Stochastic approach to kinematic reliability of open-loop mechanism with dimensional tolerance

Open-loop mechanisms are usually employed in industrial applications to position or orient an object, where high accuracy, repeatability and stability of operations are required. Deviations in link dimensions and joint clearances in manufacturing and assembling operations decrease the degree of accuracy and repeatability of the systems. Due to the random nature of dimensional tolerance and clearance, a stochastic approach to figure out reliability of the open-loop mechanism should be required. In this work, firstly, with the assumption that all kinematical parameters are normally distributed random variables, stochastic model of links with dimensional tolerances and of revolute joints with clearances are presented. The kinematical reliability for the positioning and orientation repeatability is then calculated analytically based on an advanced first-order second moment (AFOSM) method and verified with a Monte Carlo simulation method. Finally, the proposed methods are numerically illustrated with an RRR spatial manipulator.