Time-dependent reliability-based dimensional synthesis for planar linkages with unknown but bounded joint clearances

Linkage mechanisms are typically designed to generate a specific functional relationship or path. Because the uncertain dimensions and joint clearances severely affect the output motion accuracy, designers urgently need a reliability-based design approach with high confidence and efficiency. However, the traditional kinematic reliability synthesis, which focuses on several discrete time points, cannot satisfy the accuracy requirement over a continuous time interval. Accordingly, to ensure high accuracy over a time period, this study presents a reliability synthesis approach that considers the time-dependency effect of motion error. The exact statistical characteristics of clearances and dimensions may be unavailable because of the limited sample information in practical engineering. Thus, by qualifying the uncertainties as unknown but bounded variables, the time-dependent reliability index is assessed based on a combination of the nonprobabilistic interval process and first-passage theories. Two engineering examples are presented to demonstrate the validity and applicability of the developed methodology.