Auxetic regions in large deformations of periodic frameworks

In materials science, auxetic behavior refers to lateral widening upon stretching. We investigate the problem of finding domains of auxeticity in global deformation spaces of periodic frameworks. Case studies include planar periodic mechanisms constructed from quadrilaterals with diagonals as periods and other frameworks with two vertex orbits. We relate several geometric and kinematic descriptions.Comment: Presented at the International Conference on "Interdisciplinary Applications of Kinematics" (IAK18), Lima, Peru, March 201

기구학적 특성과 컴플라이언스 특성을 동시에 고려한 기구 위상 및 형상 통합 최적설계

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 기계항공공학부(멀티스케일 기계설계전공), 2020. 8. 김윤영.Mechanism synthesis based on topology optimization has recently received much attention as an efficient design approach. The main thrust behind this trend is the capability of this method to determine automatically the topology and dimensions of linkage mechanisms. Towards this direction, there have been many investigations, but they have thus far focused mainly on mechanism synthesis considering kinematic characteristics describing a desired path or motion. Here, we propose a new topology optimization method that synthesizes a linkage mechanism considering not only kinematic but also compliance (K&C) characteristics simultaneously, as compliance characteristics can also significantly affect the linkage mechanism performance; compliance characteristics dictate how elastic components, such as bushings in a vehicle suspension, are deformed by external forces. To achieve our objective, we use the spring-connected rigid block model (SBM) developed earlier for mechanism synthesis considering only kinematic characteristics, but we make it suitable for the simultaneous consideration of K&C characteristics during mechanism synthesis by making its zero-length springs multifunctional. Variable-stiffness springs were used to identify the mechanism kinematic configuration only, but now in the proposed approach, they serve to determine not only the mechanism kinematic configuration but also the compliance element distribution. In particular, the ground-anchoring springs used to anchor a linkage mechanism to the ground are functionalized to simulate actual bushings as well as to identify the desired linkage kinematic chain. After the proposed formulation and numerical implementation are presented, three case studies to synthesize planar linkage mechanisms were considered. Through these case studies, we verified the validation of the proposed approach and proved that the proposed methodology could solve problems when existing methods could not. After the effectiveness of the proposed method is demonstrated with a simplified two-dimensional vehicle suspension design problem, the proposed methodology is applied to design a three-dimensional suspension. To deal with three-dimensional mechanisms, a spatial SBM is newly developed because only planar SBMs have been developed. Furthermore, a set of design variables which can vary bushing stiffness are newly introduced. Using the proposed method, it was possible to successfully synthesize two types of suspension mechanisms which have similar kinematic characteristics to each other but different compliance characteristics. By using the proposed method simultaneously considering kinematic and compliance characteristics, a unique suspension mechanism having an integral module which is known to improve R&H performances was synthesized. In this study, although applications were made only to the design of vehicle suspensions, other practical design problems for which K&C characteristics must be considered simultaneously can be also effectively solved by the proposed approach. This study is expected to pave the way to advance the topology optimization method for general linkage mechanisms considering kinematic characteristics but also the other characteristics such as force-related characteristics.위상 최적화(topology optimization) 기법을 이용한 한 기구 합성(mechanism synthesis)은 그 효율성으로 인해 최근 많은 주목을 받고 있다. 이러한 추세의 주 원인은 기구 위상 최적화 기법으로 인해 기구의 위상(topology)과 치수(dimension)를 자동으로 합성할 수 있기 때문이다. 이러한 방향성을 가지고 지금까지 많은 연구들이 진행되어 왔지만, 지금까지 진행된 연구들은 모두 경로 합성이나 운동 합성과 같이 기구학적 특성을 고려하는 데에만 관심이 집중되었다. 본 연구에서는 기구의 기구학적 특성(kinematic characteristics)과 컴플라이언스 특성(compliance characteristics)을 동시에 고려할 수 있는 새로운 기구 위상 최적화 기법을 제안한다. 기구학적 특성은 기구 설계에 있어 매우 중요한 특성이지만, 외력이 작용하였을 때 자동차 서스펜션(vehicle suspension)의 부싱(bushing)과 같은 탄성 요소들의 변형으로 인해 나타나는 컴플라이언스 특성 또한 기구 설계 시 고려해야 할 중요한 특성이기 때문이다. 새로운 기구 위상 최적화 기법을 위해 우리는 기구학적 특성만을 고려하기 위해 개발되었던 스프링-연결 블록 모델(spring-connected block model)을 기구학적 특성과 컴플라이언스 특성을 동시에 고려할 수 있도록 고안하였다. 기존의 스프링-연결 블록 모델에서는 기구학적 연결 관계만을 표현하는데 사용되던 가변 강성 스프링을 본 연구에서는 기구학적 연결 관계뿐 아니라 실제 부싱을 표현하도록 다목적으로 활용하여 기구학적 특성과 컴플라이언스 특성을 하나의 모델링을 통해 성공적으로 표현하였다. 개발한 방법론의 효과를 입증하기 위해 평면 기구 합성을 목표로 한 세 종류의 사례 연구(case study)를 진행하였고, 이러한 사례 연구를 통해 우리는 제안한 방법이 기존의 방법으로는 해결할 수 없는 문제 상황을 해결할 수 있음을 확인하였다. 개발한 방법론을 보다 실용적인 문제에 적용하기 위해 3차원 자동차 서스펜션(vehicle suspension) 설계 하고자 하였으며, 이를 위해 스프링-연결 블록 모델을 3차원으로 확장하였다. 또한, 보다 실용적인 설계 결과 도출을 위해 2차원 사례 연구에서는 사용하지 않았던 부싱 강성 조절 설계 변수를 추가적으로 도입하여, 부싱 강성도 동시에 설계를 진행하였다. 3차원 서스펜션 설계는 기구학적 조건은 동일하지만, 컴플라이언스 특성은 다른 두 가지 조건에 대해 진행되었으며, 두 설계 조건에서 모두 서스펜션 합성에 성공하였다. 특히, 두 서스펜션의 결과 위상이 서로 다른 것을 확인할 수 있었는데, 이를 통해 기구학적 조건은 동일하되 컴플라이언스 조건이 달라지면 결과 위상이 달라질 수 있음을 확인하였고, 개발한 방법론을 통해 설계 조건에 맞는 기구의 위상과 치수 그리고 필요한 부싱 강성까지도 성공적으로 설계할 수 있음을 증명하였다. 본 연구는 컴플라이언스 조건이 특히 중요시 되는 자동차 서스펜션을 설계하는데 집중하였지만, 개발한 방법론은 기구학적 특성과 컴플라이언스 특성이 모두 요구되는 다른 설계 문제에도 적용될 수 있을 것으로 기대된다. 또한, 이 연구는 기구학적 특성뿐만 아니라 힘과 관련된 다른 특성을 고려한 일반적인 기구 위상 최적화 기법으로의 발전에 기여할 것으로 기대된다.CHAPTER 1. Introduction 1 1.1 Motivation and related literatures 1 1.2 Research objectives 6 1.3 Background research 8 1.3.1 Linkage mechanism synthesis based on the spring-connected rigid block model (SBM) 8 1.3.2 Determination of the systems degree-of-freedom (DOF) based on the work transmittance efficiency function 10 1.4 Outline of thesis 12 CHAPTER 2. Unified topology and shape optimization method for the mechanism synthesis simultaneously considering kinematic and compliance (K&C) characteristics 18 2.1 Overview 18 2.2 Modeling and analysis 23 2.2.1 Modeling 23 2.2.2 Kinematic and compliance analyses with the SBM 26 2.3 Optimization Formulation 33 2.3.1 Design variable and interpolation 33 2.3.2 Objective and constraint functions 35 2.3.3 Sensitivity analysis 39 2.4 Case studies 43 2.4.1 Case study 1 - Validation of the proposed method 43 2.4.2 Case study 2 - Demonstration of the advantage of the proposed method 46 2.4.3 Case study 3 - Application to the design of a 2D vehicle suspension 50 2.5 Summary 57 CHAPTER 3. Design of vehicle suspensions for rear using topology optimization method considering K&C characteristics 78 3.1 Overview 78 3.2 Modeling and analysis based on the spatial SBM 81 3.2.1 The spatial SBM for the design of a vehicle suspension 81 3.2.2 Kinematic and compliance analyses by the spatial SBM 83 3.3 Optimization Formulation 90 3.3.1 Design variable and interpolation 90 3.3.2 Objective and constraint functions 93 3.3.3 Sensitivity analysis 95 3.4 Design of vehicle suspensions for rear using the proposed method 99 3.4.1 Definition of problem 99 3.4.2 Design Case 1 - Recovery of a double wishbone suspension 101 3.4.3 Design Case 2 - Suspension synthesis for improving ride and handling (R&H) performances 104 3.5 Summary 110 CHAPTER 4. Conclusions 133 APPENDIX A. Target cascading process for deriving K&C characteristics of a suspension to improve vehicles R&H performances 138 A.1 Overview 138 A.2 Ride and handling (R&H) performances 139 A.3 Analysis procedure to evaluate R&H performances using a double wishbone suspension 140 A.4 Design optimization of a double wishbone suspension for deriving K&C characteristics to improve R&H performances 141 A.4.1 Design variable and interpolation 141 A.4.2 Metamodeling 142 A.4.3 Optimization formulation 144 A.4.4 Optimization result 145 APPENDIX B. Technique to suppress floating blocks 158 B.1 Overview 158 B.2 Explanation of techniques to suppress floating blocks 159 B.3 Revisit Case study 3 for applying the technique to suppress floating blocks 161 APPENDIX C. Investigation of mesh dependency issue 167 C.1 Overview 167 C.2 Re-consideration of Case study 1 with the more number of rigid blocks 168 REFERENCES 172 ABSTRACT (KOREAN) 181 ACKNOWLEDTEMENTS 184Docto

Deformation Control in Rest-to-Rest Motion of Mechanisms with Flexible Links

This paper develops and validates experimentally a feedback strategy for the reduction of the link deformations in rest-to-rest motion of mechanisms with flexible links, named Delayed Reference Control (DRC). The technique takes advantage of the inertial coupling between rigid-bodymotion and elasticmotion to control the undesired link deformations by shifting in time the position reference through an action reference parameter. The action reference parameter is computed on the fly based on the sensed strains by solving analytically an optimization problem. An outer control loop is closed to compute the references for the position controllers of each actuator, which can be thought of as the inner control loop. The resulting multiloop architecture of the DRC is a relevant advantage over several traditional feedback controllers: DRC can be implemented by just adding an outer control loop to standard position controllers. A validation of the proposed control strategy is provided by applying the DRC to the real-time control of a four-bar linkage