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

传统的机构产生必要的变形，以执行其任务，通过相对运动的部件滑动或滚动在对方。另一方面，柔顺机构使用弹性应变，这带来了许多优点。由顺应机制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）和非期望的变形之间存在明确的分离。在柔性机构中，期望和不期望的变形都是基于弹性应变的，并且没有一种只考虑期望部分的数学建模选项。因此，柔性机构的综合变得非常复杂。一种可能的合成方法是基于连续体的合成方法。在这里，机构被建模为一个弹性连续体，机构的几何形状是自由可调的。目前，有许多基于连续体的合成方法，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，而复杂的任务，如形状适应很少涉及。此外，这些方法只考虑了有限范围的横向荷载。申请人提出了将机构的特征属性作为综合（模态过程）的主题的想法，提出了一种有希望的方法来解决这两个缺点。这种想法的核心优势是运动学设计的可能性，即不涉及特定负载情况的设计。除此之外，这只能用于传统机构，以及设计柔顺机构的某些方法（伪刚体方法），然而，对于这种方法，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，详细阐述了一种新的方法，使已经存在的程序更加健壮。此外，将模态过程推广到具有多个拟运动度的机构的综合情况。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量，并且可以与传统机构的迁移率相关。然而，迄今为止，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的情况。这个扩展将提供一个强大的工具，允许合成具有大变形的复杂兼容机制。

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.