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论文类型：期刊论文

发表时间：2019-12-01

发表刊物：MECHANISM AND MACHINE THEORY

收录刊物：EI、SCIE

卷号：142

ISSN号：0094-114X

关键字：The special Euclidean group; Exponential map; Multi-parameter family; Envelope theory

摘要：This paper is mainly divided into three parts. In the first part, we give the descriptions of the bases of two and three dimensional Lie subalgebras of se(3). In the second part, we construct submanifolds of SE(3) via several two and three dimensional Lie subalgebras of se(3). In the final part, we focus on the multi-parameter families of curves in E-3 generated by actions of the constructed submanifolds of SE(3) on a segment of curve. The geometrical properties of the envelopes of these families of curves are further studied and the expressions of Gauss and mean curvatures in each case are given. (C) 2019 Elsevier Ltd. All rights reserved.