scholarly journals A discrete mechanics approach to the Cosserat rod theory-Part 1: static equilibria

2010 ◽  
Vol 85 (1) ◽  
pp. 31-60 ◽  
Author(s):  
Pascal Jung ◽  
Sigrid Leyendecker ◽  
Joachim Linn ◽  
Michael Ortiz
Keyword(s):  
Discrete Mechanics ◽  
Rod Theory ◽  
Cosserat Rod

scholarly journals Conveyance of texture signals along a rat whisker

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Maysam Oladazimi ◽  
Thibaut Putelat ◽  
Robert Szalai ◽  
Kentaro Noda ◽  
Isao Shimoyama ◽  
...  
Keyword(s):  
Friction Model ◽  
Primary Afferents ◽  
Geometrically Nonlinear ◽  
Tactile Sensors ◽  
Stick Slip ◽  
Physical Constraints ◽  
Normal Forces ◽  
Rod Theory ◽  
Cosserat Rod ◽  
Dynamic Variables

AbstractNeuronal activities underlying a percept are constrained by the physics of sensory signals. In the tactile sense such constraints are frictional stick–slip events, occurring, amongst other vibrotactile features, when tactile sensors are in contact with objects. We reveal new biomechanical phenomena about the transmission of these microNewton forces at the tip of a rat’s whisker, where they occur, to the base where they engage primary afferents. Using high resolution videography and accurate measurement of axial and normal forces at the follicle, we show that the conical and curved rat whisker acts as a sign-converting amplification filter for moment to robustly engage primary afferents. Furthermore, we present a model based on geometrically nonlinear Cosserat rod theory and a friction model that recreates the observed whole-beam whisker dynamics. The model quantifies the relation between kinematics (positions and velocities) and dynamic variables (forces and moments). Thus, only videographic assessment of acceleration is required to estimate forces and moments measured by the primary afferents. Our study highlights how sensory systems deal with complex physical constraints of perceptual targets and sensors.

scholarly journals Modeling and Fabrication of Soft Actuators Based on Fiber-Reinforced Elastomeric Enclosures

Actuators ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 127
Author(s):  
Zhi Chen ◽  
Aicheng Zou ◽  
Zhantian Qin ◽  
Xingguo Han ◽  
Tianming Li ◽  
...  
Keyword(s):  
Virtual Work ◽  
Fiber Reinforced ◽  
Complex Environments ◽  
Manufacturing Method ◽  
Soft Actuator ◽  
Rod Theory ◽  
Cosserat Rod ◽  
Proposed Model ◽  
Soft Actuators ◽  
The Relationship

Unlike rigid actuators, soft actuators can easily adapt to complex environments. Understanding the relationship between the deformation of soft actuators and external factors such as pressure would enable rapid designs based on specific requirements, such as flexible, compliant endoscopes. An effective model is demonstrated that predicts the deformation of a soft actuator based on the virtual work principle and the geometrically exact Cosserat rod theory. The deformation process is analyzed for extension, bending, and twisting modules. A new manufacturing method is then introduced. Through any combination of modules, the soft actuator can have a greater workspace and more dexterity. The proposed model was verified for various fiber-reinforced elastomeric enclosures. There is good agreement between the model analysis and the experimental data, which indicates the effectiveness of the model.

Optimal, Model-Based Design of Soft Robotic Manipulators

2007 ◽  
Author(s):  
Deepak Trivedi ◽  
Dustin Dienno ◽  
Christopher D. Rahn
Keyword(s):  
Nonlinear Models ◽  
Load Capacity ◽  
Robotic Manipulators ◽  
Maximum Pressure ◽  
Cluttered Environments ◽  
Rod Theory ◽  
Cosserat Rod ◽  
Manipulator Design ◽  
Air Muscle ◽  
Muscle Actuators

Soft robotic manipulators, unlike their rigid-linked counterparts, deform continuously along their lengths similar to elephant trunks and octopus arms. Their excellent dexterity enables them to navigate through unstructured and cluttered environments and handle fragile objects using whole arm manipulation. Soft robotic manipulator design involves the specification of air muscle actuators and the number, length and configuration of sections that maximize dexterity and load capacity for a given maximum actuation pressure. This paper uses nonlinear models of the actuators and arm structure to optimally design soft robotic manipulators. The manipulator model is based on Cosserat rod theory, accounts for large curvatures, extensions, and shear strains, and is coupled to nonlinear Mooney-Rivlin actuator model. Given a dexterity constraint for each section, a genetic algorithm-based optimizer maximizes the arm load capacity by varying the actuator and section dimensions. The method generates design rules that simplify the optimization process. These rules are then applied to the design of pneumatically and hydraulically actuated soft robotic manipulators, using 100 psi and 1000 psi maximum pressure, respectively.

scholarly journals A Generalized Approach for Reconstructing the Three-Dimensional Shape of Slender Structures Including the Effects of Curvature, Shear, Torsion, and Elongation

2017 ◽  
Vol 84 (4) ◽  
Author(s):  
Mayank Chadha ◽  
Michael D. Todd
Keyword(s):  
Three Dimensional ◽  
Surface Strain ◽  
Cross Sectional ◽  
Rod Theory ◽  
Cosserat Rod ◽  
Measured Strain ◽  
Dimensional Shape ◽  
Three Dimensional Shape ◽  
Slender Structures

This paper extends the approach for determining the three-dimensional global displaced shape of slender structures from a limited set of scalar surface strain measurements. It is an exhaustive approach that captures the effect of curvature, shear, torsion, and elongation. The theory developed provides both a determination of the uniaxial strain (in a given direction) anywhere in the structure and the deformed shape, given a set of strain values. The approach utilizes Cosserat rod theory and exploits a localized linearization approach that helps to obtain a local basis function set for the displacement solution in the Cosserat frame. For the assumed deformed shape (both the midcurve and the cross-sectional orientation), the uniaxial value of strain in any given direction is obtained analytically, and this strain model is the basis used to predict the shape via an approximate local linearized solution strategy. Error analysis due to noise in measured strain values and in uncertainty in the proximal boundary condition is performed showing uniform convergence with increased sensor count.

Dynamics of Beams Using a Geometrically Exact Elastic Rod Approach

2006 ◽  
Author(s):  
Fredy Coral Alamo ◽  
Hans Ingo Weber
Keyword(s):  
Virtual Work ◽  
Fundamental Problem ◽  
Equations Of Motion ◽  
Approximate Solutions ◽  
Dynamic Responses ◽  
Elastic Rod ◽  
Rod Theory ◽  
Cosserat Rod ◽  
Slender Beams ◽  
Nonlinear Equations Of Motion

The dynamics of a long slender beam, intrinsically straight, is addressed systematically for 3-D problems using the Cosserat rod theory. The model developed allows for bending, extension/compression and torsion, thus enabling the study of the dynamics of various types of elastic deformations. In this work a linear constitutive relation is used, also, the Bernoulli hypothesis is considered and the shear deformations are neglected. The fundamental problem when using any finite element (FE) formulation is the choice of the displacement functions. When using Cosserat rod theory this problem is handled using approximate solutions of the nonlinear equations of motion (in quasi-static sense). These nonlinear displacement functions are functions of generic nodal displacements and rotations. Based on the Lagrangian approach formed by the kinetic and strain energy expressions, the principle of virtual work is used to derive the nonlinear ordinary differential equations of motion that are solved numerically. As an application, a curved rod, formed by many straight elements is investigated numerically. When using the Cosserat rod approach, that take into account all the geometric nonlinearities in the rod, the higher accuracy of the dynamic responses is achieved by dividing the system into a few elements which is much less than the traditional FE methods, this is the main advantage when using this approach. Overall, the Cosserat model provides an accurate way of modelling long slender beams and simulation times are greatly reduced through this approach.

Optimal, Model-Based Design of Soft Robotic Manipulators

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
Deepak Trivedi ◽  
Dustin Dienno ◽  
Christopher D. Rahn
Keyword(s):  
Nonlinear Models ◽  
Load Capacity ◽  
Robotic Manipulators ◽  
Cluttered Environments ◽  
Rod Theory ◽  
Cosserat Rod ◽  
Manipulator Design ◽  
Air Muscle ◽  
Muscle Actuators ◽  
General Method

Soft robotic manipulators, unlike their rigid-linked counterparts, deform continuously along their lengths similar to elephant trunks and octopus arms. Their excellent dexterity enables them to navigate through unstructured and cluttered environments and to handle fragile objects using whole arm manipulation. This paper develops optimal designs for OctArm manipulators, i.e., multisection, trunklike soft arms. OctArm manipulator design involves the specification of air muscle actuators and the number, length, and configuration of sections that maximize dexterity and load capacity for a given maximum actuation pressure. A general method of optimal design for OctArm manipulators using nonlinear models of the actuators and arm mechanics is developed. The manipulator model is based on Cosserat rod theory, accounts for large curvatures, extensions, and shear strains, and is coupled to the nonlinear Mooney–Rivlin actuator model. Given a dexterity constraint for each section, a genetic algorithm-based optimizer maximizes the arm load capacity by varying the actuator and section dimensions. The method generates design rules that simplify the optimization process. These rules are then applied to the design of pneumatically and hydraulically actuated OctArm manipulators using 100psi and 1000psi maximum pressures, respectively.

scholarly journals Towards Viscoplastic Constitutive Models for Cosserat Rods

2016 ◽  
Vol 63 (2) ◽  
pp. 215-230 ◽  
Author(s):  
Vanessa Dörlich ◽  
Joachim Linn ◽  
Tobias Scheffer ◽  
Stefan Diebels
Keyword(s):  
Constitutive Models ◽  
Constitutive Law ◽  
Viscoplastic Material ◽  
Three Point Bending ◽  
Material Parameters ◽  
Rod Theory ◽  
Cosserat Rod ◽  
Cosserat Rods ◽  
Electric Cables ◽  
Deformation Modes

Abstract Flexible, slender structures like cables, hoses or wires can be described by the geometrically exact Cosserat rod theory. Due to their complex multilayer structure, consisting of various materials, viscoplastic behavior has to be expected for cables under load. Classical experiments like uniaxial tension, torsion or three-point bending already show that the behavior of e.g. electric cables is viscoplastic. A suitable constitutive law for the observed load case is crucial for a realistic simulation of the deformation of a component. Consequently, this contribution aims at a viscoplastic constitutive law formulated in the terms of sectional quantities of Cosserat rods. Since the loading of cables in applications is in most cases not represented by these mostly uniaxial classical experiments, but rather multiaxial, new experiments for cables have to be designed. They have to illustrate viscoplastic effects, enable access to (viscoplastic) material parameters and account for coupling effects between different deformation modes. This work focuses on the design of such experiments.

Instability of a Whirling Conducting Rod in the Presence of a Magnetic Field: Application to the Problem of Space Tethers

2005 ◽  
Author(s):  
J. Valverde ◽  
G. van der Heijden
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Molecular Wires ◽  
Field Application ◽  
Elastic Structure ◽  
Rod Theory ◽  
Cosserat Rod ◽  
Post Buckling ◽  
Space Tethers ◽  
Magnetic Field Application

We study the effect of a magnetic field on the behaviour of a slender conducting elastic structure subject to end forces. Both statical (buckling) and dynamical (whirling) instability are considered and we also compute post-buckling configurations. The theory used is the geometrically exact Cosserat rod theory. We consider two types of boundary conditions: the traditional welded boundary conditions (for tether-like applications) and a novel set of boundary conditions that give rise to exact helical post-buckling solutions. Our results are relevant for current designs of electrodynamic space tethers and potentially for future applications in nano- and molecular wires.

A Cosserat Rod Model of Multi-Symplectic Structure and its Numerical Treatment

2013 ◽  
Vol 712-715 ◽  
pp. 1395-1400
Author(s):  
Hou Bin Zhang ◽  
Mao Sheng Jiang ◽  
Ying Wu
Keyword(s):  
Symplectic Structure ◽  
Hamiltonian Formulation ◽  
Numerical Treatment ◽  
Symplectic Algorithm ◽  
Numerical Example ◽  
Model Based ◽  
Rod Theory ◽  
Cosserat Rod ◽  
Rod Model

In this paper, a Hamiltonian formulation of the Cosserat rod model is proposed. The model, based on the Cossert rod theory incorporates shear, elongation, flexure and twist deformation, is of multi-symplectic structure. A multi-symplectic algorithm is employed to discretize the equation and a numerical example is giving.

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