Mobility identification and rectification of planar multiloop mechanisms

Mobility identification is a common problem frequently encountered in linkage analysis and synthesis. Mobility of linkages, i.e., assembly mode, refers to the problems related to branch (or continuity) defect, sub-branch (or singularity) defect, full rotatability, and order of motion. Mobility analysis becomes much more complex not only in single degree-of-freedom (DOF) multiloop planar linkages but also in multiple-DOF planar linkages. This dissertation was to establish a systematical and automated mobility identification approach to treat these issues. The mobility theory gained from this study will offer the essential support to the synthesis and programming of complex linkage manipulators and definitely benefit to the automated computer-aided linkage design.;This study presented the first successful attempt that extends the discriminant method to the mobility analysis of non-bimodal linkages. The singularity condition and the joint rotation space (JRS) were expressed and identified by the discriminant functions. The method was algebraic and the discriminant function was derived based on the form of equations essential for the displacement analysis of the linkage. It is applicable to any single-DOF planar and spherical double-loop linkages regardless the choice of the input, output, or fixed link. It is also applicable to spatial linkages with the similar displacement equation form. Later, the method was extended for the mobility identification of a group of single-DOF planar eight-bar linkages. A complete and automated mobility identification method was presented for the first time and thus it may represent a breakthrough on the recognition and understanding of complex linkage mobility in higher group. Based on the concept of JRS, this study also proposed a unified treatment for the full rotatability identification and singularity of six-bar and geared five-bar linkages and a unified method for the mobility identification of any planar and spherical six-bar linkages.;Based on the concept of JRS, the branches, sub-branches of the two-DOF seven-bar linkages were solved. A unified method to treat the singularity of the planar two-DOF seven-bar linkages was offered and it can be extended for the singularity analysis of other multiple-DOF multiloop planar linkages. For multiloop parallel manipulators, this research may represent the first mobility analysis method that cannot only decisively and unambiguously rectify motion continuity between discrete positions but also provide clear geometric insight or interpretation regarding the formation of branch, singularity and sub-branch of the two-DOF seven-bar linkages. It casts light for the mobility analysis of other multiple-DOF multiloop linkages.