Kinematic reliability evaluation of planar parallel manipulators with non-uniform joint clearances

The accuracy of planar parallel manipulators (PPMs) is heavily affected by the clearances present in their joints. Wear is inevitable in the joint during the operation of the manipulators, which results in non-uniform clearances. Previous research has been confined to examining the precision of planar parallel manipulators under the assumption of consistent joint clearances. Therefore, this research undertakes a kinematic reliability assessment of planar parallel manipulators, considering the presence of non-uniform clearances in their joints. Initially, the non-uniform clearances are characterized using a B-spline curve for their parametric representation. Then, the position error model of a planar parallel manipulator is established considering non-uniform joint clearances, uncertainty of input data, and errors of linkage dimensions. The matrix of the mean and covariance of the distribution of the position error are analytically derived. The probability density function (PDF) of the distribution of position error is calculated using the central limit theorem. Subsequently, the kinematic reliability in the workspace can be calculated by a direct integral over the obtained PDF. The proposed method is available for a mechanism with any irregular joint clearance when wear occurs. The efficacy and precision of proposed method are confirmed through a comparison against Monte Carlo simulation.