Self-Collision Detection in Spatial Closed Chains

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
John S. Ketchel ◽  
Pierre M. Larochelle
Keyword(s):  
Motion Planning ◽  
Finite Length ◽  
Collision Detection ◽  
Three Dimensional ◽  
Detection Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Circular Cylinders ◽  
Infinite Length ◽  
Kinematic Chains

A novel methodology for detecting self-collisions in spatial closed kinematic chains is presented. In general these chains generate complex three dimensional motions in which their own links will collide with each other (i.e., a self-collision) without effective motion planning. The self-collision detection is accomplished via a novel algorithm for definitively detecting collisions of right circular, cylindrically shaped, rigid bodies moving in three dimensions. The algorithm uses line geometry and dual number algebra to exploit the geometry of right circular cylindrical objects to facilitate the detection of collisions. In the first stage of the algorithm, cylindrically shaped rigid bodies are modeled by infinite length right circular cylinders. Sufficient and necessary conditions are then used to determine if a pair of infinite length cylinders collide. If the actual finite length rigid bodies collide, then it is necessary that their associate infinite length cylinder models collide, and we proceed to the next stage of the algorithm where the bodies are modeled with finite length cylinders and a definitive necessary and sufficient collision detection algorithm is employed. The result is an efficient approach of detecting collisions of cylindrically shaped bodies moving in three dimensions that has applications in spatial mechanism design and motion planning. A case study examining a spatial 4C mechanism for self-collisions is included.

Collision Detection of Cylindrical Rigid Bodies Using Line Geometry

2005 ◽  
Author(s):  
John S. Ketchel ◽  
Pierre M. Larochelle
Keyword(s):  
Collision Detection ◽  
Nuclear Physics ◽  
Detection Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Necessary Condition ◽  
Infinite Length ◽  
Line Geometry ◽  
Well Drilling ◽  
Necessary And Sufficient

This paper presents a novel methodology for detecting collisions of cylindrically shaped rigid bodies moving in three dimensions. This algorithm uses line geometry and dual number algebra to exploit the geometry of right circular cylindrical objects to facilitate the detection of collisions. First, the rigid bodies are modelled with infinite length cylinders and a necessary condition for collision is evaluated. If the necessary condition is not satisfied then the two bodies are not capable of collision. If the necessary condition is satisfied then a collision between the bodies may occur and we proceed to the next stage of the algorithm. In the second stage the bodies are modelled with finite length cylinders and a definitive necessary and sufficient collision detection algorithm is employed. The result is a straight-forward and efficient means of detecting collisions of cylindrically shaped bodies moving in three dimensions. This methodology has applications in spatial mechanism design, robot motion planning, workspace analysis of parallel kinematic machines such as Stewart-Gough platforms, nuclear physics, medical research, computer graphics and well drilling. A case study examining a spatial 4C robotic mechanism for self collisions is included.

Line Based Collision Detection of Cylindrical Rigid Bodies

2004 ◽  
Author(s):  
John S. Ketchel ◽  
Pierre M. Larochelle
Keyword(s):  
Collision Detection ◽  
Detection Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Necessary Condition ◽  
Second Stage ◽  
Parallel Kinematic ◽  
Necessary And Sufficient ◽  
Two Bodies

This paper presents a novel methodology for detecting collisions of cylindrically shaped rigid bodies moving in three dimensions. This algorithm uses line geometry and dual number algebra to exploit the geometry of cylindrical objects to facilitate the detection of collisions. First, the rigid bodies are modelled with infinite cylinders and a necessary condition for collision is evaluated. If the necessary condition is not satisfied then the two bodies do not collide. If the necessary condition is satisfied then a collision between the bodies may occur and we proceed to the next stage of the algorithm. In the second stage the bodies are modelled with finite cylinders and a definitive necessary and sufficient collision detection algorithm is employed. The result is a straight-forward and efficient means of detecting collisions of cylindrically shaped bodies moving in three dimensions. This methodology has applications in spatial mechanism design, robot motion planning, and workspace analyses of parallel kinematic machines such as Stewart-Gough platforms. A case study examining a spatial 4C mechanism for self collisions is included.

Shear-Driven Flow in a Toroid of Square Cross Section

2003 ◽  
Vol 125 (1) ◽  
pp. 130-137 ◽  
Author(s):  
J. A. C. Humphrey ◽  
J. Cushner ◽  
M. Al-Shannag ◽  
J. Herrero ◽  
F. Giralt
Keyword(s):  
Cross Section ◽  
Finite Length ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Radius Of Curvature ◽  
Infinite Length ◽  
Core Flow ◽  
Reynolds Number Flow ◽  
End Wall

The two-dimensional wall-driven flow in a plane rectangular enclosure and the three-dimensional wall-driven flow in a parallelepiped of infinite length are limiting cases of the more general shear-driven flow that can be realized experimentally and modeled numerically in a toroid of rectangular cross section. Present visualization observations and numerical calculations of the shear-driven flow in a toroid of square cross section of characteristic side length D and radius of curvature Rc reveal many of the features displayed by sheared fluids in plane enclosures and in parallelepipeds of infinite as well as finite length. These include: the recirculating core flow and its associated counterrotating corner eddies; above a critical value of the Reynolds (or corresponding Goertler) number, the appearance of Goertler vortices aligned with the recirculating core flow; at higher values of the Reynolds number, flow unsteadiness, and vortex meandering as precursors to more disorganized forms of motion and eventual transition to turbulence. Present calculations also show that, for any fixed location in a toroid, the Goertler vortex passing through that location can alternate its sense of rotation periodically as a function of time, and that this alternation in sign of rotation occurs simultaneously for all the vortices in a toroid. This phenomenon has not been previously reported and, apparently, has not been observed for the wall-driven flow in a finite-length parallelepiped where the sense of rotation of the Goertler vortices is determined and stabilized by the end wall vortices. Unlike the wall-driven flow in a finite-length parallelepiped, the shear-driven flow in a toroid is devoid of contaminating end wall effects. For this reason, and because the toroid geometry allows a continuous variation of the curvature parameter, δ=D/Rc, this flow configuration represents a more general paradigm for fluid mechanics research.

The Qualitative Synthesis of Parallel Manipulators

2004 ◽  
Vol 126 (4) ◽  
pp. 617-624 ◽  
Author(s):  
Jorge Angeles
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Qualitative Reasoning ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Qualitative Synthesis ◽  
Motion Representation ◽  
Six Degrees Of Freedom ◽  
Three Degrees Of Freedom

As shown in this paper, when designing parallel manipulators for tasks involving less than six degrees of freedom, the topology can be laid out by resorting to qualitative reasoning. More specifically, the paper focuses on cases whereby the manipulation tasks pertain to displacements with the algebraic structure of a group. Besides the well-known planar and spherical displacements, this is the case of displacements involving: rotation about a given axis and translation in the direction of the same axis (cylindrical subgroup); translation in two and three dimensions (two- and three-dimensional translation subgroups); three independent translations and rotation about an axis of fixed direction, what is known as the Scho¨nflies subgroup; and similar to the Scho¨nflies subgroup, but with the rotation and the translation in the direction of the axis of rotation replaced by a screw displacement. For completeness, the fundamental concepts of motion representation and groups of displacements, as pertaining to rigid bodies, are first recalled. Finally, the concept of Π-joint, introduced elsewhere, is generalized to two and three degrees of freedom, thereby ending up with the Π2-and the Π3-joints, respectively.

scholarly journals Collision Detection for Point Cloud Models With Bounding Spheres Hierarchies

2012 ◽  
Vol 11 (2) ◽  
pp. 37-43
Author(s):  
Mauro Figueiredo ◽  
João Pereira ◽  
João Oliveira ◽  
Bruno Araújo
Keyword(s):  
Collision Detection ◽  
Point Cloud ◽  
Complex Geometry ◽  
Shape Representation ◽  
Three Dimensional ◽  
Detection Algorithm ◽  
Empty Cell ◽  
Cloud Models ◽  
Bounding Volume ◽  
Common Shape

Point cloud models are a common shape representation for several reasons. Three-dimensional scanning devices are widely used nowadays and points are an attractive primitive for rendering complex geometry. Nevertheless, there is not much literature on collision detection for point cloud models. This paper presents a novel collision detection algorithm for large point cloud models using voxels, octrees and bounding spheres hierarchies (BSH). The scene graph is divided in voxels. The objects of each voxel are organized intoan octree. Due to the high number of points in the scene, each non-empty cell of the octree is organized in a bounding sphere hierarchy, based on an R-tree hierarchy like structure. The BSH hierarchies are used to group neighboring points and filter out very quickly parts of objects that do not interact with other models. Points derived from laser scanned data typically are not segmented and can have arbitrary spatial resolution thus introducing computational and modeling issues. We address these issues and our results show that the proposed collision detection algorithm effectively finds intersections between point cloud models since it is able to reduce the number of bounding volume checks and updates

ProtoFold: Part I — Nanokinematics for Analysis of Protein Molecules

2004 ◽  
Author(s):  
Kazem Kazerounian ◽  
Khalid Latif ◽  
Kimberly Rodriguez ◽  
Carlos Alvarado
Keyword(s):  
Three Dimensional ◽  
Linear Structure ◽  
Rigid Bodies ◽  
Dynamics Simulation ◽  
Kinematic Chains ◽  
Simulation Techniques ◽  
Revolute Joints ◽  
Zero Position ◽  
Ab Initio Prediction ◽  
Protein Molecules

Proteins are evolution’s mechanisms of choice. Study of nano-mechanical systems must encompass an understanding of the geometry and conformation of protein molecules. Proteins are open or closed loop kinematic chains of miniature rigid bodies connected by revolute joints. The Kinematics community is in a unique position to extend the boundaries of knowledge in nano biomechanical systems. ProtoFold is a software package that implements novel and comprehensive methodologies for ab initio prediction of the final three-dimensional conformation of a protein, given only its linear structure. In this paper, we present the methods utilized in the kinematics notion and kinematics analysis of protein molecules. The kinematics portion of ProtoFold incorporates the Zero-Position Analysis Method and draws upon other recent advances in robot manipulation theories. We claim that the methodology presented is a computationally superior and more stable alternative to traditional molecular dynamics simulation techniques.

A Real-Time Algorithm for Accurate Collision Detection for Deformable Polyhedral Objects

1998 ◽  
Vol 7 (1) ◽  
pp. 36-52 ◽  
Author(s):  
Yoshifumi Kitamura ◽  
Andrew Smith ◽  
Haruo Takemura ◽  
Fumio Kishino
Keyword(s):  
Collision Detection ◽  
Three Dimensional ◽  
Time Algorithm ◽  
Detection Algorithm ◽  
Boundary Representation ◽  
Multiple Objects ◽  
Auxiliary Data ◽  
Spatial Subdivision ◽  
Polyhedral Objects ◽  
Separating Plane

We propose an accurate collision detection algorithm for use in virtual reality applications. The algorithm works for three-dimensional graphical environments where multiple objects, represented as polyhedra (boundary representation), are undergoing arbitrary motion (translation and rotation). The algorithm can be used directly for both convex and concave objects and objects can be deformed (nonrigid) during motion. The algorithm works efficiently by first reducing the number of face pairs that need to be checked accurately for interference, by first localizing possible collision regions using bounding box and spatial subdivision techniques. Face pairs that remain after this pruning stage are then accurately checked for interference. The algorithm is efficient, simple to implement, and does not require any memory-intensive auxiliary data structures to be precomputed and updated. The performance of the proposed algorithm is compared directly against other existing algorithms, e.g., the separating plane algorithm, octree update method, and distance-based method. Results are given to show the efficiency of the proposed method in a general environment.

Research on Collision Detection Algorithm Based on OBB

2013 ◽  
Vol 433-435 ◽  
pp. 936-939 ◽  
Author(s):  
Xue Jing Ding
Keyword(s):  
Real Time ◽  
Virtual Environment ◽  
Collision Detection ◽  
Detection Algorithm ◽  
Rigid Bodies ◽  
The Real ◽  
Bounding Box

To enhance the real-time and accuracy of collision detection in virtual environment, introduces oriented bounding box (OBB) technology of hierarchical bounding box collision detection algorithm:construction of bounding box, generation of bounding box tree, implementation of collision detection algorithm,overlap judgement of bounding box. Collision detection algorithm based on OBB in this article is applied to solve the problem of collision detection between rigid bodies.

A Joint Coordinate System for the Clinical Description of Three-Dimensional Motions: Application to the Knee

1983 ◽  
Vol 105 (2) ◽  
pp. 136-144 ◽  
Author(s):  
E. S. Grood ◽  
W. J. Suntay
Keyword(s):  
Coordinate System ◽  
Translational Motion ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Joint Motion ◽  
Large Joint ◽  
Knee Joint Motion ◽  
Clinical Description ◽  
Joint Coordinate System

The experimental study of joint kinematics in three dimensions requires the description and measurement of six motion components. An important aspect of any method of description is the ease with which it is communicated to those who use the data. This paper presents a joint coordinate system that provides a simple geometric description of the three-dimensional rotational and translational motion between two rigid bodies. The coordinate system is applied to the knee and related to the commonly used clinical terms for knee joint motion. A convenient characteristic of the coordinate system shared by spatial linkages is that large joint displacements are independent of the order in which the component translations and rotations occur.

Nano-Kinematics for Analysis Of Protein Molecules

2004 ◽  
Vol 127 (4) ◽  
pp. 699-711 ◽  
Author(s):  
Kazem Kazerounian ◽  
Khalid Latif ◽  
Kimberly Rodriguez ◽  
Carlos Alvarado
Keyword(s):  
Software Package ◽  
Three Dimensional ◽  
Computer Software ◽  
Linear Structure ◽  
Data Bank ◽  
Kinematic Parameter ◽  
Rigid Bodies ◽  
Protein Chain ◽  
Kinematic Chains ◽  
Protein Molecules

Proteins are evolution’s mechanisms of choice. The study of nano-mechanical systems must encompass an understanding of the geometry and conformation of protein molecules. Proteins are open or closed loop kinematic chains of miniature rigid bodies connected by revolute joints. The Kinematics community is in a unique position to extend the boundaries of knowledge in nano biomechanical systems. In this work, we have presented a comprehensive methodology for kinematics notation and direct kinematics for protein molecules. These methods utilize the zero-position analysis method and draws upon other recent advances in robot manipulation theories. The procedures involved in finding the coordinates of every atom in the protein chain as a function of the dihedral and Rotamer angles are computationally the most efficient formulation developed to date. The notation and the methodologies of this paper are incorporated in the computer software package PROTOFOLD and will be made available to individuals interested in using it. PROTOFOLD is a software package that implements novel and comprehensive methodologies for ab initio prediction of the final three-dimensional conformation of a protein, given only its linear structure. In addition to the new kinematics methodologies mentioned above, we have also included all the basic kinematic parameter values that are needed in any kinematic analysis involving proteins. While these values are based on a body of knowledge recorded in the protein data bank, they are presented in a form conducive to kinematics.

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