Computer-Aided Design With Spatial Rational B-Spline Motions

1996 ◽  
Vol 118 (2) ◽  
pp. 193-201 ◽  
Author(s):  
B. Ju¨ttler ◽  
M. G. Wagner
Keyword(s):  
Computer Animation ◽  
Computer Aided Design ◽  
Control Structure ◽  
Basic Theory ◽  
Linear Control ◽  
Geometry Processing ◽  
B Spline ◽  
Computer Aided ◽  
Interpolation Techniques ◽  
Aided Design

Using rational motions it is possible to apply many fundamental B-spline techniques to the design of motions. The present paper summarizes the basic theory of rational motions and introduces a linear control structure for piecewise rational motions suitable for geometry processing. Moreover it provides algorithms for the calculation of the surface which is swept out by a moving polyhedron and examines interpolation techniques. The methods presented in this paper can be applied to various problems in computer animation as well as in robotics.

Computer Aided Geometric Design of Two-Parameter Freeform Motions

1999 ◽  
Vol 121 (4) ◽  
pp. 502-506 ◽  
Author(s):  
Q. J. Ge ◽  
M. Sirchia
Keyword(s):  
Computer Aided Design ◽  
Control Structure ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Kinematic Control ◽  
Computer Aided ◽  
Cad Cam ◽  
Aided Design ◽  
Two Parameter ◽  
And Robotics

This paper brings together the notion of analytically defined two-parameter motion in Theoretical Kinematics and the notion of freeform surfaces in Computer Aided Geometric Design (CAGD) to develop methods for computer aided design of two-parameter freeform motions. In particular, a rational Be´zier representation for two-parameter freeform motions is developed. It has been shown that the trajectory surface of such a motion is a tensor-product rational Be´zier surface and that such a kinematically generated surface has a geometric as well as a kinematic control structure. The results have not only theoretical interest in CAGD and kinematics but also applications in CAD/CAM and Robotics.

Review on Non Uniform Rational B-Spline (NURBS): Concept and Optimization

2014 ◽  
Vol 903 ◽  
pp. 338-343
Author(s):  
Ali Munira ◽  
Nur Najmiyah Jaafar ◽  
Abdul Aziz Fazilah ◽  
Z. Nooraizedfiza
Keyword(s):  
Image Processing ◽  
Literature Review ◽  
Computer Aided Design ◽  
B Spline ◽  
B Splines ◽  
Curves And Surfaces ◽  
Geometry Design ◽  
Nurbs Curves ◽  
Computer Aided ◽  
Aided Design

This paper is to provide literature review of the Non Uniform Rational B-Splines (NURBS) formulation in the curve and surface constructions. NURBS curves and surfaces have a wide application in Computer Aided Geometry Design (CAGD), Computer Aided Design (CAD), image processing and etc. The formulation of NURBS showing that NURBS curves and surfaces requires three important parameters in controlling the curve and also modifying the shape of the curves and surfaces. Yet, curves and surfaces fitting are still the major problems in the geometrical modeling. With this, the researches that have been conducted in optimizing the parameters in order to construct the intended curves and surfaces are highlighted in this paper.

Ideal Compliant Joints and Integration of Computer Aided Design and Analysis

2014 ◽  
Author(s):  
Ashraf M. Hamed ◽  
Paramsothy Jayakumar ◽  
Michael D. Letherwood ◽  
David J. Gorsich ◽  
Antonio M. Recuero ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Large Scale ◽  
Algebraic Equations ◽  
B Spline ◽  
Constraint Equations ◽  
Compliant Joints ◽  
Linear Algebraic Equations ◽  
Dependent Variables ◽  
Computer Aided ◽  
Aided Design

This paper discusses fundamental issues related to the integration of computer aided design and analysis (I-CAD-A) by introducing a new class of ideal compliant joints that account for the distributed inertia and elasticity. The absolute nodal coordinate formulation (ANCF) degrees of freedom are used in order to capture modes of deformation that cannot be captured using existing formulations. The ideal compliant joints developed can be formulated, for the most part, using linear algebraic equations, allowing for the elimination of the dependent variables at a preprocessing stage, thereby significantly reducing the problem dimension and array storage needed. Furthermore, the constraint equations are automatically satisfied at the position, velocity, and acceleration levels. When using the proposed approach to model large scale chain systems, differences in computational efficiency between the augmented formulation and the recursive methods are eliminated, and the CPU times resulting from the use of the two formulations become similar regardless of the complexity of the system. The elimination of the joint constraint equations and the associated dependent variables also contribute to the solution of a fundamental singularity problem encountered in the analysis of closed loop chains and mechanisms by eliminating the need to repeatedly change the chain or mechanism independent coordinates. It is shown that the concept of the knot multiplicity used in computational geometry methods, such as B-spline and NURBS (Non-Uniform Rational B-Spline), to control the degree of continuity at the breakpoints is not suited for the formulation of many ideal compliant joints. As explained in this paper, this issue is closely related to the inability of B-spline and NURBS to model structural discontinuities. Another contribution of this paper is demonstrating that large deformation ANCF finite elements can be effective, in some MBS application, in solving small deformation problems. This is demonstrated using a heavily constrained tracked vehicle with flexible link chains. Without using the proposed approach, modeling such a complex system with flexible links can be very challenging. The analysis presented in this paper also demonstrates that adding significant model details does not necessarily imply increasing the complexity of the MBS algorithm.

Computer-Aided Design of Curved Surfaces With Automatic Model Generation

1982 ◽  
Vol 104 (4) ◽  
pp. 817-824 ◽  
Author(s):  
S. M. Staley ◽  
R. B. Jerard ◽  
P. R. White
Keyword(s):  
Computer System ◽  
Computer Aided Design ◽  
Three Dimensional ◽  
Model Generation ◽  
Curved Surfaces ◽  
B Spline ◽  
Three Dimensional Objects ◽  
Computer Aided ◽  
Automatic Model Generation ◽  
Aided Design

The design and visualization of three-dimensional objects with curved surfaces have always been difficult. This paper describes a computer system that facilitates both the design and visualization of such surfaces. The system enhances the design of these surfaces by virtue of various interactive techniques coupled with the application of B-Spline theory. Visualization is facilitated by including a specially built model-making machine that produces three-dimensional foam models. Thus the system permits the designer to define an object and, with little additional effort, produce an inexpensive model of the object which is suitable for evaluation and presentation.

Ideal Compliant Joints and Integration of Computer Aided Design and Analysis

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Ashraf M. Hamed ◽  
Paramsothy Jayakumar ◽  
Michael D. Letherwood ◽  
David J. Gorsich ◽  
Antonio M. Recuero ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Processing Unit ◽  
B Spline ◽  
Constraint Equations ◽  
Central Processing ◽  
Compliant Joints ◽  
Linear Algebraic Equations ◽  
Dependent Variables ◽  
Computer Aided ◽  
Aided Design

This paper discusses fundamental issues related to the integration of computer aided design and analysis (I-CAD-A) by introducing a new class of ideal compliant joints that account for the distributed inertia and elasticity. The absolute nodal coordinate formulation (ANCF) degrees of freedom are used in order to capture modes of deformation that cannot be captured using existing formulations. The ideal compliant joints developed can be formulated, for the most part, using linear algebraic equations, allowing for the elimination of the dependent variables at a preprocessing stage, thereby significantly reducing the problem dimension and array storage needed. Furthermore, the constraint equations are automatically satisfied at the position, velocity, and acceleration levels. When using the proposed approach to model large scale chain systems, differences in computational efficiency between the augmented formulation and the recursive methods are eliminated, and the central processing unit (CPU) times resulting from the use of the two formulations become similar regardless of the complexity of the system. The elimination of the joint constraint equations and the associated dependent variables also contribute to the solution of a fundamental singularity problem encountered in the analysis of closed loop chains and mechanisms by eliminating the need to repeatedly change the chain or mechanism independent coordinates. It is shown that the concept of the knot multiplicity used in computational geometry methods, such as B-spline and NURBS (nonuniform rational B-spline), to control the degree of continuity at the breakpoints is not suited for the formulation of many ideal compliant joints. As explained in this paper, this issue is closely related to the inability of B-spline and NURBS to model structural discontinuities. Another contribution of this paper is demonstrating that large deformation ANCF finite elements can be effective, in some multibody systems (MBS) applications, in solving small deformation problems. This is demonstrated using a heavily constrained tracked vehicle with flexible-link chains. Without using the proposed approach, modeling such a complex system with flexible links can be very challenging. The analysis presented in this paper also demonstrates that adding significant model details does not necessarily imply increasing the complexity of the MBS algorithm.

Program Package for Computer Aided Design of Linear Control Systems

1979 ◽  
Vol 12 (7) ◽  
pp. 319-324
Author(s):  
M.M. Konstantinov ◽  
S.P. Patarinski ◽  
P.Hr. Petkov ◽  
N.D. Christov
Keyword(s):  
Control Systems ◽  
Computer Aided Design ◽  
Program Package ◽  
Linear Control ◽  
Linear Control Systems ◽  
Computer Aided ◽  
Aided Design

AN ALGORITHM TO CONSTRUCT THE CAD MODEL OF A RESIDUAL LIMB

2001 ◽  
Vol 13 (03) ◽  
pp. 149-158 ◽  
Author(s):  
LAI-HSING HSU ◽  
FU-MEI HSU ◽  
YOU-LI CHOU ◽  
JU-YI HSU ◽  
HANG LEONG ◽  
...  
Keyword(s):  
Computer Aided Design ◽  
Numerical Control ◽  
Prototype System ◽  
Cad Model ◽  
Residual Limb ◽  
Cnc Machine ◽  
B Spline ◽  
Spline Curve ◽  
Computer Aided ◽  
Aided Design

A duplicated mold of the residual limb of an amputee is usually needed to make the socket of prosthesis for the patient. However, traditional means to duplicate a positive mold is time-consuming, patient suffering and intensive manual-efforts required. The study has developed a prototype system that allows a prosthetist to construct the computer-aided design(CAD) model of residual limb easily using it's digitized points based on the concept of reverse engineering. First of all, the topographic data of a residual limb is captured using a non-intrusive scanning machine. The scanned data is then used as the input of a self-developed system that is based on the theories of B-spline curve and lofted surface to process the digitized points. The CAD model can then be built and transferred to a computer-aided manufacturing(CAM) system to generate the code for a computer numerical control(CNC) machine to make the duplicated mold of the residual limb.

Representation of Developable Surfaces and Achievement of the Algorithm

2006 ◽  
Vol 532-533 ◽  
pp. 813-816
Author(s):  
Min Zhou ◽  
Zheng Lin Ye ◽  
Guo Hua Peng ◽  
Yun Qing Yang ◽  
Hong Chan Zheng
Keyword(s):  
Efficient Method ◽  
Computer Aided Design ◽  
Control Parameter ◽  
Geometric Design ◽  
B Spline ◽  
Developable Surfaces ◽  
Computer Aided ◽  
Aided Design ◽  
Traditional Approaches

In order to overcome the difficulties in representation of developable surfaces utilizing traditional approaches, and resolve the problems in adjusting and controlling the position and shape of developable surfaces that often faced in Engineering. In this paper, we propose a directly explicit and efficient method of computer-aided design for developable surfaces based on triangle-B spline. The shapes of developable surfaces can be adjusted using a control parameter. Meanwhile, we show that the techniques for the geometric design of developable surfaces in this paper have all the characteristics of existing approaches for curves design. The algorithms are explained in detail, and demonstrated with the examples in the paper.

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