A benchmark study on accuracy-controlled distance calculation between superellipsoid and superovoid contact geometries

Gonçalves, Artur; Bernardino, Alexandre; Jorge, Joaquim; Lopes, Daniel Simões

doi:10.1016/j.mechmachtheory.2017.04.008

Cited by 16 publications

(21 citation statements)

References 17 publications

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“…Additional ellipsoids could be added to the model so that more of the surface is modelled (for example, based on Figure 6, a fourth ellipsoid at the lateral edge of the foot may improve the fit). The use of more complex, analytical shapes could also be explored, such as superellipsoids or superovoids [19]. These methods could improve the accuracy, but would also result in larger and likely more complex equations, decreasing the computational efficiency of the model.…”

Section: Calibration Resultsmentioning

confidence: 99%

“…Alternatively, point contact models can be modified by using various geometries to represent the contact surface (such as spheres, disks, or superellipsoids) [15], [17], [18]; this geometry determines the central or most important point of contact at which the contact forces are calculated. In cases like this, it is more computationally efficient to use analytical shapes, such as spheres or superellipsoids, than meshes to represent the contact surfaces [19]. A balance is needed between a simplified model that will be computationally efficient, and an accurate model.…”

Section: Introductionmentioning

confidence: 99%

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A 3D ellipsoidal volumetric foot–ground contact model for forward dynamics

Brown

McPhee

2017

Multibody Syst Dyn

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Foot-ground contact models are an important part of forward dynamic biomechanic models, particularly those used to model gait, and have many challenges associated with them. Contact models can dramatically increase the complexity of the multibody system equations, especially if the contact surface is relatively large or conforming. Since foot-ground contact has a large potential contact area, creating a computationally efficient model is challenging. This is particularly problematic in predictive simulations, which may determine optimal performance by running a model simulation thousands of times. An ideal contact model must find a balance between accuracy for large, conforming surfaces, and computational efficiency.Volumetric contact modelling is explored as a computationally efficient model for footground contact. Previous foot models have used volumetric contact before, but were limited to 2D motion and approximated the surfaces as spheres or 2D shapes. The model presented here improves on current work by using ellipsoid contact geometry and considering 3D motion and geometry. A gait experiment was used to parametrise and validate the model. The model ran over 100 times faster than real-time (in an inverse simulation at 128 fps) and matched experimental normal force and centre of pressure location with less than 7% root-mean-square error.In most gait studies, only the net reaction forces, centre of pressure, and body motions are recorded and used to identify parameters. In this study, contact pressure was also recorded and used as a part of the identification, which was found to increase parameter optimisation time from 10 s to 164 s (due to the additional time needed to calculate the pressure distribution) but helped the results converge to a more realistic model. The model matched experimental pressures with 33-45% root-mean-square error, though some of this was due to measurement errors.The same parametrisation was done with friction included in the foot model. It was determined that the velocity-based friction model that was used was inappropriate for use in an inverse-dynamics simulation. Attempting to optimise the model to match experimental friction resulted in a poor match for friction forces, inaccurate values for the coefficient of friction, and a poorer match to the experimental normal force.

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Section: Calibration Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A 3D ellipsoidal volumetric foot–ground contact model for forward dynamics

Brown

McPhee

2017

Multibody Syst Dyn

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“…In this section, two different contact detection methodologies are discussed. First, the minimum distance method is described, which has been widely utilized for searching the potential contact points between convex surfaces [3,41,69,70]. Subsequently, an alternative approach for the wheelrail contact is introduced which can be applied to real wheel profiles that comprise non-convex regions.…”

Section: Contact Detection Methodologymentioning

confidence: 99%

A three-dimensional approach for contact detection between realistic wheel and rail surfaces for improved railway dynamic analysis

Marques

Magalhães

Pombo

et al. 2020

Mechanism and Machine Theory

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The wheel-rail contact modelling problem assumes a preponderant role on the dynamic analysis of railway systems using multibody systems formulations. The accurate and efficient evaluation of both location and magnitude of the wheel-rail contact forces is fundamental for the development of reliable computational tools. The wheel concave zone might be a source of numerical difficulties when searching the contact points, which has been neglected in several works. Here, it is demonstrated that the minimum distance method does not always converge when the wheel surface is not fully convex, being an alternative methodology proposed to perform the contact detection. This approach examines independently the contact between each wheel strip and the rail, where the maximum virtual penetration is determined and associated with the location of the contact point. Then, an Hertzian-based force model is considered for both normal and tangential forces. The results obtained from dynamic simulations show that the minimum distance method and the proposed methodology provide a similar response for simplified wheel profiles. However, the new approach described here is reliable in the identification of the contact point when realistic wheel profiles are considered, which is not the case with the minimum distance method.

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“…Ellipsoids have widely been used as bounding volumes in various applications, such as computer vision [Liang et al 2016], robotics [Lee et al 2017], mechanism and machine theory [Goncalves et al 2017], molecular dynamics [Ghossein and Lévesque 2013], computational particle mechanics [Rubio-Largo et al 2015] as well as in material science [Xu and Chen 2016]. In particular, ellipsoids have been a popular candidate for bounding volumes in collision detection; see for examples [Choi et al 2009[Choi et al , 2006Jia et al 2011;Ju et al 2001;Liu et al 2007;Lu et al 2007;Rimon and Boyd 1977;Shiang et al 2000;Wang et al 2004].…”

Section: Ellipsoidsmentioning

confidence: 99%

“…Ellipsoids have superior capability of shape approximation and relatively low algebraic degree, hence have widely been used as bounding volumes in various applications, such as computer vision [Liang et al 2016], robotics [Lee et al 2017], mechanism and machine theory [Goncalves et al 2017], molecular dynamics [Ghossein and Lévesque 2013], computational particle mechanics [Rubio-Largo et al 2015] as well as in material science [Xu and Chen 2016]. See Fig.…”

Section: Introductionmentioning

confidence: 99%

Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids

Jia

Mourrain

et al. 2020

ACM Trans. Graph.

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Arrangements of geometric objects refer to the spatial partitions formed by the objects and they serve as an underlining structure of motion design, analysis and planning in CAD/CAM, robotics, molecular modeling, manufacturing and computer-assisted radiosurgery. Arrangements are especially useful to collision detection, which is a key task in various applications such as computer animation, virtual reality, computer games, robotics, CAD/CAM and computational physics. Ellipsoids are commonly used as bounding volumes in approximating complex geometric objects in collision detection. In this paper we present an in-depth study on the arrangements formed by two ellipsoids. Specifically, we present a classification of these arrangements and propose an efficient algorithm for determining the arrangement formed by any particular pair of ellipsoids. A stratification diagram is also established to show the connections among all the arrangements formed by two ellipsoids. Our results for the first time elucidate all possible relative positions between two arbitrary ellipsoids and provides an efficient and robust algorithm for determining the relative position of any two given ellipsoids, therefore providing the necessary foundation for developing practical and trustworthy methods for processing ellipsoids for collision analysis or simulation in various applications.

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A benchmark study on accuracy-controlled distance calculation between superellipsoid and superovoid contact geometries

Cited by 16 publications

References 17 publications

A 3D ellipsoidal volumetric foot–ground contact model for forward dynamics

A 3D ellipsoidal volumetric foot–ground contact model for forward dynamics

A three-dimensional approach for contact detection between realistic wheel and rail surfaces for improved railway dynamic analysis

Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids

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