Compliant systems

Mechanics of elastically deformable mechanisms, actuators and sensors

Lena Zentner, Sebastian Linß

• Publisher: De Gruyter Oldenbourg
• Year: 2019
• eBook ISBN: 9783110477405
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

Compliant mechanisms and actuators are growing in importance due to their benefits in robotics, medical technology, sensor applications, or in handling compressible objects. This book helps to understand the mechanical behavior of compliant systems. Suggested classifications and different modeling methods are shown that allow for the description of compliant systems.

1Introduction

Compliance is no longer considered a disadvantage of mechanical systems. Instead, the resulting advantages, such as the utilization of elastic restoring forces, possibilities for energy storage, structure coherence etc., are used specifically to provide a system with new qualitative properties. In many application areas, such as in medical technology and human-machine interaction, specific and differentiated compliance is even a requirement for technical systems ([7], [125]). Conventional rigid-body mechanisms are being successfully supplemented or replaced more and more with compliant systems even in classical branches of mechanical engineering, often to take over motion or force transmission tasks, for example in gripping devices (Fig. 1.1). This tendency is being facilitated by the development of new materials and corresponding production technologies. Highly-elastic materials allow for actuators that can be designed and integrated into a compliant system in such a way that such systems take on inherent actuator properties. In combination with the use of functional materials, a system can be given inherent sensing properties, while allowing for a compact design and higher multi-functionality of the system as a whole.

Fig. 1.1: Examples of different gripper systems; a – conventional two-finger parallel gripper; b – compliant parallel gripper with concentrated compliance and piezo actuators; c – compliant parallel gripper with distributed compliance and inherent actuation based on ferroelastomers

By first investigating thoroughly its complex behavior, both in deformation and motion, a focused application of the actuators and functional materials can be guaranteed, while also ensuring a sensitive design for the compliant system as a whole. The most suitable method is by using model-based investigations, especially if an analytical model can be constructed to this end. The complex relationships between different parameters can thus be written in a transparent way, and dependencies between them can be revealed. Even if a solution cannot be achieved entirely through analysis, the resulting relationships between the mechanical parameters of a system can help in understanding it and comprehending its behavior. Compliant systems are considered under the effects of different loads, which are mostly caused by moments and forces or distributed moments and forces designated as line loads or area loads. These loads as well as other vector parameters, such as radius vectors or displacements are characterized by both a direction and a value. The terms for the vectors are given in bold text, e. g. F for a force vector, while the values of the vectors or scalar parameters are given in italics, such as the value of a force: F. In order to differentiate them from vectors, matrices are written in bold and underlined: T.

In the following chapters, classifications of compliant systems are first presented, which have been collected and systematized in the field of compliant mechanisms and actuators. Compliant systems with linear elastic properties are the focus of the modeling. Linear theory, which leads to the linear differential equations, is used to describe the actual behaviors of elastic deflections in a system undergoing small deflections. For large deflections, non-linear theory should be used when constructing a usable model for given deflections. Both methods of modeling are based on classical methods and have been both expanded upon and methodically generalized, in order to account for special cases, while also providing a formalism for simplifying the modeling process.

Before choosing an analytical method for describing the deformation of a compliant system, the character of this system, mirrored in its geometry and material, should first be established. In this step, a decision is made about which parts of the system must be modeled as compliant bodies and which as rigid bodies, thus excluding the compliant system parts to be modeled from the mechanical system as a whole. Subsequently, a decision must be made about which modeling methods are suitable for a given situation, based on the behavior and the uses of the system. The behavior of a system is understood here as both the deformation behavior of a compliant system part, as well as its motion behavior. The expected deformations, regarded as either large or small deflections, should be modeled accordingly using either a non-linear or linear theory. The intended application area of the system and corresponding objectives should also be taken into account. The next important step before formulating a mathematical model is determining the boundary conditions. Decisions are made here about where in the system loads will be applied, and which loads can be modeled as idealized concentrated forces and moments, or as distributed forces and moments. This also includes decisions about the bearing of the compliant system parts, which determines the boundary conditions for forces and moments.

After completing the modeling process, the calculated results of the model and the model-based simulation should be evaluated, based on the assumptions made and the starting requirements. If, for example, a compliant element with a cross-section measuring a third of its length is described using the theory for thin rods, it can be assumed that the results will correlate less accurately, if at all, than real deformations in an actual thin rod. The success of a model-based investigation depends on a keen examination of modeling method theory and a critical consideration of the results.

Based on existing research, a simple, usable method, based on the rigid-body replacement approach, of synthesizing compliant mechanisms with concentrated compliance is presented in the final chapter. The numerous possibilities of realizing a flexure hinge are first listed and evaluated based on their uses in precision engineering technology. A synthesis method based on the rotation angles of all hinges is especially suitable for mechanisms with different optimized flexure hinge contours, and is explained using the example of a four-bar mechanism.

The derivations of the modeling methods and their solutions to the examples presented are kept both clear and concise, in order to minimize the time and effort required to become acquainted with the material and to learn the methods. The calculations of mathematical equations are carried out using the software Mathematica® and MATLAB®. Finite elements method (FEM) simulations are performed with ANSYS Workbench®. Where possible, analytical solutions have been preferred over numerical solutions.

2Definition and classification of compliant systems

To give an overview of the possible applications of compliant systems, these must first be classified according to their characteristics. The structural considerations of compliant systems and their properties are especially important when planning and building accurate models. In this way, it is possible to consider only the characteristics of a system that partly or wholly influence its functionality. This simplifies the development and modeling of compliant systems for specific purposes. A compliant system can be considered as a compliant mechanism, a compliant actuator and/or a compliant sensor according to its function (Fig. 2.1).

Fig. 2.1: Compliant systems; a – four-bar compliant path-generating mechanism with flexure hinges; b – compliant fluid-mechanical actuator made from a highly elastic polymer; c – compliant sensor used to detect shear forces

Compliance, as an important property of compliant systems, as well as its causes and effects on a system will be considered first of all. Compliant systems will accordingly be broken down according to their motion behavior. The definitions that follow in this chapter are based on the terminology for compliant mechanisms according to the International Federation for the Promotion of Mechanism and Machine Science (IFToMM), but also go further to supplement these. The following descriptions and classifications should assist in the selection, modeling and design of compliant systems, and are also used in later chapters.

2.1Compliance

Compliance, as basic property of compliant systems should first be considered more specifically, thus allowing for a sensible and purposeful application in mechanical systems. Understanding the factors that can change or manipulate compliance, allows this property to be adjusted deliberately to external conditions. Thus, compliant systems can be designed in such a way that they can change their mechanical properties depending on variable conditions, using either a control system or of their own accord.

2.1.1Classification of compliance

Compliance is the measure of the ability of a system, body or body segment to exhibit a deformation due to the action of external forces (reciprocal of stiffness). The term compliance and not elasticity is purposefully used here, because...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• Contents
• 1 Introduction (L. Zentner, S. Linß)
• 2 Definition and classification of compliant systems (L. Zentner, S. Linß)
• 3 Modeling compliant systems as rigid-body systems (L. Zentner)
• 4 Modeling large deflections of curved rod-like structures (L. Zentner)
• 5 Examples of modeling large deflections of curved rod-like structures (L. Zentner)
• 6 Synthesis of compliant mechanisms and design of flexure hinges (S. Linß)
• References
• Index