Continuum-based design of selectively compliant mechanisms taking into account large deformations

传统机构通过部件在彼此上滑动或滚动的相对运动产生执行其任务所需的变形。另一方面，柔顺机构使用弹性应变，这导致了许多优点。从顺从机构的工作原理直接产生的数学公式的复杂性迄今阻碍了该领域的进展。在传统的机制中，基于潜在的物理原理，在功能性(期望的)和不期望的变形之间存在明显的分离。在柔顺机构中，期望和不期望的变形都是基于弹性应变的，并且没有仅考虑期望部分的数学建模选项。因此，柔顺机构的综合是非常复杂的，其中一种可能的综合方法是基于连续介质的综合方法。这里，机构被建模为弹性连续体，机构的几何形状是自由可调的。目前，有许多基于连续谱的合成方法，但它们都有一些主要的缺点。大多数合成方法只适用于相对简单的任务，而形状适应等复杂任务很少涉及。此外，这些方法只考虑有限范围的横向载荷。申请人提出了一种有希望的方法来解决这两个缺点，即将机构的特征特性作为综合的主题(模态程序)。这个想法的主要优点是可以进行运动学设计，即不涉及特定载荷情况的设计。这只能用于传统机构以及某些柔顺机构的设计方法(伪刚体方法)，但机构几何形状的选择受到严重限制。在上一个项目的过程中，制定了一种新的方法，使现有的程序更加健壮。此外，还将模态法推广到具有多个伪运动的机构综合。伪迁移率定义了识别柔顺机构的单个期望变形所需的标量参数的数目，并且可以与传统机构的迁移率相关。然而，到目前为止，所开发的方法的有效性仅限于几何线性机构。本应用旨在将其推广到几何非线性情况。这一扩展将提供一个强大的工具，允许综合具有大变形的复杂柔顺机构。

Conventional mechanisms generate the deformations necessary to perform their task through relative motions of components sliding or rolling on each other. Compliant mechanisms, on the other hand, use elastic strain, which leads to many advantages. The complexity in the mathematical formulation that arises directly from the operating principle of compliant mechanisms has hindered progress in the field to date. In conventional mechanisms, there is a clear separation between functional (desired) and undesired deformations based on the underlying physical principle. In compliant mechanisms, both desired and undesired deformations are based on elastic strain and an option for mathematical modeling, which only considers the desired part, is not available. For this reason, the synthesis of compliant mechanisms turns out to be very complex.One possible way for synthesis are continuum-based synthesis methods. Here, the mechanism is modeled as an elastic continuum and the geometry of the mechanism is freely adjustable. Currently, there are numerous continuum-based synthesis approaches, but they have some central shortcomings. Most synthesis approaches are only suitable for relatively simple tasks, while complex tasks such as shape adaptation are rarely covered. Moreover, only a limited range of transverse loads is considered in these approaches.With the idea of making the eigenproperties of the mechanism the subject of the synthesis (modal procedure), the applicant proposed a promising way to address these two shortcomings. The central advantage of this idea is the possibility of a kinematic design, i.e. a design that does not refer to specific load cases. This is otherwise only possible for conventional mechanisms, as well as with certain methods for designing compliant mechanisms (pseudo-rigid body approach), for which, however, the choice of the geometry of the mechanism is severely limited.In the course of the previous project , a new approach was elaborated that made the already existing procedures more robust. In addition, the modal procedure was extended to the case of the synthesis of mechanisms with multiple pseudo-mobility. The pseudo-mobility defines the number of scalar parameters needed to identify a single desired deformation of a compliant mechanism and can be related to the mobility of conventional mechanisms. However, the validity of the developed approach has so far been limited to geometrically linear mechanisms. The present application aims to extend it to the geometrically nonlinear case. This extension will provide a powerful tool that allows for the synthesis of complex compliant mechanisms with large deformations.