Synthesis of planar compliant mechanisms with selective compliance for shape adaptation


Details zur Publikation

Autor(en): Hasse A
Verlag: Eidgenössische Technische Hochschule ETH Zürich
Verlagsort: Zürich
Jahr der Veröffentlichung: 2011
Sprache: Englisch


In many technical problems, e.g. the shape adaptation of wings or rotor

blades, it is desired that the changing of the structure's shape is smooth in

order to operate as eciently as possible. Even where loads are not exactly

predictable, a defined shape is required. Nevertheless, the complexity of

the actuator system and of the mechanics should be as low as possible.

It is within this context that this thesis presents the concept and the

synthesis of compliant mechanisms with selective compliance.

In contrast to classical mechanisms, which realize their motion through

classical joints (e.g. bearings), compliant mechanisms use the deformability

of the material to produce a particular movement. They therefore

present several advantages, ranging from the absence of wear and

backlash, to lower noise levels, clean operation, easier maintenance and

reduced manufacturing eort. In addition, the deformation is not constrained

to the joint areas, as in the case of a classical mechanism, rather

it can be distributed continuously over the structure - this is advantageous

in terms of a smooth shape adaptation. However, the kinematic

behavior of compliant mechanisms is mostly load-dependent, i.e. a large

number of possible deformation patterns can be obtained by altering the

load acting on the system. This is not the case with classical mechanisms,

as they usually have a defined number of kinematic degrees of freedom.

The compliant mechanisms with selective compliance presented in this

thesis combine both of these advantages: their kinematics may include a

distributed deformation and they are virtually constrained to a defined

number of kinematic degrees of freedom.

The aim of this study is to develop an automated design method for

compliant mechanisms with selective compliance. In this context, the design

requirements are identified and classified. A design criterion based

on eigenvalues and eigenvectors is presented after a modal analysis of various

compliant structures. In order to be able to determine the compliant

mechanism by means of numerical structural optimization, a modal objective

function is introduced, the minimization of which leads to a structure

that meets the design criterion. The modal objective function is validated

by dierent design tasks. A force-inverter problem is taken from literature

and is subjected to the developed methods. In addition, structures

are presented which have complex kinematics, including smooth surface


Since the dawn of aviation, engineers have tried to design shape adaptive

wings in order to improve the eciency of aircrafts at different flight

conditions. Concepts using conventional mechanics turned out to be too

heavy and too complex. The belt-rib concept is a new approach: the classical

ribs, which define the shape of the wing, are replaced by so-called

"belt ribs". These are compliant mechanisms with selective compliance,

consisting of an outer belt and an inner stiening structure, which are

virtually limited to one kinematic degree of freedom. The kinematics depicted

by a belt rib show a defined profile change. So far, the realizable

profile changes have been limited, due to the chosen inner stiening structure

and the synthesis methods available. With the findings of this thesis,

it is now possible to design belt ribs describing an arbitrary profile change.

In this thesis, an example of this is given in the form of a rib belt whose

profile can be adapted from a NACA 0012 to a NACA 2412.

FAU-Autoren / FAU-Herausgeber

Hasse, Alexander Prof. Dr.
Professur für Mechatronische Systeme


Hasse, A. (2011). Synthesis of planar compliant mechanisms with selective compliance for shape adaptation (Dissertation).

Hasse, Alexander. Synthesis of planar compliant mechanisms with selective compliance for shape adaptation. Dissertation, Zürich: Eidgenössische Technische Hochschule ETH Zürich, 2011.


Zuletzt aktualisiert 2018-10-08 um 02:41