Analysis and synthesis of mechanical error in path generating linkages based on reliability

In this paper, the reliability of linkage mechanisms for path generation is defined as the probability with which a coupler point of the mechanism will generate its intended design motion with specified precision. A reliability-based analysis approach to mechanical error for the path generation mechanisms is presented. The reliability index is taken as a measure for the deviation of the actual path of the coupler point from the desired one. A reliability-based synthesis procedure of the mechanical error for path generating linkages to allocate optimal tolerances and clearances is developed. Reliability synthesis of mechanisms is formulated as a deterministic optimization problem by taking cost minimization as an objective function, reliability indexes as constraints and the tolerances and clearances as design variables. The presented procedure can help designers to compute optimal assignments of manufacturing tolerances and clearances to individual link dimensions and moving hinges which give the desired mechanism reliability while minimizing the overall cost. Finally, a four-bar path generating mechanism is considered for numerical illustration.