Finding straight line generators through the approximate synthesis of symmetric four-bar coupler curves
Finding straight line generators through the approximate synthesis of symmetric four-bar coupler curves
复制标题
通过对称四杆耦合器曲线的近似合成找到直线发生器
DOI：
10.1016/j.mechmachtheory.2023.105310
复制
发表时间：
2023
影响因子：
5.2
通讯作者：
Hauenstein, Jonathan D.
中科院分区：
文献类型：
--
作者：
Baskar, Aravind;Plecnik, Mark;Hauenstein, Jonathan D.
给出了具有对称连杆曲线的四杆机构的近似轨迹综合。这包括多项式优化问题的表述，临界点最大数目的刻画，同伦延拓的完整数值解，以及在直线生成器设计中的应用。我们的方法指定了一条所需的曲线，并找到了几个最优的四杆机构，其连杆轨迹与之接近。所提出的目标同时加强了运动学精度、回路闭合，并导致多项式一阶必要条件，其结构对于任何期望的轨迹保持不变，从而导致广义结果。将地面枢轴位置设置为选定的参数，结果表明，该目标最多有73个临界点。将理论工作应用于直线路径的设计。对1440种不同的地面枢轴进行了参数同伦运行，以进行彻底的探索。这些计算找到了预期的链接，即瓦特、埃文斯、罗伯茨、切比雪夫和其他以前未报告的链接，这些链接使用UMAP算法组织成2D地图集。
The approximate path synthesis of four-bar linkages with symmetric coupler curves is presented. This includes the formulation of a polynomial optimization problem, a characterization of the maximum number of critical points, a complete numerical solution by homotopy continuation, and application to the design of straight line generators. Our approach specifies a desired curve and finds several optimal four-bar linkages with a coupler trace that approximates it. The objective posed simultaneously enforces kinematic accuracy, loop closure, and leads to polynomial first order necessary conditions with a structure that remains the same for any desired trace leading to a generalized result. Ground pivot locations are set as chosen parameters, and it is shown that the objective has a maximum of 73 critical points. The theoretical work is applied to the design of straight line paths. Parameter homotopy runs are executed for 1440 different choices of ground pivots for a thorough exploration. These computations found the expected linkages, namely, Watt, Evans, Roberts, Chebyshev, and other previously unreported linkages which are organized into a 2D atlas using the UMAP algorithm.