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.

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.

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.

Closed-Form Determination of the Location of a Rigid Body by Seven In-Parallel Linear Transducers

1996 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Rigid Body ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Body Location ◽  
Position And Orientation ◽  
General Geometry ◽  
Two Bodies

Abstract The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

Institutions and Collective Action: The New Telecommunications in Western Europe

1993 ◽  
Vol 45 (2) ◽  
pp. 242-270 ◽  
Author(s):  
Wayne Sandholtz
Keyword(s):  
Collective Action ◽  
Western Europe ◽  
National Level ◽  
Development Planning ◽  
Three Dimensions ◽  
Necessary Condition ◽  
International Leadership ◽  
Policy Adaptation ◽  
Future Networks

The member states of the European community are not just liberalizing telecommunications but are cooperating extensively in the sector. Breaking with a past dominated by rigid national monopolies (the PTTs), EC states in the 1980s undertook collective action in research and development, planning future networks, setting standards, and opening markets. This article seeks to explain telecoms liberalization and cooperation in Europe. Two conditions are necessary for international collective action to emerge. The first is policy adaptation at the national level, such that governments are willing to consider alternatives to pure unilateralism. In telecommunications, technological changes induced widespread policy adaptation in EC states. This adaptation was a necessary prerequisite for European cooperation. The second necessary condition is international leadership to organize the collective action. This paper extends the analysis of international leadership by outlining the conditions under which international organizations can exercise leadership to organize collective action. The case study, focusing on three dimensions of EC telecoms reform, shows how the Commission of the EC led in organizing collective action.

An Algorithm to Study the Elastodynamics of Parallel Kinematic Machines With Lower Kinematic Pairs

2012 ◽  
Vol 5 (1) ◽  
Author(s):  
Alessandro Cammarata ◽  
Davide Condorelli ◽  
Rosario Sinatra
Keyword(s):  
Stiffness Matrix ◽  
Rigid Bodies ◽  
Parallel Kinematic Machine ◽  
Element Analysis ◽  
Stiffness Matrices ◽  
The Matrix ◽  
Parallel Kinematic ◽  
Global Stiffness Matrix ◽  
Local Stiffness

In this paper, an algorithm to help designers to integrate the elastodynamics analysis along with the inverse positioning and orienting problems of a parallel kinematic machine (PKM) into a single package is conceived. The proposed algorithm applies concepts from the matrix structural analysis (MSA) and finite element analysis (FEA) to determine the generalized stiffness matrix and the linearized elastodynamics equations of a PKM with only lower kinematic pairs. A PKM is modeled as a system of flexible links and rigid bodies connected by means of joints. Three cases are analyzed to consider the combinations between flexible and rigid bodies in order to find the local stiffness matrices. The latter are combined to obtain the limb matrices and, then, the global stiffness matrix of the whole robotic system. The same nodes coming from the links discretization are considered to include joint masses/inertias into the model. Finally, a case study is proposed to show some feasible applications and to compare results to commercial software for validation.

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.

Closed-Form Determination of the Location of a Rigid Body by Seven In-Parallel Linear Transducers

1998 ◽  
Vol 120 (2) ◽  
pp. 293-298 ◽  
Author(s):  
C. Innocenti
Keyword(s):  
Rigid Body ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Body Location ◽  
Position And Orientation ◽  
General Geometry ◽  
Two Bodies

The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

Researching American Muslims: A Case Study of Surveillance and Racialized State Control

2021 ◽  
pp. 1-16
Author(s):  
Hajer Al-Faham
Keyword(s):  
United States ◽  
Science Research ◽  
The United States ◽  
State Control ◽  
Limited Data ◽  
American Muslims ◽  
State Repression ◽  
Second Stage ◽  
Selection Of

How does surveillance shape political science research in the United States? In comparative and international politics, there is a rich literature concerning the conduct of research amid conditions of conflict and state repression. As this literature locates “the field” in distant contexts “over there,” the United States continues to be saturated with various forms of state control. What this portends for American politics research has thus far been examined by a limited selection of scholars. Expanding on their insights, I situate “the field” in the United States and examine surveillance of American Muslims, an understudied case of racialized state control. Drawing on qualitative data from a case study of sixty-nine interviews with Arab and Black American Muslims, I argue that surveillance operated as a two-stage political mechanism that mapped onto research methodologically and substantively. In the first stage, surveillance reconfigured the researcher-researchee dynamic, hindered recruitment and access, and limited data-collection. In the second stage, surveillance colored the self-perceptions, political attitudes, and civic engagement of respondents, thereby indicating a political socialization unfolding among Muslims. The implications of this study suggest that researchers can mitigate against some, but not all, of the challenges presented by surveillance and concomitant forms of state control.

Some generalized characters associated to a transitive permutation group

2020 ◽  
Vol 23 (3) ◽  
pp. 393-397
Author(s):  
Wolfgang Knapp ◽  
Peter Schmid
Keyword(s):  
Positive Integer ◽  
Permutation Group ◽  
Frobenius Group ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Transitive Permutation Group ◽  
Point Stabilizer ◽  
Necessary And Sufficient ◽  
Regular Character ◽  
Permutation Character

AbstractLet G be a finite transitive permutation group of degree n, with point stabilizer {H\neq 1} and permutation character π. For every positive integer t, we consider the generalized character {\psi_{t}=\rho_{G}-t(\pi-1_{G})}, where {\rho_{G}} is the regular character of G and {1_{G}} the 1-character. We give necessary and sufficient conditions on t (and G) which guarantee that {\psi_{t}} is a character of G. A necessary condition is that {t\leq\min\{n-1,\lvert H\rvert\}}, and it turns out that {\psi_{t}} is a character of G for {t=n-1} resp. {t=\lvert H\rvert} precisely when G is 2-transitive resp. a Frobenius group.

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