Modeling of Elastically Coupled Bodies: Part I—General Theory and Geometric Potential Function Method

Fasse, Ernest D.; Breedveld, Pieter C.

doi:10.1115/1.2801491

Cited by 23 publications

(13 citation statements)

References 7 publications

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“…where E b a = η b a I −ẽ b a . Fasse et al 12 prove several useful properties of their potential function. It is sufficiently diverse and therefore can model arbitrary local stiffness.…”

Section: Dof Stiffnessmentioning

confidence: 99%

“…Fasse et al 13,59 furthered the methods of Caccavale et al 7,8 to model elastically coupled rigid bodies. The model presented in this section uses the quaternion-based potential function in Zhang et al 59 We use the notation of Fasse et al 12 where p a b is the displacement of frame b relative to frame a written in the coordinates of a. Frames a and b are rigidly attached to bodies A and B, respectively. The columns of R a b are the basis vectors of frame b written in the coordinates of a.…”

Section: Dof Stiffnessmentioning

confidence: 99%

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A general stiffness model for programmable matter and modular robotic structures

et al. 2011

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SUMMARYThe fields of modular reconfigurable robotics and programmable matter study how to compose functionally useful systems from configurations of modules. In addition to the external shape of a module configuration, the internal arrangement of modules and bonds between them can greatly impact functionally relevant mechanical properties such as load bearing ability. A fast method to evaluate the mechanical property aids the search for an arrangement of modules achieving a desired mechanical property as the space of possible configurations grows combinatorially. We present a fast approximate method where the bonds between modules are represented with stiffness matrices that are general enough to represent a wide variety of systems and follows the natural modular decomposition of the system. The method includes nonlinear modeling such as anisotropic bonds and properties that vary as components flex. We show that the arrangement of two types of bonds within a programmable matter systems enables programming the apparent elasticity of the structure. We also present a method to experimentally determine the stiffness matrix for chain style reconfigurable robots. The efficacy of applying the method is demonstrated on the CKBot modular robot and two programmable matter systems: the Rubik's snake folding chain toy and a right angle tetrahedron chain called RATChET7mm. By allowing the design space to be rapidly explored we open the door to optimizing modular structures for desired mechanical properties such as enhanced load bearing and robustness.

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Section: Dof Stiffnessmentioning

confidence: 99%

Section: Dof Stiffnessmentioning

confidence: 99%

A general stiffness model for programmable matter and modular robotic structures

et al. 2011

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“…(22) and (19) of subsection 3.2. The above potential energy representation of the screw theory can be divided into four terms in the classical form [13] as follows:…”

Section: Potential Energymentioning

confidence: 99%

Screw theoretic view on dynamics of spatially compliant beam

Ding

Selig

2010

Appl. Math. Mech.-Engl. Ed.

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Beams with spatial compliance can be deformed as bending in a plane, twisting, and extending. In terms of the screw theory on rigid body motions, the concept of "deflection screw" is introduced, a spatial compliant beam theory via the deflection screw is proposed, and the spatial compliance of such a beam system is presented and analysed based on the material theory and fundamental kinematic assumptions. To study the dynamics of the spatially compliant beam, the potential energy and the kinetic energy of the beam are discussed by using the screw theory to obtain the Lagrangian. The Rayleigh-Ritz method is used to compute the vibrational frequencies based on discussions of boundary conditions and shape functions. The eigenfrequencies of the beam with spatial compliance are compared with those of individual deformation cases, pure bending, extension, or torsion. Finally, dynamics of a robot with two spatial compliant links and perpendicular joints is studied using the spatial compliant beam theory. Coupling between the joint rigid body motions and the deformations of spatial compliant links can easily be found in dynamic simulation. The study shows the effectiveness of using the screw theory to deal with the problems of dynamic modeling and analysis of mechanisms with spatially compliant links.

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“…where K t , K o , and K c represent the 3 × 3 translational, rotational, and coupling stiffness matrices respectively. We choose frames a and b to be located at the center of stiffness because it is a unique point that maximally decouples K [45]. The stiffness terms can be determined from elasticity theory or finite element analysis [46].…”

Section: Modelmentioning

confidence: 99%

A Toolchain for the Design and Simulation of Foldable Programmable Matter

Gray

Seo

White

et al. 2010

Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts a and B

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This paper presents a toolchain for the design and simulation of reconfigurable robots that can be built from a single rigid sheet of smart material with embedded actuators and sensors along regular crease patterns. We call such sheets Foldable Programmable Matter (FPM). The toolchain we have created comprises an editor for drafting or modifying FPM, including locations and angles for folds. Algorithms for generating a class of folding structures are available for use. Also included is a dynamic simulation of the fold process, which provides collision detection and visualization. Thus our Foldable Programmable Matter Editor allows us to synthesize and design FPMs and simulate them in a virtual environment before committing to manufacture. The toolchain also incorporates a method of strength analysis, which is used to determine the suitability of a folded shape for specific loadings. Examples are shown for each subsection, including a beam example spanning the toolchain.

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Modeling of Elastically Coupled Bodies: Part I—General Theory and Geometric Potential Function Method

Cited by 23 publications

References 7 publications

A general stiffness model for programmable matter and modular robotic structures

A general stiffness model for programmable matter and modular robotic structures

Screw theoretic view on dynamics of spatially compliant beam

A Toolchain for the Design and Simulation of Foldable Programmable Matter

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