Compliant mechanisms and joints: control and tailored stiffness via architectured metamaterials

Abstract

In this work the compliance matrix method is used to develop an analytical methodology for the kinetostatic analysis of Flexure-Based Compliant Parallel Mechanisms (FBCPM) under arbitrary force and displacements conditions. Furthermore, the characteristics of metamaterials, specifically the zero Poisson's ratio lattice structures, are used to design a novel type of prismatic compliant joints namely Zero Poisson's ratio Prismatic Compliant Joints (ZP-PCJ) with advantageous features such as high flexibility in a desired direction while achieving favorable levels of stiffness in the non-desired directions, and accurate analytical models that allow their implementation in FBCPM. In the first chapter, the relevant concepts are presented, in addition, the main problem, hypothesis and objectives are stated. The second chapter presents the literature review on the state of the art in the topics of the kinematic analysis of compliant mechanisms and the use of metamaterials for compliance purposes. Chapter three deals with the theoretical background corresponding to the Compliance Matrix Method (CMM) and the kinematic analysis of FBCPM using this method, ending with a summary of the CMM that synthesizes and unifies all the variants commonly found in the literature. In chapter four the proposed analytical method for the kinematic analysis of FBCPM is presented and successfully validated by three cases: i) using a 2D-FBCPM comparing with FEA-simulation results, ii) using a 3D-FBCPM comparing with FEA-simulation results, and iii) using a Compliant Spherical Parallel Mechanism (CSPM) comparing with both FEA-simulation and experimental results where input displacements were also used. Chapter five deals with the concept of meta-flexures, introducing the new type of prismatic compliant joints called ZP-PCJ based on the advantageous characteristics of zero Poisson's lattice structures. The compliance matrices of these ZP-PCJs are obtained analytically using Castigliano's second theorem and compliance simplification, and successfully validated with both FEA-simulations and experimental tests. In addition, the proposed ZP-PCJs are implemented in a 2D-FBCPM whose kinetostatic analysis is performed with the method presented in the previous chapter, demonstrating via FEA-simulations, the validity and accuracy of their analytical models. Finally, conclusions and future work are described in chapter six.