Synthesis of Spatial RCCC and 4C Linkages for Line-Angle Problems

• Main Authors: Ching-LungLai, 賴慶隆
• Other Authors: Chintien Huang
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/43473336013744981019

碩士 === 國立成功大學 === 機械工程學系碩博士班 === 98 === This thesis deals with the spatial generalizations of two classical planar synthesis problems: the path generation and point-angle problems. The planar path generation problem involves the guidance of a point through specified positions by using planar four-bar linkages. If we are also concerned with the changes of crank angles when guiding the point, it becomes a point-angle problem. In spatial generalizations, we are concerned with the guidance of a line by using spatial 4C linkages. The coupler curve of the 4C and RCCC linkage have been investigated recently. However, they were generated by coupler points of the linkages. This thesis takes a different approach by considering a coupler line because a point in planar linkages corresponds to a line in spatial linkages. The equivalent screw triangle is employed to derive the synthesis equations of the spatial 4C linkage. The synthesis of the RCCC linkage is achieved by constraining the translational motion in the driving C joint of the 4C linkages. We also employ the D-H transformation matrices to derive the coupler surface of the 4C and RCCC linkages. Our results show that the synthesis of the 4C linkage for line guidance yields the same maximum number of positions as the planar 4-bar linkage for point guidance. The maximum number of positions of the path generation of a line is nine, while that of the line-angle problem is five. Furthermore, the maximum number of positions in the synthesis of the RCCC linkage for line guidance and line-angle problem are five and six, respectively. In addition, the locus of the coupler line of a RCCC linkage is a ruled surface, while that of a 4C linkage is a line complex. The numerical results obtained in the thesis are verified by using SolidWorks. In addition to presenting the spatial generalizations of planar synthesis problems, the results provided in this paper can be used in the design of spatial four-bar linkages to match line specifications, in which only an infinitely-extended line, such as a laser beam, is of interest.