A contact detection algorithm for superellipsoids based on the common‐normal concept

Wellmann, Christian; Lillie, Claudia; Wriggers, Peter

doi:10.1108/02644400810881374

Cited by 125 publications

(56 citation statements)

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“…Contrary to most contact detection procedures that involve superellipsoids, the main characteristic of the applied contact model consists of formulating the minimum distance problem taking as an unknown variable the common normal direction vector (Wellmann et al 2008) instead of the contact points coordinates (Lopes et al 2010). Within the superellipsoid family, Barr's surface type (Barr 1981) presents a propitious analytical property for an efficient minimum distance calculation: given a unitary vector, the superellipsoid's radii and exponents along with the surface position and orientation, it is possible to deduce a closed-form expression of the surface point locations that share a common direction with the given vector.…”

Section: A3 Minimum Distance Pointsmentioning

confidence: 99%

“…The minimum distance points between a superellipsoid and plane are defined as the surface points that satisfy the common normal conditions (Johnson 1985;Wellmann et al 2008) and, simultaneously, have the shortest distance between surfaces. The common normal concept consists of the line segment that connects two points, one on each surface, whose normal vectors share a common direction (Figure 6(a)).…”

Section: A2 Common Normal Conceptmentioning

confidence: 99%

“…Furthermore, a superellipsoid can also be represented parametrically using angle-center parameters (Wellmann et al 2008): …”

Section: Appendix -Closest Point On a Superellipsoid To A Given Planementioning

confidence: 99%

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A superellipsoid-plane model for simulating foot-ground contact during human gait

Lopes

Neptune

Ambrósio

et al. 2015

Computer Methods in Biomechanics and Biomedical Engineering

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Musculoskeletal models and forward dynamics simulations of human movement often include foot-ground interactions, with the foot-ground contact forces often determined using a constitutive model that depends on material properties and contact kinematics. When using soft constraints to model the foot-ground interactions, the kinematics of the minimum distance between the foot and planar ground needs to be computed. Due to their geometric simplicity, a considerable number of studies have used point-plane elements to represent these interacting bodies, but few studies have provided comparisons between point contact elements and other geometrically based analytical solutions. The objective of this work was to develop a more general-purpose superellipsoid-plane contact model that can be used to determine the three-dimensional foot-ground contact forces. As an example application, the model was used in a forward dynamics simulation of human walking. Simulation results and execution times were compared with a point-like viscoelastic contact model. Both models produced realistic ground reaction forces and kinematics with similar computational efficiency. However, solving the equations of motion with the surface contact model was found to be more efficient (~18% faster), and on average numerically ~37% less stiff. The superellipsoid-plane elements are also more versatile than point-like elements in that they allow for volumetric contact during three-dimensional motions (e.g. rotating, rolling, and sliding). In addition, the superellipsoid-plane element is geometrically accurate and easily integrated within multibody simulation code. These advantages make the use of superellipsoid-plane contact models in musculoskeletal simulations an appealing alternative to point-like elements.

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Section: A3 Minimum Distance Pointsmentioning

confidence: 99%

Section: A2 Common Normal Conceptmentioning

confidence: 99%

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A superellipsoid-plane model for simulating foot-ground contact during human gait

Lopes

Neptune

Ambrósio

et al. 2015

Computer Methods in Biomechanics and Biomedical Engineering

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“…Contact between analytically well-defined shapes is basically restricted to super-ellipsoidal (Wellmann et al, 2008) or super-quadric shaped particles (Lu et al, 2012).…”

Section: Direct Application Of Shm To Demmentioning

confidence: 99%

Determining the shape of agricultural materials using spherical harmonics

Radvilaitź

Ramírez-Gómez

Kačianauskas

2016

Computers and Electronics in Agriculture

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“…Recently, however, the multi-sphere method [221], which has proved highly effective in the modelling of other system geometries [222][223][224], has begun to be applied to vibrated and vibrofluidised beds. Using the multisphere approach, each non-spherical particle within a system is composed of a number of smaller objects, creating 'composite particles', the modelling of which is often more computationally efficient than for complex shapes represented using single particle models [225,226]. Work by Chung et al [227], for example, demonstrates, for the case of simple paired particles, an excellent, quantitative agreement between experiment and simulation, providing strong support for the validity and applicability of the multi-sphere model in vibrated beds.…”

Section: Vibrated Systemsmentioning

confidence: 99%

Polydisperse granular flows over inclined channels

Tunuguntla¹

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POLYDISPERSE GRANULAR FLOWS OVER INCLINED CHANNELS DISSERTATIONto obtain the degree of doctor at the University of Twente, on the authority of the rector magnificus, Prof. dr. H. Brinksma, on account of the decision of the graduation committee, to be publicly defended on Friday 9 October 2015 at 16:45 hrs by Deepak Raju Tunuguntla born on the 3rd of November 1986 in Hyderabad, India. Granular materialsEverything seems simpler from a distance. -Gail TsukiyamaMatter exists in a variety of forms, of which granular materials -although simplebehave differently from any of the other standard forms (solid, liquid and gas). For example, a sand castle appears like a solid, which when tumbled upon, crumbles down like an avalanche. On a few occasions, this avalanche takes down the whole castle, whereas sometimes it is confined only to a thin layer on its surface (liquid). In another example, shake up some crushed ice in a cocktail mixer and it behaves like a gas, whereas when trying to pour some salt out of an orifice of a jar, the flow tends to choke and gets clogged at the orifice. Granular material has it all, solid, liquid, gas, plastic flow, glassy, etc. -it can mimic all of these behaviours. Thus exhibiting a prime reason for investing our interest in understanding these simple but, mysterious materials. HistoryOur knowledge of granular matter dates back to an era even before mankind's existence. These materials exist on a range of scales -micron sized to planetary -in a variety of forms, exhibiting multitudes of interesting phenomena. The earliest encounter between man and granular matter happened in the surroundings in which he evolved, i.e. with soil, sand, stones, rocks, etc., but more importantly it was his need for survival that ultimately led to an inevitable bond between humanity and granular matter, existing till today. Historical records indicate that primitive men often settled along the river banks where fresh food was available throughout the year. However, due to climatic changes coupled with migration of primitive tribes, new food gathering methods had to be devised. Man needed to find some way to store the nutrients for periods of time when no fresh food was available. Seeds, such as cereal grains, seemed to be one way to solve 1 1 2 Introduction Figure 1.1: Facsimile of a famous scene from a wall painting on the tomb of Djehutihotep, a pharoah (circa 1932(circa -1842. It illustrates his huge monolithic statue being transported from the quarries. In the front of the statue (near the feet) we see a workman pouring water to lubricate the sand, helping the four rows of workmen, 43 men in each, to haul the sledge smoothy (less friction). The figure is adapted from Dowson [1].the storage problems. Ultimately around 8000 BCE, during neolithic revolution, this seed storage led man towards becoming more agriculturally oriented. Grains were likely among the first cultivated crops. They could be grown relatively easily, farmed in surplus quantities and were suitable for storage in harsh cold winter climat...

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A contact detection algorithm for superellipsoids based on the common‐normal concept

Cited by 125 publications

References 19 publications

A superellipsoid-plane model for simulating foot-ground contact during human gait

A superellipsoid-plane model for simulating foot-ground contact during human gait

Determining the shape of agricultural materials using spherical harmonics

Polydisperse granular flows over inclined channels

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