Structural and Material Optimization for Automatic Synthesis of Spine-Segment Mechanisms for Humanoid Robots with Custom Stiffness Profiles

2019

Materials

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The ankle is one of the most complicated joints in the human body. Its features a plethora of elements with complex behavior. Their functions could be better understood using a planar model of the joint with low parameter count and low numerical complexity. In this study, an accurate planar model of the ankle with optimized material parameters was presented. In order to obtain the model, we proposed an optimizational approach, which fine-tuned the material parameters of two-dimensional links substituting three-dimensional ligaments of the ankle. Furthermore, the cartilage in the model was replaced with Hertzian contact pairs. The model was solved in statics under moment loads up to 5 Nm. The obtained results showed that the structure exhibited angular displacements in the range of the ankle joint and that their range was higher in dorsiflexion than plantarflexion. The structure also displayed a characteristic ramp up of the angular stiffness. The results obtained from the optimized model were in accordance with the experimental results for the ankle. Therefore, the proposed method for fine-tuning the material parameters of its links could be considered viable.

Section: Methodsmentioning

confidence: 99%

A Planar Model of an Ankle Joint with Optimized Material Parameters and Hertzian Contact Pairs

Borucka

2019

Materials

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“…A detailed summary regarding the computation of the force vectors, their moments and more can be found in [10,12,36,37].…”

Section: Resultsmentioning

confidence: 99%

Arbitrary Prestrain Values for Ligaments Cause Numerical Issues in a Multibody Model of an Ankle Joint

2022

Symmetry

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Experimental studies report that ligaments of the ankle joint are prestrained. The prestrain is an important aspect of modern biomechanical analysis, which can be included in the models by: applying symmetrical, arbitrary prestrains to the ligaments, assuming a strain-free location for the joint or by using experimental prestrain data. The aim of the study was to comparatively analyze these approaches. In total, 4 prestraining methods were considered. In order to do so, a symmetrical model of the ankle with six nonlinear cables and two sphere–sphere contact pairs was assumed. The model was solved in statics under moment loads up to 5 Nm. The obtained results showed that the arbitrary prestrains caused an unbalanced load for the model at rest, and in turn modified its rest location in an unpredictable way. Due to the imbalance, it was impossible to enforce the assumed prestrains and thus cartilage prestrain was required to stabilize the model. The prestraining had a significant effect on the angular displacements and the load state of the model. The findings suggest that the prestrain values are patient specific and arbitrary prestrains will not be valid for most models.

“…Furthermore, the bodies also interacted through Hertzian contact pairs of a spheresphere type, which represented the cartilage. The details concerning the mathematical equations for computing the forces of the elements and the equilibrium of such systems can be found in the following publications [26][27][28][29][30][31]. Internally, within the procedure, the models were solved for static equilibrium under the following external moment loads: Mext = −5.00: 5.00 Nm in 11 steps.…”

Section: Ankle Model Assumed To Verify the Proceduresmentioning

confidence: 99%

“…. , (m − 1) and w 1i = 2 for i = [0, m]), w 2 = 10.00), ∆θ k (M ext,i ) is the angular displacement of model k (k is either A or B) under the external moment load M ext,i (the considered loads were specified in the Section 2.2), not_passed is the number of loads for which the solver did not solve the models with desired accuracy (a sum for both of the adversarial structures; a similar approach was utilized in: [29,30,33]). The solutions, which contained models that were difficult to solve for all of the assumed loads were penalized with the second element of the objective function (2).…”

Section: Objective Functionmentioning

confidence: 99%

“…A real-coded variant of genetic algorithm (RC-GA) [35] was used to minimize the objective function (2). This choice was not arbitrary as different variants of genetic algorithms [36], or evolutionary methods in general, have been proven effective in various optimizational problems [29,[37][38][39][40][41]. Furthermore, typical local methods would not perform well in this problem-some of the structures did not converge, which made the objective function discontinuous and with many local minimums.…”

Section: Optimization Proceduresmentioning

confidence: 99%

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Analyzing Uncertainty of an Ankle Joint Model with Genetic Algorithm

2020

Materials

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Recent studies in biomechanical modeling suggest a paradigm shift, in which the parameters of biomechanical models would no longer treated as fixed values but as random variables with, often unknown, distributions. In turn, novel and efficient numerical methods will be required to handle such complicated modeling problems. The main aim of this study was to introduce and verify genetic algorithm for analyzing uncertainty in biomechanical modeling. The idea of the method was to encode two adversarial models within one decision variable vector. These structures would then be concurrently optimized with the objective being the maximization of the difference between their outputs. The approach, albeit expensive numerically, offered a general formulation of the uncertainty analysis, which did not constrain the search space. The second aim of the study was to apply the proposed procedure to analyze the uncertainty of an ankle joint model with 43 parameters and flexible links. The bounds on geometrical and material parameters of the model were set to 0.50 mm and 5.00% respectively. The results obtained from the analysis were unexpected. The two obtained adversarial structures were almost visually indistinguishable and differed up to 38.52% in their angular displacements.