Dynamic Modeling of the Cable-Driven Continuum Robots in Hybrid Position-Force Actuation Mode

2020 ◽  
Vol 12 (5) ◽  
Author(s):  
Abbas Ehsani-Seresht ◽  
Shahin Hashemi-Pour Moosavi
Keyword(s):  
Dynamic Model ◽  
Dynamic Models ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Computational Effort ◽  
Continuum Robots ◽  
Friction Forces ◽  
Lagrange Formulation ◽  
Statics And Dynamics ◽  
External Forces

Abstract Dynamic models of the cable-driven continuum robots are commonly employed for those robots that are actuated by the cables’ forces. In this paper, a dynamic model is proposed for the cable-driven continuum robots actuated by position and/or force actuated cables, which is appropriate for any desired number of actuation cables and their routing. The robot is supposed to have an extensible backbone with the capability of bending and torsion in three-dimensional spaces. The proposed dynamic model is developed based on the Euler–Lagrange formulation of equations of motion taking into account all the effective forces including gravity force, cable actuation forces, external forces, and cable-disk friction forces. Furthermore, an iterative numerical solution method is presented for the dynamic model which requires much less memory and computational effort in comparison with the closed-form methods. The static model of the robots is also developed based on the dynamic model and the results obtained from the simulations and experiments are used for the validation of the static and dynamic models. The final results indicate the accuracy of the proposed models for estimating the kinematics, statics, and dynamics of the cable-driven continuum robots.

Force-based delay compensation for hardware-in-the-loop simulation divergence of 6-DOF space contact

2017 ◽  
Vol 233 (1) ◽  
pp. 151-165
Author(s):  
Qian Wang ◽  
Chenkun Qi ◽  
Feng Gao ◽  
Xianchao Zhao ◽  
Anye Ren ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Dynamic Models ◽  
Contact Process ◽  
Three Dimensional ◽  
Compensation Method ◽  
Degree Of Freedom ◽  
Hardware In The Loop ◽  
Delay Compensation ◽  
Measurement Delay ◽  
Six Degree Of Freedom

The contact process of a space docking device needs verification before launching. The verification cannot only rely on the software simulation since the contact dynamic models are not accurate enough yet, especially when the geometric shape of the device is complex. Hardware-in-the-loop simulation is a choice to perform the ground test, where the contact dynamic model is replaced by a real device and the real contact occurs. However, the Hardware-in-the-loop simulation suffers from energy increase and instability since time delay is unavoidable. The existing delay compensation methods are mainly focused on a uniaxial or three-dimensional contact. In this paper, a force-based delay compensation method is proposed for the hardware-in-the-loop simulation of a six degree-of-freedom space contact. A six degree-of-freedom dynamic model of the spacecraft motion is derived, and a six degree-of-freedom delay compensation method is proposed. The delay is divided into track delay and measurement delay, which are compensated individually. Experiment results show that the proposed delay compensation method is effective for the six degree-of-freedom space contact.

A Study on Sensitivity of Maneuverability Performance on the Hydrodynamic Coefficients for Submerged Bodies

2000 ◽  
Vol 44 (03) ◽  
pp. 186-196
Author(s):  
Debabrata Sen
Keyword(s):  
Dynamic Model ◽  
Dynamic Models ◽  
Equations Of Motion ◽  
Inertial Force ◽  
Axisymmetric Body ◽  
Hydrodynamic Coefficients ◽  
Damping Coefficients ◽  
Simulated Trajectory ◽  
Linear Damping

Based on a constant-coefficient dynamic model, a study was made to determine the influence of various hydrodynamic coefficients on the predicted maneuverability quality of submerged bodies. Two types of geometries were considered, a submarine and an axisymmetric slender geometry. For the submarine, the equations of motion used were the revised standard submarine equations (Feldman 1979) while for the latter geometry a dynamic model was developed. From computer simulation of a few selected definitive maneuvers based on these two different dynamic models for the two geometries, the sensitivity of the simulated trajectory on changes in different coefficients was found. The results quantified in form of sensitivity values are presented. It is found that the typical measures from the maneuvers do not depend significantly on most of the nonlinear coefficients. The coefficients having significant effects on the trajectories are found to be the linear damping coefficients for the submarine and the linear inertial force coefficients for the axisymmetric body.

A Three-Dimensional Dynamic Model for Determining the Equilibrium Configurations of Buoyantly Unstable Icebergs

1990 ◽  
Vol 112 (3) ◽  
pp. 253-262
Author(s):  
R. G. Jessup ◽  
S. Venkatesh
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Static Potential ◽  
Initial State ◽  
Model Simulations ◽  
Six Degrees Of Freedom ◽  
Equilibrium Configurations ◽  
Variation Range

This paper describes a dynamic model developed for the purpose of determining the final equilibrium configurations of buoyantly unstable icebergs. The model places no restrictions on the size, shape, or dimensionality of the iceberg, or on the variation range of the configuration coordinates. Furthermore, it includes all six degrees of freedom and is based on a Lagrangian formulation of the dynamic equations of motion. It can be used to advantage in those situations in which the iceberg has a complicated potential function and can acquire enough momentum and kinetic energy in the initial phase of its motion to make its final configuration uncertain on the basis of a static potential analysis. The behavior of the model is examined through several model simulations. The sensitivity of the final equilibrium position to the initial orientation and shape of the iceberg is clearly evident in the model simulations. Model simulations also show that when an iceberg is released from a nonequilibrium initial state, the time taken for it to settle down varies from about 40 s for a growler to nearly 400 s for a large iceberg. While these absolute times may change with better parameterization of the forces, the relative variations with iceberg size are likely to be preserved.

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.

Simplification of the dynamic model of a hydraulic rockbreaker for implementation in a model-based control scheme

2018 ◽  
Vol 42 (1) ◽  
pp. 38-48 ◽  
Author(s):  
Louis-Francis Y. Tremblay ◽  
Marc Arsenault ◽  
Meysar Zeinali
Keyword(s):  
Dynamic Model ◽  
Dynamic Models ◽  
Tracking Error ◽  
Planar Motion ◽  
Real Time Control ◽  
Joint Torques ◽  
Model Based ◽  
Lagrange Formulation ◽  
Time Control ◽  
Hydraulic Excavators

A model-based approach to control the automation of hydraulic excavators and rockbreakers necessitates an adequate dynamic model to increase the robustness of the controller and improve its performance (e.g., reduce tracking error). Most previous efforts in developing dynamic models for excavators have assumed planar motion while neglecting the dynamic effects of hydraulically driven prismatic actuators. In this paper, a dynamic model of the mechanical subsystem of a hydraulic rockbreaker is developed using the Euler–Lagrange formulation. The model considers the contributions of the hydraulic actuators and does not assume planar motion. Potential simplifications to the dynamic model are then introduced to facilitate the model’s parameterization for developing an adaptive control algorithm. To evaluate their level of accuracy, these simplified dynamic models are then evaluated based on the required joint torques for specified trajectories. It is shown that the proposed simplifications reduce the complexity of the dynamic model while preserving its accuracy, which is attractive for real-time control applications.

Static and Vibration Analyses of a Three-Dimensional Snake-Like Micropositioning Stage

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Nicola Scuor ◽  
Paolo Gallina ◽  
Marco Giovagnoni
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Dynamic Tests ◽  
Lumped Mass ◽  
Simulation Data ◽  
End Effector ◽  
Three Degrees Of Freedom

This paper presets three degrees of freedom (DOF) piezoelectric micropositioning stage. The stage is composed of a stack of piezodisk bender actuators actuated in such a way to prevent the end-effector from rotating; this way the end-effector can only translate along the x, y, and z axes. Thanks to its snake-like configuration, the system is capable of large displacements (of the order of 50 μm) with low driving voltages (of the order of 100 V). Several lumped-mass static and dynamic models of the device have been implemented. Static experimental results, which are in agreement with simulation data, confirmed the performances of the device. A dynamic model showed the natural frequencies of the mechanism. Also dynamic tests have been conducted in order to validate the dynamic model.

Dynamic Behavior of Spatial Linkages: Part 1—Exact Equations of Motion, Part 2—Small Oscillations About Equilibrium

1969 ◽  
Vol 91 (1) ◽  
pp. 251-265 ◽  
Author(s):  
J. J. Uicker
Keyword(s):  
Differential Equations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Dynamic Force ◽  
Lagrange Equations ◽  
Oscillation Analysis ◽  
Restricted Problems ◽  
The Matrix ◽  
Laplace Transformations ◽  
External Forces

Part 1: Over the past several years, the matrix method of linkage analysis has been developed to give the kinematic, static and dynamic force, error, and equilibrium analyses of three-dimensional mechanical linkages. This two-part paper is an extension of these methods to include some aspects of dynamic analysis. In Part 1, expressions are developed for the kinetic and potential energies of a system consisting of a multiloop, multi-degree-of-freedom spatial linkage having springs and damping devices in any or all of its joints, and under the influence of gravity as well as time varying external forces. Using the Lagrange equations, the exact differential equations governing the motion of such a system are derived. Although these equations cannot be solved directly, they form the basis for the solution of more restricted problems, such as a linearized small oscillation analysis which forms Part 2 of the paper. Part 2: This paper is a direct extension of Part 1 and it is assumed that the reader has a thorough knowledge of the previous material. Assuming that the spatial linkage has a stable position of static equilibrium and oscillates with small displacements and small velocities about this position, the general differential equations of motion are linearized to describe these oscillations. The equations lead to an eigenvalue problem which yields the resonant frequencies and associated damping constants of the system for the equilibrium position. Laplace transformations are then used to solve the linearized equations. Digital computer programs have been written to lest these methods and an example solution dealing with a vehicle suspension is presented.

Model Validation of an Octopus Inspired Continuum Robotic Arm for Use in Underwater Environments

2013 ◽  
Vol 5 (2) ◽  
Author(s):  
Tianjiang Zheng ◽  
David T. Branson ◽  
Emanuele Guglielmino ◽  
Rongjie Kang ◽  
Gustavo A. Medrano Cerda ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Model Validation ◽  
Degrees Of Freedom ◽  
Robotic Arm ◽  
Octopus Vulgaris ◽  
Light Weight ◽  
Continuum Robots ◽  
Continuum Structure ◽  
External Forces ◽  
Good Agreement

Octopuses are an example of dexterous animals found in nature. Their arms are flexible, can vary in stiffness, grasp objects, apply high forces with respect to their relatively light weight, and bend in all directions. Robotic structures inspired by octopus arms have to undertake the challenges of a high number of degrees of freedom (DOF), coupled with highly flexible continuum structure. This paper presents a kinematic and dynamic model for underwater continuum robots inspired by Octopus vulgaris. Mass, damping, stiffness, and external forces such as gravity, buoyancy, and hydrodynamic forces are considered in the dynamic model. A continuum arm prototype was built utilizing longitudinal and radial actuators, and comparisons between the simulated and experimental results show good agreement.

Dynamics of Shallow Cables With General Initial Shape Due to Mean-Flow Loads

2009 ◽  
Author(s):  
N. Impollonia ◽  
G. Ricciardi ◽  
F. Saitta
Keyword(s):  
Equilibrium Shape ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Initial Position ◽  
Plane Motion ◽  
Computational Effort ◽  
Mean Flow ◽  
Initial Shape ◽  
Out Of Plane ◽  
Nonlinear Equations Of Motion

In the classic cable theory, vibration of cables is usually analysed by writing the equations of motion in the nearness of the initial equilibrium configuration. Thus, a fundamental difference exists between out-of-plane motion, which substantially corresponds to the linear behaviour of a taut string, and in-plane motion, where self weight determines a sagged initial profile. This work defines a continuous approach in order to establish the initial shape when the cable is subjected to wind or fluid flow arbitrarily directed and a finite element approach in order to investigate the dynamic around the initial equilibrium shape of the cable. In particular, the equations of motion for a three dimensional case are written fully accounting for initial shape. This means that in the additional deformation also in the out-of-plane and along cable directions there is a term linked with the initial position. Stochastic solutions in the frequency domain are derived for a wind-exposed cable after linearization of the problem and by applying the Proper Orthogonal Decomposition Technique (POD) with the aim of reducing computational effort. Differences are shown with respect to the case in which out-of-plane initial displacement is neglected. In addition, a POD based approach to simulate modal wind forces is proposed and applied to the fully nonlinear equations of motion.

Nonlinear Vibration Analysis of Gas Turbine Bladings With Shroud Coupling

2008 ◽  
Author(s):  
Andreas Hohl ◽  
Christian Siewert ◽  
Lars Panning ◽  
Andreas Kayser
Keyword(s):  
Finite Element ◽  
Nonlinear Vibration ◽  
Gas Turbine ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Forced Response ◽  
Vibrational Amplitude ◽  
Friction Forces ◽  
Mapping Procedure

Rotating blades are subjected to vibrations caused by excitation forces due to a non-homogeneous pressure field of the fluid. Therefore, damping devices like tip shrouds are implemented which reduce the vibrational amplitude and apply additional stiffness and damping to the structure. To predict the resulting vibration response and stresses, a three dimensional contact model has been developed to determine the friction forces. The resulting equations of motion are solved in the frequency domain. The developed method has been implemented in a nonlinear forced response code called DATAR designed for the gas turbine division of Siemens Energy. In this paper, the transfer of common Finite Element models of bladings with shrouds or underplatform dampers to the DATAR code is presented. A mapping procedure based on Finite Element shape functions is used to couple the model with the regular contact grid used in the nonlinear vibration analysis performed with the DATAR code. As a practical example, the vibration behavior of a gas turbine blading with interlocked shrouds is investigated with the developed method.

Sign in / Sign up

Export Citation Format

Share Document