Uncertainty analysis of planar and spatial robots with joint clearances

Abstract

Joint clearance in mechanisms and robots leads to uncertainty in function deviation. Unlike the effect of the link tolerance on the performance quality, the uncertainty effect of the joint clearance to the performance can not be eliminated by calibration because of the random nature. In this paper, based on the probability theory, a general probability density function (p.d.f.) of the endpoint of planar robots is established. The p.d.f. of the endpoint of a planer robot is equivalent to that of endpoint of a string of planar joint deviation vectors. By grouping the planar joint deviation vectors and establishing the structural constraint conditions between the vector groups, a basic approach of deriving the general p.d.f. of spatial robots is also presented. Based on the general p.d.f. of the endpoint, the distribution functions of the robot endpoint for any position tolerance zone and any joint distribution type, can be derived. The method is demonstrated by using some common types of position tolerance zones with uniform as well as normal distribution for joint clearance. The distribution functions of the robot endpoint are calculated and tabulated. These distribution functions and tables provide a convenient way to obtain the probability value for a robot to position its end point within a desired tolerance zone, and to determine the joint clearance value for the desired type of tolerance zone and the prescribed probability value of position repeatability.