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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.
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Dispersive fractalisation in linear and nonlinear Fermi–Pasta–Ulam–Tsingou lattices
We investigate, both analytically and numerically, dispersive fractalisation and quantisation of solutions to periodic linear and nonlinear Fermi–Pasta–Ulam–Tsingou systems. When subject to periodic boundary conditions and discontinuous initial conditions, e.g., a step function, both the linearised and nonlinear continuum models for FPUT exhibit fractal solution profiles at irrational times (as determined by the coefficients and the length of the interval) and quantised profiles (piecewise constant or perturbations thereof) at rational times. We observe a similar effect in the linearised FPUT chain at times t where these models have validity, namely t = O( h −2 ), where h is proportional to the intermass spacing or, equivalently, the reciprocal of the number of masses. For nonlinear periodic FPUT systems, our numerical results suggest a somewhat similar behaviour in the presence of small nonlinearities, which disappears as the nonlinear force increases in magnitude. However, these phenomena are manifested on very long time intervals, posing a severe challenge for numerical integration as the number of masses increases. Even with the high-order splitting methods used here, our numerical investigations are limited to nonlinear FPUT chains with a smaller number of masses than would be needed to resolve this question unambiguously.
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- Award ID(s):
- 1913272
- PAR ID:
- 10257293
- Date Published:
- Journal Name:
- European Journal of Applied Mathematics
- ISSN:
- 0956-7925
- Page Range / eLocation ID:
- 1 to 26
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/S095679252000042X
