Analysis of angular-error uncertainty in planar multiple-loop structures with joint clearances

• A model for angular errors in multi-loop structures with joint clearances is established.
• A closed-form solution is obtained.
• The probability density functions of the angular errors are analyzed.
• The functions approach being Gaussian distributions.

A model for angular errors in multi-loop structures with joint clearances is established. A closed-form solution of the model is obtained. By using optimization methods and geometric methods, the boundaries of the studied angular errors are determined with reduced computation complexity. In a single loop, the same size joint clearances have identical contributions to the angular error; while in the proposed multi-loop design, the position of the multiple-joint also affects the angular error greatly. The probability density functions (pdfs) of the stated closed-loop errors are also analyzed based on the open loop manipulator. The functions approach being Gaussian distributions if there are many joint clearances. A simple method is presented to evaluate the average and the variance of the pdfs. The method is verified by Monte Carlo simulations.