Linear Properties of the RPRP Overconstrained Mechanism

• Main Authors: Han-Chung Tu, 涂翰宗
• Other Authors: Chin-Tien Huang
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/c75mhs

碩士 === 國立成功大學 === 機械工程學系碩博士班 === 90 === Abstract Screw is a concise mathematical model for describing rigid body motion in space. The displacement of a rigid body can be described as the combination of a rotation about an axis and a translation along the same axis, which is called a screw motion. A screw system is a set of screws closed under addition and scalar multiplication. Recently, by using a new definition of pitch, screws of finite displacements have been proved to have linear properties and form screw systems. This thesis investigates the linear properties of the R-P-R-P overconstrained linkage. An overconstrained linkage possesses mobility over a finite range of motion even though it violates the Kutzbach mobility criterion. One of the simplest overconstrained mechanisms is the spatial R-P-R-P linkage. This thesis investigates the linear properties of the finite displacements of the spatial R-P-R-P linkage. First, the input/output relations of the R-P-R-P linkage are derived. Second, the linear representation of the screw triangle is applied to obtain the finite displacement screws of the coupler of the linkage. Third, by using linear algebra, the analytic solution of the finite twist is obtained. Finally, the rank of the matrix consisting of the screws is calculated to investigate the linear properties of the finite screws. By adopting Yu’s tetrahedron model to identify the Bennett linkage, we redefine the coordinate system of the spatial R-P-R-P linkage by establishing similar geometry. This thesis demonstrates that the finite screws of the coupler of spatial R-P-R-P linkage form a two-system. We also show that the R-P-R-P linkage has two configurations. Both types of R-P-R-P linkages are shown to possess linear properties. Numerical examples are provided to verify the results.