Kinematics-Based Geometric Design of Sculptured Surfaces

1996 ◽  
Author(s):  
Q. J. Ge ◽  
Donglai Kang
Keyword(s):  
Geometric Modeling ◽  
Tool Path ◽  
Geometric Design ◽  
Geometric Shape ◽  
Shape Design ◽  
Path Generation ◽  
Sculptured Surfaces ◽  
Computer Aided ◽  
Cad Cam ◽  
Cad Models

Abstract Current practice in CAD/CAM separates the process of geometric shape design from that of CMC (Computer Numerically Controlled) tool path generation. Although successful for 3-axis machining, this strategy is not as effective for 5-axis machining of sculptured surfaces due to the difficulty in generating accurate and gouge-free 5-axis tool paths from the CAD models. This paper presents a framework for a new, kinematics-based methodology for geometric modeling that integrates sculptured-surface design with too-path generation for 5-axis CMC machining. In particular, sculptured surfaces are represented directly in terms of rational Bézier and B-spline motions of the cutting tool. The proposed framework brings together the fields of Kinematics and Computer Aided Geometric Design as well as the recent results in Computer Aided Motion Synthesis and Swept Volume Modeling and provides a basis for concurrent geometric shape design and manufacture.

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.

Parametric Continuity and Smooth Motion Interpolation

1995 ◽  
Author(s):  
Lakshmi N. Srinivasan ◽  
Q. J. Ge
Keyword(s):  
Mechanical Systems ◽  
Trajectory Generation ◽  
Geometric Design ◽  
Second Derivative ◽  
Computer Aided Geometric Design ◽  
Smooth Motion ◽  
Computer Aided ◽  
Cad Cam ◽  
C2 Continuity ◽  
Parametric Continuity

Abstract This paper deals with the design of a second derivative continuous (C2) motion that interpolates through a given set of configurations of an object. It derives conditions for blending two motion segments with C2 continuity and develops an algorithm for constructing a C2 composite Bézier type motion that has similarities to Beta-splines in the field of Computer Aided Geometric Design. A criteria for evaluating the smoothness of motion is established and is used to synthesize “globally smooth” motions. The results have applications in trajectory generation in robotics, mechanical systems animation and CAD/CAM.

HSM Strategies of CAD/CAM Systems — Part I Tool Path Generation

2010 ◽  
Vol 426-427 ◽  
pp. 520-524 ◽  
Author(s):  
Song Lin Ding ◽  
John Mo ◽  
D. Yang
Keyword(s):  
High Speed ◽  
Metal Cutting ◽  
Tool Path ◽  
Tool Path Generation ◽  
Path Generation ◽  
Cnc Machine ◽  
Technical Requirements ◽  
Cad Cam ◽  
High Feed ◽  
Cutting Processes

Owning to the ultra high feed rate and spindle speed, tool path patterns which are less important in conventional metal cutting processes becomes critical in High Speed Machining (HSM). Without an appropriate tool path strategy HSM can not be fully implemented even though the CNC machine has HSM potentials. In practice attentions are usually drawn to advanced hardware components; tool path pattern catering to HSM is often overlooked. This paper introduces the principles of tool path generation for HSM. Essential properties of HSM and its technical requirements on the CAD/CAM system are summarized. The state-of-the-art technologies and practice-oriented tool path generation methodologies are presented.

Parametric Continuous and Smooth Motion Interpolation

1996 ◽  
Vol 118 (4) ◽  
pp. 494-498 ◽  
Author(s):  
L. N. Srinivasan ◽  
Q. J. Ge
Keyword(s):  
Mechanical Systems ◽  
Trajectory Generation ◽  
Second Order ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Smooth Motion ◽  
Computer Aided ◽  
Cad Cam ◽  
C2 Continuity

This paper deals with the synthesis of a second order parametrically continuous (C2) motion that interpolates through a given set of configurations of an object. It derives conditions for blending two motion segments with C2 continuity and develops an algorithm for constructing a C2 composite Be´zier type motion that has similarities to Beta-splines in the field of Computer Aided Geometric Design. A criterion for evaluating the smoothness of a motion is established and is used to synthesize a “globally smooth” motion. The results have applications in trajectory generation in robotics, mechanical systems animation and CAD/CAM.

An Approach for Generating Variational Geometry of a Pattern of Holes With Composite Positional Tolerances

2002 ◽  
Author(s):  
Y. S. Liu ◽  
S. M. Gao
Keyword(s):  
Mathematical Models ◽  
Geometric Modeling ◽  
Mechanical Design ◽  
Cad Systems ◽  
Computer Aided ◽  
Cad Cam ◽  
Positional Tolerance

In most present CAD systems, the accurate geometry representation of a part is given but the tolerance is just a text attribute without semantics. It hampers the integration of CAD/CAM. In last two decades, much research has been conducted on computer aided tolerancing. And many approaches to generation of variational geometry for various kinds of features have been given. However how to generate the variational geometry of a pattern of holes (POH) is not well studied yet although a POH is one of the most widely-used features in mechanical design. Based on DOF, an approach is proposed for generating variational geometry of a POH with composite positional tolerance in this paper. First, the limitation conditions for variations of a POH are given. Second, the mathematical models of translational and rotational variations are systematically derived. Then the algorithm for generating variational geometry of a POH is given. At last the proposed approach has been implemented with Visual C++ based on the geometric modeling kernel ACIS5.0.

Sign in / Sign up

Export Citation Format

Share Document