Continuum Manipulator Statics Based on the Principle of Virtual Work

2012 ◽  
Author(s):  
William S. Rone ◽  
Pinhas Ben-Tzvi
Keyword(s):  
Numerical Method ◽  
Virtual Work ◽  
Lumped Parameter Model ◽  
Static Equilibrium ◽  
Principle Of Virtual Work ◽  
Single Segment ◽  
Gravitational Forces ◽  
Lumped Parameter ◽  
Continuum Robot ◽  
Continuum Manipulator

This paper presents a generalized method of determining the static shape conformation of a continuum robot based on the principle of virtual work. A lumped parameter model is utilized to model a prototypical single-segment manipulator. Elastic effects, gravitational forces and actuation loading are modeled as generalized forces and moments acting along the manipulators at discrete masses. A brief derivation of the governing static equations based on the principle of virtual work is presented, and then applied to the problem of continuum manipulator statics. The numerical method was successfully implemented numerically, capable of determining a system’s static equilibrium given a prescribed actuation.

Mechanics Modeling of Multisegment Rod-Driven Continuum Robots

2014 ◽  
Vol 6 (4) ◽  
Author(s):  
William S. Rone ◽  
Pinhas Ben-Tzvi
Keyword(s):  
Dynamic Models ◽  
Contact Forces ◽  
Lumped Parameter Model ◽  
Algebraic Equations ◽  
Continuum Robots ◽  
Modeling Approach ◽  
Lumped Parameter ◽  
Continuum Robot ◽  
Statics And Dynamics ◽  
Elastic Loading

This paper presents a novel modeling approach for the mechanics of multisegment, rod-driven continuum robots. This modeling approach utilizes a high-fidelity lumped parameter model that captures the variation in curvature along the robot while simultaneously defined by a discrete set of variables and utilizes the principle of virtual power to formulate the statics and dynamics of the continuum robot as a set of algebraic equations for the static model and as a set of coupled ordinary differential equations (ODEs) in time for the dynamic model. The actuation loading on the robot by the actuation rods is formulated based on the calculation of contact forces that result in rod equilibrium. Numerical optimization calculates the magnitudes of these forces, and an iterative solver simultaneously estimates the robot's friction and contact forces. In addition, modeling considerations including variable elastic loading among segments and mutual segment loading due to rods terminating at different disks are presented. The resulting static and dynamic models have been compared to dynamic finite element analyses and experimental results to validate their accuracy.

A Finger Model with Constant Tendon Moment Arms

1993 ◽  
Vol 37 (10) ◽  
pp. 710-714 ◽  
Author(s):  
Koo-Hyoung Lee ◽  
Karl H.E. Kroemer
Keyword(s):  
Sagittal Plane ◽  
Virtual Work ◽  
Static Equilibrium ◽  
Principle Of Virtual Work ◽  
Finger Movements ◽  
Equilibrium Equations ◽  
Finger Joints ◽  
Moment Arms ◽  
Finger Model

A kinematic finger model was developed with the assumption that the tendon moment arms at the finger joints were constant, and that the finger moved in the sagittal plane. Equations of static equilibrium for the model, derived using the principle of virtual work, were indeterminate. The number of variables was reduced based on the muscular activities in finger movements. The finger strengths were computed from the equilibrium equations, and mathematically expressed as functions of finger positions, tendon moment arms, and lengths of phalanges. Experiments were performed to measure finger strengths, and the measured finger strengths were compared to the computed results.

Introducing and Analyzing a Novel Three-Degree-of-Freedom Spatial Tensegrity Mechanism

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
Bahman Nouri Rahmat Abadi ◽  
Mehrdad Farid ◽  
Mojtaba Mahzoon
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Translational Motion ◽  
Parallel Robot ◽  
Principle Of Virtual Work ◽  
Dynamical Equations ◽  
Spatial Mechanism ◽  
Gravitational Forces ◽  
Three Degree Of Freedom ◽  
Special Case

The objective of the present paper is to introduce and analyze a particular spatial mechanism as a modification of the Stewart robot. The three limbs of the Stewart parallel robot are replaced by springs. Three hydraulic actuators control translational motion of the mechanism. Kinematics of the mechanism is studied and its static equations are derived and for a special case where external and gravitational forces are neglected, an analytical solution is presented. Also, the principle of virtual work is employed to derive the equations of motion of the proposed mechanism. Based on the dynamical equations, the motion of the system is simulated.

On the Mechanical Behavior of the Orthotropic Cord-Rubber Composite

1976 ◽  
Vol 4 (4) ◽  
pp. 219-232 ◽  
Author(s):  
Ö. Pósfalvi
Keyword(s):  
Mechanical Behavior ◽  
Uniaxial Tension ◽  
Elastic Properties ◽  
Large Deformations ◽  
Virtual Work ◽  
Poisson's Ratio ◽  
Principle Of Virtual Work ◽  
Effective Elastic Properties ◽  
Rubber Composite ◽  
Mooney Equation

Abstract The effective elastic properties of the cord-rubber composite are deduced from the principle of virtual work. Such a composite must be compliant in the noncord directions and therefore undergo large deformations. The Rivlin-Mooney equation is used to derive the effective Poisson's ratio and Young's modulus of the composite and as a basis for their measurement in uniaxial tension.

scholarly journals A Distributed Lumped Parameter Model of Blood Flow

2020 ◽  
Vol 48 (12) ◽  
pp. 2870-2886
Author(s):  
Mehran Mirramezani ◽  
Shawn C. Shadden
Keyword(s):  
Blood Flow ◽  
Lumped Parameter Model ◽  
Lumped Parameter

scholarly journals Discrete element model for general polyhedra

2021 ◽  
Author(s):  
Alfredo Gay Neto ◽  
Peter Wriggers
Keyword(s):  
Frictional Contact ◽  
Virtual Work ◽  
Particle Surface ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Element Model ◽  
Principle Of Virtual Work ◽  
Dynamics Model ◽  
Railway Ballast ◽  
Multibody Dynamics Model

AbstractWe present a version of the Discrete Element Method considering the particles as rigid polyhedra. The Principle of Virtual Work is employed as basis for a multibody dynamics model. Each particle surface is split into sub-regions, which are tracked for contact with other sub-regions of neighboring particles. Contact interactions are modeled pointwise, considering vertex-face, edge-edge, vertex-edge and vertex-vertex interactions. General polyhedra with triangular faces are considered as particles, permitting multiple pointwise interactions which are automatically detected along the model evolution. We propose a combined interface law composed of a penalty and a barrier approach, to fulfill the contact constraints. Numerical examples demonstrate that the model can handle normal and frictional contact effects in a robust manner. These include simulations of convex and non-convex particles, showing the potential of applicability to materials with complex shaped particles such as sand and railway ballast.

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