dynamics (EID), which solves all instants of time simultaneously, was proposed to overcome these limitations of the SO, but the feasibility of this procedure is limited by the size of the optimization problem that can be realistically considered. This work proposes a new method that overcomes the aforementioned limitations of the SO and EID, i.e., that is able to handle time-dependent physiological criteria and has no limitations on the size of the problem to be solved. The proposed procedure, named here Window Moving Inverse Dynamics Optimization (WMIDO), consists in considering a moving window with the size of \(k\) instants of time in which the muscle force distribution problem is solved. The window moves iteratively across all instants of time until the muscle force distribution problem has been solved. The SO, EID, and WMIDO are applied to solve an upper limb abduction in the frontal plane, for which results are widely available in the literature, to demonstrate that similar optimal solutions are obtained for a time-independent physiological criterion if the redundant problem is not too large. Although the WMIDO is not as efficient as the SO for the type of problem tested, it is significantly faster than the EID. Moreover, the WMIDO is able to solve the motion under analysis regardless of the discretization level considered, whereas the EID fails due to memory limitations. Overall, the results show the WMIDO as a viable alternative to the current optimization procedures based on inverse dynamics.

Modeling and Identification of a Realistic Spiking Neural Network and Musculoskeletal Model of the Human Arm, and an Application to the Stretch Reflex.

This study develops a multi-level neuromuscular model consisting of topological pools of spiking motor, sensory and interneurons controlling a bi-muscular model of the human arm. The spiking output of motor neuron pools were used to drive muscle actions and skeletal movement via neuromuscular junctions. Feedback information from muscle spindles were relayed via monosynaptic excitatory and disynaptic inhibitory connections, to simulate spinal afferent pathways. Subject-specific model parameters were identified from human experiments by using inverse dynamics computations and optimization methods. The identified neuromuscular model was used to simulate the biceps stretch reflex and the results were compared to an independent dataset. The proposed model was able to track the recorded data and produce dynamically consistent neural spiking patterns, muscle forces and movement kinematics under varying conditions of external forces and co-contraction levels. This additional layer of detail in neuromuscular models has important relevance to the research communities of rehabilitation and clinical movement analysis by providing a mathematical approach to studying neuromuscular pathology.

Real-time trajectory planning for UCAV air-to-surface attack using inverse dynamics optimization method and receding horizon control

This paper presents a computationally efficient real-time trajectory planning framework for typical unmanned combat aerial vehicle (UCAV) performing autonomous air-to-surface (A/S) attack. It combines the benefits of inverse dynamics optimization method and receding horizon optimal control technique. Firstly, the ground attack trajectory planning problem is mathematically formulated as a receding horizon optimal control problem (RHC-OCP). In particular, an approximate elliptic launch acceptable region (LAR) model is proposed to model the critical weapon delivery constraints. Secondly, a planning algorithm based on inverse dynamics optimization, which has high computational efficiency and good convergence properties, is developed to solve the RHC-OCP in real-time. Thirdly, in order to improve robustness and adaptivity in a dynamic and uncertain environment, a two-degree-of-freedom (2-DOF) receding horizon control architecture is introduced and a regular real-time update strategy is proposed as well, and the real-time feedback can be achieved and the not-converged situations can be handled. Finally, numerical simulations demonstrate the efficiency of this framework, and the results also show that the presented technique is well suited for real-time implementation in dynamic and uncertain environment.

Role of optimization criterion in static asymmetric analysis of lumbar spine load

A common method for load estimation in biomechanics is the inverse dynamics optimization, where the muscle activation pattern is found by minimizing or maximizing the optimization criterion. It has been shown that various optimization criteria predict remarkably similar muscle activation pattern and intra-articular contact forces during leg motion. The aim of this paper is to study the effect of the choice of optimization criterion on L4/L5 loading during static asymmetric loading. Upright standing with weight in one stretched arm was taken as a representative position. Musculoskeletal model of lumbar spine model was created from CT images of Visible Human Project. Several criteria were tested based on the minimization of muscle forces, muscle stresses, and spinal load. All criteria provide the same level of lumbar spine loading (difference is below 25%), except the criterion of minimum lumbar shear force which predicts unrealistically high spinal load and should not be considered further. Estimated spinal load and predicted muscle force activation pattern are in accordance with the intradiscal pressure measurements and EMG measurements. The L4/L5 spine loads 1312 N, 1674 N, and 1993 N were predicted for mass of weight in hand 2, 5, and 8 kg, respectively using criterion of mininum muscle stress cubed. As the optimization criteria do not considerably affect the spinal load, their choice is not critical in further clinical or ergonomic studies and computationally simpler criterion can be used.

Knee and hip joint forces – sensitivity to the degrees of freedom classification at the knee

Previous research has demonstrated that the number of degrees of freedom (DOF) modelled at a given joint affects the antagonistic muscle activity predicted by inverse dynamics optimization techniques. This higher level of muscle activity in turn results in greater joint contact forces. For instance, modelling the knee as a 3 DOF joint has been shown to result in higher hip and knee joint forces commensurate with a higher level of muscular activity than when the knee is modelled with 1 DOF. In this study, a previously described musculoskeletal model of the lower limb was used to evaluate the sensitivity of the knee and hip joint contact forces to the DOF at the knee during vertical jumping in both a 1 and a 3 DOF knee model. The 3 DOF knee was found to predict higher tibiofemoral and hip joint contact forces and lower patellofemoral joint contact forces. The magnitude of the difference in hip contact force was at least as significant as that found in previous research exploring the effect of subject-specific hip geometry on hip contact force. This study therefore demonstrates a key sensitivity of knee and hip joint contact force calculations to the DOF at the knee. Finally, it is argued that the results of this study highlight an important physiological question with practical implications for the loading of the structures of the knee; that is, the relative interaction of muscular, ligamentous, and articular structures in creating moment equilibrium at the knee.