Error Uncertainty Analysis in Planar Closed-Loop Structure with Joint Clearances

Yushu Yu,Xin Li,Jinglin Li,Yi Yang

doi:10.3390/met11111872

Abstract

For planar closed-loop structures with clearances, the angular and positional error uncertainties are studied. By using the vector translation method and geometric method, the boundaries of the errors are analyzed. The joint clearance is considered as being distributed uniformly in a circle area. A virtual link projection method is proposed to deal with the clearance affected length error probability density function (PDF) for open-loop links. The error relationship between open loop and closed loop is established. The open-loop length PDF and the closed-loop angular error PDF both approach being Gaussian distribution if there are many clearances. The angular propagation error of multi-loop structures is also investigated by using convolution. The positional errors of single and multiple loops are both discussed as joint distribution functions. Monte Carlo simulations are conducted to verify the proposed methods.

Highlights

Rigid links are often hinged together as a fixed structure to fulfill the requirements of various tasks
If the structure is transformed from a deployable mechanism, which is widely used in the space environment, such as the solar panel array system or an antenna support structure, the possible joint clearances may have a great effect on its accuracy
Zhu and Watkins have shown that the same dimension joint clearances contributed to the direction error in a single loop structure [26]

Summary

Introduction

Rigid links are often hinged together as a fixed structure to fulfill the requirements of various tasks. Compared to the previous research, a more general error analysis methodology for closed-loop structures is proposed in this paper. Type 2 can be seen as a connection of two sets of type 1 In this model, each joint clearance with its adjacent links can be seen as a RPR (Revolute joint–Prismatic joint–Revolute joint) kinematic chain. Further statistic simulations are on the basis of the proposed models in this subsection

The Angular Error and Positional Error Boundaries

Error PDF Analysis and Simulation Method

Numerical Simulations

Conclusions