Abstract

The exact and approximate path synthesis problems require different synthesis methods, and mastering multiple design methods increases the engineers’ burden. A unified drawing method can solve the synthesis problem of four and five positions in the existed studies. In this article, a novel unified synthesis method is proposed for the exact and approximate timing-path synthesis. The approximate timing-path synthesis problem is recombining into many groups of the exact timing-path synthesis. The exact timing-path synthesis formulas are derived based on the classical dyad method, while the simplified synthesis formulas are obtained by the linear elimination method with a specific order of elimination. A distance error formula is proposed to find the optimal group from all groups of solutions, where each group of solutions is the possible solution of the pre-recombination synthesis problem. Exact timing-path synthesis usually obtains several groups (12 or 2 groups, theoretically may be 0) of solutions with different kinematic properties, then the error formula is used to find the group of solutions that has the smallest rounding error. Finally, three cases test the proposed method and prove the effectiveness of the method in solving the timing-path synthesis problem by comparing the errors with the literature results.

摘要

精确路径综合问题和近似路径综合问题需要不同的综合方法，掌握多种设计方法增加了工程师的负担。统一的绘图方法可以解决现有研究中四位置和五位置的合成问题。在本文中，提出了一种新颖的统一综合方法，用于精确和近似时序路径综合。近似时序路径综合问题被重新组合成许多组精确时序路径综合。精确的时序路径综合公式是基于经典的二元法推导出来的，而简化的综合公式是通过具有特定消去顺序的线性消元法得到的。提出了一个距离误差公式来从所有解组中找到最优组，其中每组解都是预重组合成问题的可能解。精确时序路径综合通常会得到几组（12或2组，理论上可能是0）具有不同运动学特性的解，然后利用误差公式找到舍入误差最小的一组解。最后通过三个案例测试了所提出的方法，通过与文献结果的误差比较，证明了该方法解决时序路径综合问题的有效性。