Comprehensive analysis and real-time synthesis of four-bar mechanisms via a 10-parameter model and an implicit curve fitting approach

Abstract

In the kinematic analysis of the coupler curve, a parametric equation with nine parameters, which are dependent on the mechanism dimensions, is commonly used. In this study, we extend the analysis of a four-bar mechanism by introducing a 10th parameter, referred to as the closure parameter. Additionally, we present a comprehensive, practical, and fast simulation that displays real-time values of 16 kinematic variables throughout motion. The accuracy of this simulation is validated through comparisons with a manually constructed mechanism and tested successfully across various mechanism configurations. Another novelty of this work is the introduction of the general coupler curve equation curve fitting method (GCCE-CFM), which enables fast and practical kinematic synthesis of the coupler curve. This method derives explicit expressions for the 16 coefficients of the sixth-degree general coupler curve equation (GCCE), also known as the algebraic coupler curve equation, in terms of the mechanism parameters. Subsequently, real-time curve fitting is applied to 40 points sampled from a known coupler curve, successfully recovering the mechanism dimensions with high accuracy in just a few seconds. The proposed model achieves a high-precision curve fit with a root-mean-square error (RMSE) of 6.85e–5, demonstrating its effectiveness in accurately capturing the target coupler path.

Keywords

Kinematic analysis kinematic synthesis coupler curve path generation

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