Dynamic performance optimization of a planar mechanism with cam clearance joint based on non-uniform rational B-spline and reinforcement learning

The collision forces generated by clearance in the cam pair lead to poor dynamic performance and undesirable vibrations of cam mechanisms. Existing approaches improve the dynamic characteristics through optimizing the contact parameters of the cam joint elements. However, adjusting these parameters may exceed the limits of a specified material since the material properties vary discretely from one to another. To fill this gap, a dynamic characteristics optimization method using non-uniform rational B-spline (NURBS) and reiforcement learning (RL) is proposed for cam mechanisms with clearance joints. A NURBS curve is used to reconstruct the cam profile whose shape can be locally changed by the weighting factors of corresponding control points. Then, the nonlinear dynamics equations of the cam mechanism with clearance joint are established to solve the output acceleration ac\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a}_{c}$$\end{document} and the joint's contact force Fc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F}_{c}$$\end{document}. Finally, a RL agent is trained to learn the optimal policy for the weighting factors to minimize the mean vibrations of ac\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a}_{c}$$\end{document} and Fc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F}_{c}$$\end{document}. In addition, dynamics optimization of a beat-up mechanism considering cam clearance joint is conducted to validate the adaptability and reliability of the proposed approach. The results show that the mean vibrations of ac\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a}_{c}$$\end{document} and Fc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F}_{c}$$\end{document} are respectively decreased by 46.7% and 44.6% after optimization. It indicates that optimizing local features of a cam profile by adjusting weighting factors assigned to the control points effectively enhances the contact state between the cam and roller, thereby improving the dynamic performance of the cam mechanism.