Continuous Approximate Synthesis of Planar and Spatial Mechanisms

平面和空间机构的连续近似综合

• 批准号: RGPIN-2017-06327
• 负责人: Hayes, John
• 金额: $ 1.6万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=712201
• 关键词: Continuous; Approximate; Synthesis; Planar; Spatial

Mechanism synthesis is an important branch of mechanism science that has developed over the last millennium. A mechanism is a collection of interconnected components individually called links. The connection between two adjacent links is a joint. Four-bar linkages are an important class of mechanism that consist of a relatively fixed rigid link to which an input and an output link are attached, typically by rotary, or linear joints. The input and output links are additionally connected to a fourth link which couples the motion of the input to that of the output, forming a closed loop. Four-bar linkages have important applications to function generation (the motions of the input and output links are coordinated according to an algebraic function), rigid body guidance, and trajectory generation. The current approach is to prescribe a finite set of positions and orientations of the coupler, link 4, or a finite set of values for pairs of input and output link angles, and then to use numerical procedures to synthesise the geometry of a linkage that can approximate the desired motions with the least error, but relative to only the prescribed values. This is termed discrete approximate synthesis because of the finite number of discrete specified configurations. What occurs between each configuration is not accounted for and tends to make the design process inefficient. This research program consists of developing a fundamentally new branch of mechanism science, which we call continuous approximate synthesis (CAS). Instead of discrete sets, we propose to use calculus and geometry to expand the finite sets into continuous infinite sets. Because we take into account the entire range of motion, the resulting linkage represents the very best that is viable, performing with the smallest possible error throughout the entire range of motion. The long term goal of this work is to create design tools for any type of rigid mechanical linkage, connected both serially (analogous to a single human arm) or in parallel (analogous to two human arms connected to each other, both at the chest and hands, forming a closed loop), that yields the very best linkage relative to a particular error. There are four short term goals, comprising the focus of this grant application: 1) prove that for planar function generating four-bar linkages, the one which minimises a critical non-linear performance index can be identified by solving a set of linear equations; 2) adapt the results to arbitrary planar and spatial closed loop linkages; 3) extend the results to CAS for rigid body guidance; 4) further extend the results to trajectory generation. The concept of CAS has already received strong support from the Canadian mechanism design community, it is therefore expected that the proposed work will make a significant positive impact on the research and industrial sectors of the mechanism design community both within Canada and internationally.

机理综合是近千年发展起来的机理科学的一个重要分支。机制是互连组件的集合，这些组件分别称为链接。两个相邻链节之间的连接是接头。四杆连杆机构是一类重要的机构，由相对固定的刚性连杆组成，输入连杆和输出连杆通常通过旋转或线性接头连接到该刚性连杆上。输入和输出连杆还连接到第四连杆，第四连杆将输入的运动耦合到输出的运动，形成闭环。四连杆机构在函数生成（输入和输出连杆的运动根据代数函数进行协调）、刚体引导和轨迹生成方面具有重要应用。当前的方法是规定耦合器、连杆 4 的一组有限位置和方向，或输入和输出连杆角度对的一组有限值，然后使用数值程序来合成连杆的几何形状，该几何形状可以以最小的误差逼近所需的运动，但仅相对于规定值。由于离散指定配置的数量有限，因此这被称为离散近似综合。每种配置之间发生的情况并未得到考虑，并且往往会导致设计过程效率低下。该研究计划包括开发机制科学的一个全新分支，我们称之为连续近似合成（CAS）。我们建议使用微积分和几何将有限集扩展为连续无限集，而不是离散集。因为我们考虑了整个运动范围，所以最终的连杆代表了可行的最佳连接，在整个运动范围内以尽可能小的误差执行。这项工作的长期目标是为任何类型的刚性机械连杆创建设计工具，串联连接（类似于单个人的手臂）或并联（类似于彼此连接的两个人的手臂，无论是在胸部还是在胸部）。手，形成一个闭环），从而产生相对于特定错误的最佳链接。有四个短期目标，构成了本次拨款申请的重点：1）证明对于生成四杆机构的平面函数，可以通过求解一组线性方程来确定最小化关键非线性性能指数的目标； 2）使结果适应任意平面和空间闭环连接； 3）将结果扩展到CAS用于刚体制导； 4）进一步将结果扩展到轨迹生成。 CAS的概念已经得到了加拿大机构设计界的大力支持，因此预计拟议的工作将对加拿大和国际机构设计界的研究和工业部门产生重大积极影响。