A Separating Channel Decomposition Algorithm for Non-Convex Polygons With Application in Interference Detection

1988 ◽  
Author(s):  
T. S. Ku ◽  
B. Ravani
Keyword(s):  
Computer Aided Design ◽  
Companion Paper ◽  
Detection Algorithm ◽  
Geometric Constraints ◽  
Decomposition Algorithm ◽  
Interference Detection ◽  
Convex Polygons ◽  
Aided Design ◽  
Computational Basis ◽  
Channel Decomposition

Abstract An algorithm for efficient decomposition of interface channels between non-convex polygons in a Computer-Aided Design (CAD) environment is presented. This algorithm forms the computational basis for the solution of several design automation problems. In this paper, the channel decomposition algorithm is presented and applied to the problem of interference detection between non-convex polygons. The resulting interference detection algorithm does not require preprocessing of the data and uses a simple data structure. In a companion paper (Ku and Ravani 1988), the channel decomposition algorithm is applied to the problem of model-based rigid-body guidance in presence of geometric constraints.

A Separating Channel Decomposition Algorithm for Nonconvex Polygons With Application in Interference Detection

1989 ◽  
Vol 111 (2) ◽  
pp. 270-277 ◽  
Author(s):  
T. S. Ku ◽  
B. Ravani
Keyword(s):  
Design Automation ◽  
Computer Aided Design ◽  
Companion Paper ◽  
Detection Algorithm ◽  
Geometric Constraints ◽  
Decomposition Algorithm ◽  
Interference Detection ◽  
Aided Design ◽  
Computational Basis ◽  
Channel Decomposition

An algorithm for efficient decomposition of interface channels between nonconvex polygons in a Computer-Aided Design (CAD) environment is presented. This algorithm forms the computational basis for the solution of several design automation problems. In this paper, the channel decomposition algorithm is presented and applied to the problem of interference detection between nonconvex polygons. The resulting interference detection algorithm does not require preprocessing of the data and uses a simple data structure. In a companion paper (Ku and Ravani, 1989), the rigid channel decomposition algorithm is applied to the problem of model-based rigid-body guidance in presence of geometric constraints.

Boundary Surface Recovery From Skeleton Elements: Part I — Skeleton Curves

1992 ◽  
Author(s):  
Sean M. Gelston ◽  
Debasish Dutta
Keyword(s):  
Inverse Problem ◽  
Computer Aided Design ◽  
Boundary Surface ◽  
Reconstruction Algorithm ◽  
Companion Paper ◽  
Active Area ◽  
Curves And Surfaces ◽  
Computer Aided ◽  
Aided Design ◽  
Boundary Surfaces

Abstract Skeleton curves and surfaces have many applications in computer aided design and analysis. Construction of skeletons is an active area of research. We consider the inverse problem that of recovering boundary surfaces from given skeleton elements. The skeleton of any 3D object will, in general, consist of curves and surfaces. Therefore, any boundary reconstruction algorithm must systematically process the surfaces generated by the skeletal curves and the skeletal surfaces. In this paper (Part I) we present algorithms for reconstructing boundary surfaces corresponding to skeletal curves. Implemented examples are also included. In a companion paper (Part II) we consider skeletal elements that are surfaces.

Boundary Surface Recovery From Skeleton Elements: Part II — Skeleton Surfaces

1992 ◽  
Author(s):  
Sean M. Gelston ◽  
Debasish Dutta
Keyword(s):  
Inverse Problem ◽  
Computer Aided Design ◽  
Boundary Surface ◽  
Reconstruction Algorithm ◽  
Companion Paper ◽  
Active Area ◽  
Curves And Surfaces ◽  
Computer Aided ◽  
Aided Design ◽  
Boundary Surfaces

Abstract Skeleton curves and surfaces have many applications in computer aided design and analysis and the construction of skeletons has been an active area of research. We consider the inverse problem that of recovering boundary surfaces from given skeleton elements. The skeleton of any 3D object will, in general, consist of curves and surfaces. Therefore, any boundary reconstruction algorithm must systematically process the surfaces generated by the skeletal curves and the skeletal surfaces. In a companion paper (Part I) we considered the reconstruction of boundaries corresponding to skeletal curves. In this paper (Part II) we consider the reconstruction of boundaries corresponding to skeletal elements that are surfaces. Implemented examples are also included.

Interference Detection of Non-Convex Solids for Manipulators

1994 ◽  
Author(s):  
Karim A. Abdel-Malek ◽  
Burton Paul
Keyword(s):  
Computer Aided Design ◽  
Analytical Study ◽  
Moving Objects ◽  
Computational Method ◽  
Interference Detection ◽  
Curved Surfaces ◽  
Multiply Connected ◽  
Points Of Interest ◽  
Intersection Points ◽  
Aided Design

Abstract When performing a computer simulation on analytical study of robot motions it is possible to unwittingly require a part of the robot (e.g. the hand) to interpenetrate (i.e. to interfere with) another part (e.g. an arm). It is therefore important to be able to predict in advance whether self interference or collision of any type occurs. This problem arises in fields of interest other than robotics, e.g. computer aided design and computer graphics. In this report, we have developed a computational method which predicts interference of moving objects in space. The method works for non-convex solids and multiply-connected solids (solids containing holes). The method checks the boundaries of surfaces enveloping solids for interference. Every pair of surfaces (one on each body) are examined for points of intersection. Points of interest are then studied to determine whether any two solids do interfere. The theory is developed for planar, ruled, and double curved surfaces.

Kinematic Synthesis for Infinitesimally and Multiply Separated Positions Using Geometric Constraint Programming

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
James P. Schmiedeler ◽  
Barrett C. Clark ◽  
Edward C. Kinzel ◽  
Gordon R. Pennock
Keyword(s):  
Undergraduate Students ◽  
Constraint Programming ◽  
Computer Aided Design ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Design Software ◽  
Aided Design

Geometric constraint programming (GCP) is an approach to synthesizing planar mechanisms in the sketching mode of commercial parametric computer-aided design software by imposing geometric constraints using the software's existing graphical user interface. GCP complements the accuracy of analytical methods with the intuition developed from graphical methods. Its applicability to motion generation, function generation, and path generation for finitely separated positions has been previously reported. By implementing existing, well-known theory, this technical brief demonstrates how GCP can be applied to kinematic synthesis for motion generation involving infinitesimally and multiply separated positions. For these cases, the graphically imposed geometric constraints alone will in general not provide a solution, so the designer must parametrically relate dimensions of entities within the graphical construction to achieve designs that automatically update when a defining parameter is altered. For three infinitesimally separated positions, the designer constructs an acceleration polygon to locate the inflection circle defined by the desired motion state. With the inflection circle in place, the designer can rapidly explore the design space using the graphical second Bobillier construction. For multiply separated position problems in which only two infinitesimally separated positions are considered, the designer constrains the instant center of the mechanism to be in the desired location. For example, four-bar linkages are designed using these techniques with three infinitesimally separated positions and two different combinations of four multiply separated positions. The ease of implementing the techniques may make synthesis for infinitesimally and multiply separated positions more accessible to mechanism designers and undergraduate students.

Function Generation With Finitely-Separated Precision Points Using Geometric Constraint Programming

2006 ◽  
Author(s):  
Edward C. Kinzel ◽  
James P. Schmiedeler ◽  
Gordon R. Pennock
Keyword(s):  
Constraint Programming ◽  
Computer Aided Design ◽  
Linear Equations ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Function Generation ◽  
Design Software ◽  
Aided Design ◽  
Four Bar Linkage ◽  
Non Linear Equations

This paper explains how Geometric Constraint Programming can be applied to solve function generation problems with finitely-separated positions using a number of different mechanisms. Geometric Constraint Programming uses the sketching mode of commercial parametric computer-aided design software to create kinematic diagrams whose elements are parametrically related so that when a parameter is changed, the design is modified automatically. Geometric constraints are imposed graphically through the user interface, and the numerical solvers integrated into the software solve the relevant systems of non-linear equations without the user explicitly formulating those equations. A key advantage of using Geometric Constraint Programming for function generation is that the same approach can be applied to any mechanism, so no unique algorithms are required. Furthermore, because the implementation is relatively straightforward regardless of the chosen mechanism, the designer can quickly and easily generate solutions for a large number of precision points and/or with complex mechanisms to provide a very accurate match to the desired function. Examples of function generation with a four-bar linkage, a six-bar linkage, and a seven-bar linkage illustrate the benefits of the proposed methodology.

Kinematic Synthesis for Infinitesimally and Multiply Separated Positions Using Geometric Constraint Programming

2011 ◽  
Author(s):  
James P. Schmiedeler ◽  
Barrett C. Clark ◽  
Edward C. Kinzel ◽  
Gordon R. Pennock
Keyword(s):  
Constraint Programming ◽  
Computer Aided Design ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Motion Generation ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Function Generation ◽  
Design Software ◽  
Aided Design

Geometric Constraint Programming (GCP) is an approach to synthesizing planar mechanisms in the sketching mode of commercial parametric computer-aided design software by imposing geometric constraints using the software’s existing graphical user interface. GCP complements the accuracy of analytical methods with the intuition developed from graphical methods. Its applicability to motion generation, function generation, and path generation for finitely separated positions has been previously reported. This paper demonstrates how GCP can be applied to kinematic synthesis for motion generation involving infinitesimally and multiply separated positions. For these cases, the graphically imposed geometric constraints alone will in general not provide a solution, so the designer must parametrically relate dimensions of entities within the graphical construction to achieve designs that automatically update when a defining parameter is altered. For three infinitesimally separated positions, the designer constructs an acceleration polygon to locate the inflection circle defined by the desired motion state. With the inflection circle in place, the designer can rapidly explore the design space using the graphical second Bobillier construction. For multiply separated position problems in which only two infinitesimally separated positions are considered, the designer constrains the instant center of the mechanism to be in the desired location. Example four-bar linkages are designed using these techniques with three infinitesimally separated positions and two different combinations of four multiply separated positions.

Model Based Rigid Body Guidance in Presence of Nonconvex Geometric Constraints

1989 ◽  
Vol 111 (4) ◽  
pp. 570-580 ◽  
Author(s):  
T. S. Ku ◽  
B. Ravani
Keyword(s):  
Rigid Body ◽  
Motion Planning ◽  
Mobile Robots ◽  
Line Segment ◽  
Efficient Algorithm ◽  
Computer Aided Design ◽  
Geometric Constraints ◽  
Model Based ◽  
Computer Aided ◽  
Aided Design

This paper presents an efficient algorithm for guidance of a convex rigid body in-between nonconvex polygonal objects in a Computer-Aided Design (CAD) environment. A shrinking procedure is used that separates the kinematic from the shape constraints by reducing the problem to that of guidance of a line segment in an expanded environment. A slicing technique together with an algorithm for decomposition of the interface channel between the nonconvex objects is used to generate the motion program for the line segment. The results can be applied to model based guidance of mobile robots or automatic motion planning for robot manipulators.

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