A Rapid Fitting Method for the Estimation of Kinematic Errors in 3-RPR Robots Using Small Sample Sizes

Since the inverse kinematics of the 3-RPR mechanism involves a 6th-degree equation, it does not have an analytical solution. However, when calculating kinematic precision down to the micrometer level in practical applications, the error becomes significant. Traditional approaches using neural networks or deep learning algorithms to compensate these errors often need a lot of data and tends to over-fitting. In this article, we focus on a platform based on the 3-RPR parallel mechanism, proposing a systematic method to reduce the inverse kinematic error to micrometer level. This article analyzed the components of system error. A method is proposed that allows for the rapid estimation of error model parameters using a subset of sampling points in practical applications. This provides a practical solution for quickly re-calibrating the machinery during disassembly and maintenance. A potential application of this method to forward kinematics is also discussed.