The Principal Pitches and Principal Screws of Screw Systems
首发时间:2009-02-10
Abstract:This paper investigates the principal screws and their pitches of screw systems from the viewpoint of line geometry. It starts from the fact that any independent screws pertaining to a specified -screw system can be utilized to determine the system, and the pitch of a unit screw is the half of the reciprocal product with itself. Therefore, the pitch of any screw of a screw system can be represented by a homogeneous quadratic form of the linear combination coefficients. As a matter of fact, the homogeneous quadratic equation of the pitch of a screw system represents a conic curve in two-system and an ellipsoid or a hyperboloid in three-system. The reciprocal product matrix of a screw matrix is then defined to determine the principal pitches and the directions of the principal screw axes of the system. By matrix diagonalization, one can ultimately obtain the principal pitches and the principal screws.
keywords: Screw Theory Principal Pitch Principal Screw Reciprocal Product Matrix Matrix Diagonalization
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The Principal Pitches and Principal Screws of Screw Systems
摘要:This paper investigates the principal screws and their pitches of screw systems from the viewpoint of line geometry. It starts from the fact that any independent screws pertaining to a specified -screw system can be utilized to determine the system, and the pitch of a unit screw is the half of the reciprocal product with itself. Therefore, the pitch of any screw of a screw system can be represented by a homogeneous quadratic form of the linear combination coefficients. As a matter of fact, the homogeneous quadratic equation of the pitch of a screw system represents a conic curve in two-system and an ellipsoid or a hyperboloid in three-system. The reciprocal product matrix of a screw matrix is then defined to determine the principal pitches and the directions of the principal screw axes of the system. By matrix diagonalization, one can ultimately obtain the principal pitches and the principal screws.
关键词: Screw Theory; Principal Pitch; Principal Screw; Reciprocal Product Matrix; Matrix Diagonalization.
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