Line Geometry of the Finite Screw Systems Associated with Spatial Linkages

• Main Authors: Tzu-cheng Hsing, 邢資正
• Other Authors: Chintien Huang
• Format: Others
• Language: zh-TW
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/58103210888877492643

碩士 === 國立成功大學 === 機械工程學系碩博士班 === 95 === Screw is very useful in describing rigid body motion in space. The displacement of a rigid body can be described as the combination of a rotation about a screw axis and a translation along the same axis. A screw system is a set of screws closed under addition and scalar multiplication. In instantaneous kinematics, infinitesimal twists have linear properties and form screw systems. By using new definitions of pitch, some screws of finite displacement also have linear properties and form screw systems. Specific correspondence between screw theory and line geometry enables us to study spatial kinematics using line geometry. A set of lines formed by the linear combination of five independent lines is called a linear line complex, which contains lines. Furthermore, a linear line complex is reciprocal to a screw that describes a rigid body motion. Namely, the screw and every line in the linear line complex conform to the reciprocal condition. This thesis shows that the line geometric figure obtained from the intersection of linear line complexes corresponds to a screw system. This thesis finds the line geometric figure corresponding to the infinitesimal screw system of the coupler of a 7R linkage by using intersection of linear line complexes. Then the geometric figures corresponding to the finite screw systems of the coupler of the Bennett 4R and RPRP overconstrained linkages are investigated. This thesis precisely presents the relations between spatial mechanisms and corresponding line geometric figures by CAD software. Furthermore, this thesis develops an approach to fit the line geometric figure of a closed-loop mechanism by using of the line geometric figures of related open chains.