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Abstract In this study, the fatigue progression and optimal motion trajectory during repetitive lifting task is predicted by using a 10 degrees of freedom (DOFs) two-dimensional (2D) digital human model and a three-compartment controller (3CC) fatigue model. The numerical analysis is further validated by conducting an experiment under similar conditions. The human is modeled using Denavit-Hartenberg (DH) representation. The task is mathematically formulated as a nonlinear optimization problem where the dynamic effort of the joints is minimized subjected to physical and task specific constraints. A sequential quadratic programming method is used for the optimization process. The design variables include control points of (1) quartic B-splines of the joint angle profiles; and (2) the three compartment sizes profiles for the six physical joints of interest — spine, shoulder, elbow, hip, knee, and ankle. Both numerical and experimental liftings are performed with a 15.2 kg box as external load. The simulation reports the human joint torque profiles and the progression of joint fatigue. The joint torque profiles show periodic trends. A maximum of 17 cycles are predicted before the repetitive lifting task fails, which also reasonably agrees with that of the experimental results (16 cycles). This formulation is also a generalized one, hence it can be used for other repetitive motion studies as well. 

The ability to predict the decline in muscle strength over the course of an activity (i.e., fatigue) can be a crucial aid to task design, injury prevention, and rehabilitation efforts. Current models of muscle fatigue have been hitherto validated only for isometric contractions, but most real-world tasks are dynamic in nature, involving continuously varying joint velocities. It has previously been proposed that a three-compartment-controller (3CC) model might be used to predict fatigue for such tasks by using it in conjunction with joint- and direction-specific torque-velocity-angle (TVA) surfaces. This allows for the calculation of a time-varying target load parameter that can be used by the 3CC model, but it increases model complexity and has not been validated by experimental data. An alternative approach is proposed where the effect of joint velocity is modeled by a velocity parameter and integrated into the fatigue model equations, removing the dependence on external TVA surfaces. The predictions using both methods are contrasted against experimental data collected from 20 subjects in a series of isokinetic tests involving the knee and shoulder joints, covering a range of velocities encountered in day-to-day tasks. A much lower degree of fatigue is observed for moderate velocities compared to that for very low or very high velocities. Predictions using the integrated velocity parameter are computationally less expensive than using TVA surfaces and are also closer to experimentally obtained values. The modified fatigue model can therefore be applied to dynamic tasks with varying velocities when the task is discretized into several isokinetic tasks. 

Lifting is a main task for manual material handling (MMH), and it is also associated with lower back pain. There are many studies in the literature on predicting lifting strategies, optimizing lifting motions, and reducing lower back injury risks. This survey focuses on optimization-based biomechanical lifting models for MMH. The models can be classified as two-dimensional and three-dimensional models, as well as skeletal and musculoskeletal models. The optimization formulations for lifting simulations with various cost functions and constraints are reviewed. The corresponding equations of motion and sensitivity analysis are briefly summarized. Different optimization algorithms are utilized to solve the lifting optimization problem, such as sequential quadratic programming, genetic algorithm, and particle swarm optimization. Finally, the applications of the optimization-based lifting models to digital human modeling which refers to modeling and simulation of humans in a virtual environment, back injury prevention, and ergonomic safety design are summarized.