Citation:
Zhang Qunli, Huang Jun, Cheng Jian, Lin Taotao. Lie Group and Lie Algebra Method in Architectural Geometric Modeling. Journal of Information Technologyin Civil Engineering and Architecture,
2014, 6(1): 29-36,50.
2014, 6(1): 29-36,50.
Lie Group and Lie Algebra Method in Architectural Geometric Modeling
ZheJiang Prov. Institute of Architectural Design and Research, Hangzhou 310006, China |
Lie group and Lie algebra theory have wide application in robot mechanism. Continuous motion of the rigid body in E3 corresponding to a continuous curve in SE (3) of Lie group. Motion screw is the Lie algebra element in SE (3) of Lie group and integrates rigid motion with SE (3) of Lie group. Constructing the forward motion index product formula of serial robot based on exponential map and rigid body motion superposition theorem, thereby resolving expression of virtual rigid body motion. The edge of rigid body sweeps a curved surface in E3 space with space motion of the rigid body. Finally, obtaining building geometry swept surface which can be expressed by nurbs and corresponding to rigid motion by using computer graphics and geometric modeling approaches.
| [1] |
赵旭安.李群和李代数[M].北京师范大学出版集团.2012.9 |
| [2] |
丁汉, 朱利民.复杂曲面数字化制造的几何学理论和方法[M].北京:科学出版社, 2011. |
| [3] |
项武义, 候自新, 孟道骥.李群讲义[M].北京大学出版社.1992.6 |
| [4] |
胡茂林.空间和变换[M].科学出版社.2007.6 |
| [5] |
Jerrold E. Marsden, Tudor S. Ratiu著(译者: 王丽瑾刘学深). 力学和对称性导论[M]. 清华大学出版. 2006. 8 |
| [6] |
(美)理查德. 摩雷, (中)李泽湘, (美)夏恩卡. 萨思特里著(译者: 徐卫良, 钱瑞明). 机器人操作的数学导论[M]. 机械工业出版社. 1989. 6 |
| [7] |
于靖军, 刘辛军, 丁希伦, 戴建生.机器人机构学的数学基础[M].机械工业出版社.2009.4 |
| [8] |
黄俊, 张群力, 程健, 冯武强.莫比乌斯环面上的建筑结构数字建模[M].杭州:浙江建筑2013.7 |
| [9] |
绳圈的数学[M]. 姜伯驹, 大连理工大学出版社. 大连. 2011. 5 |
| [10] |
丁希伦. 空间弹性变形构件的李群李代数分析方法[J]. 机械工程学报. 第41卷第1期, 2005. 1 |
| [11] |
丁希伦, 刘颖. 用李群李代数分析具有空间柔性变形杆件的机器人动力学[J]. 机械工程学报. 第43卷第12期. 2007. 12 |
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