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CAD/CAM ALGORITHM OF RULED SURFACE BASED ON line geometry

Chinese Journal of Mechanical Engineering 1998年第3期11卷 44-48页

作者： Hu Zhanqi Cui Yunqi Qiao Lei Li Yupeng Mechanical Engineering Institute, Yanshan University Yanshan Univ China

A new concept of design and manufacturing of ruled surface based on line geometry is proposed. Some practical algorithm for CAD system is derived. Some problems in design and manufacturing of ruled surface can be solv... 详细信息

关键词： Ruled surface line geometry Wire cut EDM

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AFFINE SPINOR DECOMPOSITION IN THREE-DIMENSIONAL AFFINE geometry

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Acta Mathematica Scientia 2022年第6期42卷 2301-2335页

作者： Chengran WU Hongbo LI Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China Academy of Mathematics and Systems Science University of Chinese Academy of SciencesChinese Academy of SciencesBeijing 100190China

Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and *** threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line *** this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.

关键词： spin group spinor decomposition affine transformation line geometry afine line reflection

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Conditions for Parallel Realizable Configurations in Synthesis of Constraint-based Flexure Mechanisms

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Chinese Journal of Mechanical Engineering 2012年第6期25卷 1086-1095页

作者： LI Shouzhong, YU Jingjun*, and ZONG Guanghua Robotics Institute, Beihang University, Beijing 100191, China 1. Robotics Institute Beihang University Beijing 100191 China

In synthesis of flexure mechanism, parallel arrangement is paid more attention due to its advantages, such as compact structure and higher stiffness. Researchers have derived many parallel flexure mechanisms, but seldom discuss which kind of flexure mechanism can be realized via fully parallel arrangement. The realizable conditions proposed in current work are complicated to engineering applications. To solve two problems on how to judge whether a flexure mechanism can be realized via fully parallel arrangement and how to realize those flexure mechanisms which cannot be realized via fully parallel arrangement, the algebraic condition is derived to judge whether a freedom space is parallel realizable after introducing the definition of parallel realizable and some propositions, and the condition is there exist 6-n independent line constraints in constraint space reciprocal to dimensional freedom space. Then the realizable constraint spaces reciprocal to freedom spaces with 1-3 dimensions are provided. As a result, not all freedom spaces are parallel realizable. For freedom spaces that are not parallel realizable, the criterion of decomposing DOF is proposed to achieve all motion patterns via parallel or hybrid arrangement, that is a high dimensional freedom space can be realized via combining several low dimensional freedom spaces which are parallel realizable. Specific decomposing strategies for 4 and 5 DOF are provided and a complete flowchart is presented to guide designing flexure mechanisms, particularly those which are not parallel realizable. As case studies, synthesis processes of two helical and 3T1R motions are provided to illustrate the proposed approach. The proposed method provides a feasible approach to realize all motion patterns.

关键词： flexure mechanism type synthesis screw theory line geometry constraint design

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The Exact Representation for the Intersection of Ruled Surface with a Plane

International Journal of Systems and Control

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International Journal of Systems and Control 2008年第3期 146-157页

作者： CHIANG Ching-Shoei Department of Computer and Information Science Soochow University 56

This article presents an efficient and robust algorithm that compute the intersection curve of a ruling surface with a plane. These ruling surface is represented by S(s,t)=B(t)+sV(t) where B(t) is the degree n directrix of S and V(t) is the degree m ruling direction. We proved that the intersection curve of S(s,t) with a plane ax+by+cz+d=0 is a rational Bezier curve with degree m+n. We further find the weight and control points for the intersection curves. Finally, we give two more algorithms to find the intersection point of a ruling surface with a line, and check whether a point p is on the surface S.

关键词： ruled surface surface/surface intersection line geometry variable elimination

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