A-posteriori adjustment of the stiffness of compliant mechanisms considering geometrical nonlinearities

柔顺机构使用材料中的弹性应变来产生其任务所需的变形。这与传统的机制不同，传统的机制基于滑动或滚动界面的有限相对运动。与传统的替代方案不同，柔顺机构需要定义的机械功来产生功能变形，这些变形以应变能的形式存储在机构的弹性变形、柔顺区域中。这意味着柔顺机构产生恢复力，这对于某些应用是不希望的。这项建议涉及通过有针对性地使用预紧力来修改柔性机构的刚度(以及它们产生恢复力的趋势)。这是“柔顺机构刚度的后验调整”项目的后续应用。后续项目将消除在前一个项目中开发的方法的三个限制：a)该方法仅限于线性行为。B)优化公式可以得到一个简化的解，但由于它可能提供具有大量预紧力的最优解，因此不利于实际情况的使用。C)该方法只处理即使在机构受到外力加载时仍保持恒定的预紧力。这也是相当不切实际的。如果预紧力是使用被动元件实现的，则必须考虑随机构上的载荷(具有线性、递进或递减特性)改变预紧力的可能性。工作计划由四个主要工作包(HAP)组成，这些工作包又细分为工作包(AP)。首先，作为HAP 1的第一步，提供了一个适当的参数化分析模块，能够在考虑大变形的情况下计算具有分布柔度的柔性机构(理想化为梁桁架)。进一步的步骤是使用项目所需的属性逐步更新分析模块，例如将运动学减少到一个运动自由度(理想的选择行为)的模式投影，引入标量坐标来标记单个变形(变形坐标)，以及选择将预紧力单元与一般二次特性相结合。之后，将前一方案中的方法逐步应用于几何非线性情况。该项目通过对离散优化方法的研究、对理想选择行为假设的似然分析、对非线性特性的分析以及演示程序的实现和测试来完成。

Compliant mechanisms use elastic strains in the material to generate the deformations necessary for their task. This differentiates them from conventional mechanisms, which are, based, instead, on finite relative movement of sliding or rolling interfaces. In contrast to its conventional alternative, a compliant mechanism requires a defined amount of mechanical work to generate functional deformations, which is stored as strain energy in the elastically deformed, compliant areas of the mechanism. This implies that the compliant mechanism produces restoring forces, which are undesirable for certain applications. This proposal deals with modifying the stiffness of flexible mechanisms (and thus their tendency to produce restoring forces) through the targeted use of preload forces. This is a follow-up application to the project "A posteriori adjustment of the stiffness of compliant mechanisms“. Three limitations of the method that was developed in the previous project are to be removed by the follow-up project: a) the method is restricted to linear behavior. b) the optimization formulation leads to a simplified solution; However, it is unfavorable for use in practical cases, since it may provide optimal solutions with a large number of preload forces. c) the method only deals with preload forces that remain constant even when the mechanism is loaded by external forces. This is also quite unrealistic. If the preload is implemented using passive elements, the possibility of changing the preload force with the load on the mechanism (with a linear, progressive or degressive characteristic) must be taken into account. The work program consists of four main work packages (HAP), which, in turn, are subdivided into work packages (AP). First, an appropriately parameterized analysis module, capable of calculating flexible mechanisms with distributed compliance, idealized as beam trusses, under consideration of large deformations is provided as first step of the HAP 1. Further steps progressively update the analysis module with the properties necessary for the purposes of the project, such as a modal projection to reduce the kinematics to one kinematic degree of freedom (ideally selective behavior), the introduction of a scalar coordinate to label the single deformations (deformation coordinate) and the option of integrating preload elements with a general quadratic characteristic. After that, the method from the previous project is gradually adapted to the geometrically non-linear case. The project is completed by the investigation of discrete optimization methods, a plausibility analysis of the assumption of ideally selective behavior, an analysis of the non-linear character and the realization and testing of a demonstrator.