Experimental determination of kinematic parameters in assembled parallel kinematic mechanisms

Over the last decade, a new breed of multi-axis machine tools and robots based on parallel kinematic mechanisms (PKMs) have been developed and marketed worldwide. The success of these machines in the manufacturing sector will ultimately depend on their reliability, versatility and the accuracy with which they perform their tasks. Positional accuracy in these machines is controlled by accurate knowledge of the geometry (joint locations and distances between joint pairs) of the mechanism. Since these machines tend to be rather large, the kinematic parameters are difficult to determine when these machines are in their fully assembled state. Successful determination of the kinematic parameters in fully assembled PKMs up to this point has been done by global optimization methods. However, these method are time consuming to execute, typically require precision artifacts and involve calculating the difficult forward kinematic solution. In this study, a new method for determining the kinematic parameters of assembled PKMs is developed. In the novel approach presented, each kinematic parameter is determined individually and independently from the others. The proposed method is subjected to two uncertainty analyses. The first analysis is to determine the effects of data quality and machine positional uncertainty on the calculated kinematic parameters. The second analysis is to determine the effects of the calculated parameters on the uncertainty of the position of the platform using a specific machine and measuring instrument combination. The sequential determination technique was executed and the results implemented on a machine in the field. Results for Renishaw ball bar circles before and after calibration are presented.