Synthesis and Application of Reduced-Dimension Optimization for Rigid-Body Guidance of Stephenson-III Six-Bar Linkages on the Basis of Fourier Harmonic Characteristics

Abstract Rigid-body guidance synthesis of linkages must satisfy the requirements of position and posture simultaneously, which increases the difficulty of dimensional synthesis. Extraction of harmonic characteristic parameters via a Fourier series to describe the output motion of the linkage, followed by rigid-body guidance synthesis, is a simple and efficient approach. However, current research on this method has focused mainly on four-bar linkages and simple spherical and spatial mechanisms. There is less research on six-bar linkages, primarily due to the large number of design parameters, the complexity of the motion output, and the difficulty of dimensional synthesis. This article establishes a reduced-dimension optimization synthesis method for rigid-body guidance of the Stephenson-III six-bar linkage on the basis of Fourier harmonic characteristics. The optimization variables do not include the installation dimensions, allowing for the optimization space to be reduced by four dimensions, thereby reducing the optimization complexity. Constraints such as the link length nonnegativity condition, the crank existence condition, the transmission angle condition, and the link length ratio condition are established to ensure the feasibility of the final solution. Finally, on the basis of the task poses at the human ankle joint, a single-degree-of-freedom (DOF) end-traction Stephenson-III six-bar gait rehabilitation training mechanism was synthesized and designed via the proposed rigid-body guidance synthesis method. The trajectory and posture angle curves generated by the prototype experiment were essentially consistent with the theoretical design, verifying the correctness of the theoretical design method and manufacturing assembly as well as the feasibility of the rehabilitation training program.