Synthesis and analysis of spherical five-bar linkages and adjustable four-bar linkages with applications

The synthesis and analysis of adjustable spherical linkages and spherical five-bar linkages are the focus of this research. The applications of these types of linkages are scarce. This dissertation also has an emphasis on design applications.; New methods to synthesize adjustable linkages are developed. Two types of adjustment are discussed: (1) adjustable link lengths, and (2) adjustable ground pivot locations. A new concept of Burmester curves for adjustable linkages is introduced. The characteristics of these Burmester curves are investigated. This concept also leads to a new method for five-position synthesis of non-adjustable linkages.; The range of motion of spherical five-bar linkages and the rotatability of the input angles are investigated. Two new theorems are created to determine the rotatability of each input angle. A procedure is developed to classify spherical linkages based on rotatability, and to calculate the range of rotation when input angles are not rotatable. A new kinematic index is created to quantify the workspace of the spherical linkages.; Jacobian matrixes are derived from the displacement and velocity analysis. Based on the definition of matrix norm and condition number for Jacobian matrix, the absolute displacement error index and the relative velocity error index are created. A procedure is also established to evaluate errors from all sources.; The above synthesis theories are applied to three examples: Adjustable spherical four-bar linkages are used to design continuous passive motion (CPM) machines for ankle joint rehabilitation; A novel mechanical digitizer is designed with spherical five-bar linkages; An anticoagulant medication delivery system is designed based on spherical five-bar linkages.