文档介绍：Available online at hanism
and
Machine Theory
Mechanism and Machine Theory 43 (2008) 50–56
ate/mechmt
The correspondence between finite screw systems
and projective spaces
Chintien Huang a,*, Koichi Sugimoto b, Ian Parkin c
a Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan
b Department of Mechanical Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan
c School of Information Technologies, University of Sydney, Sydney, Australia
Received 1 December 2005; received in revised form 19 July 2006; accepted 9 January 2007
Available online 13 March 2007
Abstract
This paper discusses the correspondence between vector subspaces and screw systems. The goal is to differentiate finite
screw systems from screw systems arising in instantaneous kinematics and statics. This paper shows that a finite screw sys-
tem corresponds to the projective space associated with the vector subspace spanned by the basis screws of the screw sys-
tem. As a result, if finite displacement screws of a body constitute a screw system, the number of degrees of freedom of the
motion of the body is one less than the order of the screw system.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Finite displacement; Screw theory; Finite screw system; Vector subspace; Projective space
1. Introduction
Many mathematical methods, such as dual