scholarly journals On the Optimal Design of Parallel Robots Taking Into Account Their Deformations and Natural Frequencies

2009 ◽  
Author(s):  
Se´bastien Briot ◽  
Anatol Pashkevich ◽  
Damien Chablat
Keyword(s):  
Optimal Design ◽  
Natural Frequencies ◽  
Jacobian Matrix ◽  
Parallel Robots ◽  
Drive System ◽  
Simplified Model ◽  
Simplified Models ◽  
Vibration Model ◽  
Dynamic Performances ◽  
High Dynamic

This paper discusses the utility of using simple stiffness and vibrations models, based on the Jacobian matrix of a manipulator and only the rigidity of the actuators, whenever its geometry is optimised. In many works, these simplified models are used to propose optimal design of robots. However, the elasticity of the drive system is often negligible in comparison with the elasticity of the elements, especially in applications where high dynamic performances are needed. Therefore, the use of such a simplified model may lead to the creation of robots with long legs, which will be submitted to large bending and twisting deformations. This paper presents an example of manipulator for which it is preferable to use a complete stiffness or vibration model to obtain the most suitable design and shows that the use of simplified models can lead to mechanisms with poorer rigidity.

scholarly journals Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots

2005 ◽  
Vol 128 (1) ◽  
pp. 199-206 ◽  
Author(s):  
J. P. Merlet
Keyword(s):  
Optimal Design ◽  
Condition Number ◽  
Jacobian Matrix ◽  
Parallel Robots ◽  
Condition Numbers ◽  
Accuracy Index ◽  
Positioning Errors ◽  
Local Accuracy ◽  
Early Beginning ◽  
Accuracy Indices

Although the concepts of Jacobian matrix, manipulability, and condition number have existed since the very early beginning of robotics their real significance is not always well understood. In this paper we revisit these concepts for parallel robots as accuracy indices in view of optimal design. We first show that the usual Jacobian matrix derived from the input-output velocities equations may not be sufficient to analyze the positioning errors of the platform. We then examine the concept of manipulability and show that its classical interpretation is erroneous. We then consider various common local dexterity indices, most of which are based on the condition number of the Jacobian matrix. It is emphasized that even for a given robot in a particular pose there are a variety of condition numbers and that their values are not coherent between themselves but also with what we may expect from an accuracy index. Global conditioning indices are then examined. Apart from the problem of being based on the local accuracy indices that are questionable, there is a computational problem in their calculation that is neglected most of the time. Finally, we examine what other indices may be used for optimal design and show that their calculation is most challenging.

Parallel robots with configurable platforms: Fundamental aspects of a new class of robotic architectures

2015 ◽  
Vol 230 (3) ◽  
pp. 463-472 ◽  
Author(s):  
Patrice Lambert ◽  
Just L Herder
Keyword(s):  
Closed Loop ◽  
Jacobian Matrix ◽  
Dynamic Performance ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
New Class ◽  
Contact Points ◽  
The Subject ◽  
High Dynamic

This paper introduces general and fundamental aspects of a new class of parallel robots termed “parallel robots with configurable platforms”. The concept behind parallel mechanisms with configurable platforms is that the rigid link (non-configurable) end-effector is replaced by an additional closed-loop chain (the configurable platform). Some of the links of this closed loop are attached to the limbs so both the position and the configuration of the platform can be fully controlled from the motors located on the base. They retain the advantages of classical parallel robots, i.e. that all the motors are grounded on the base, while offering mechanical grasping capabilities via multiple contact points. Despite the few studies that have been done yet on the subject, the possible range of applications for this type of architecture is promising since it would be suitable for any application requiring both controlled grasping capabilities and high dynamic performance. This paper provides some preliminary results regarding the topology, mobility, overconstraints, Jacobian matrix, singularities and type synthesis of parallel robots with configurable platforms.

Dynamic Modeling of the Torsional Vibration of the Slewing Mechanism of a Hydraulic Excavator

2012 ◽  
Vol 253-255 ◽  
pp. 2102-2106 ◽  
Author(s):  
Xu Juan Yang ◽  
Zong Hua Wu ◽  
Zhao Jun Li ◽  
Gan Wei Cai
Keyword(s):  
Torsional Vibration ◽  
Natural Frequencies ◽  
Planetary Gear ◽  
Moment Of Inertia ◽  
Hydraulic Excavator ◽  
Planetary Gear Trains ◽  
Vibration Model ◽  
Gear Trains ◽  
The Moment ◽  
Relationship Of

A torsional vibration model of the slewing mechanism of a hydraulic excavator is developed to predict its free vibration characteristics with consideration of many fundamental factors, such as the mesh stiffness of gear pairs, the coupling relationship of a two stage planetary gear trains and the variety of moment of inertia of the input end caused by the motion of work equipment. The natural frequencies are solved using the corresponding eigenvalue problem. Taking the moment of inertia of the input end for example to illustrate the relationship between the natural frequencies of the slewing mechanism and its parameters, based on the simulation results, just the first order frequency varies significantly with the moment of inertia of the input end of the slewing mechanism.

Split Vibration Modes in Acoustically-Coupled Disk Stacks

1995 ◽  
Author(s):  
Jung-Ge Tseng ◽  
Jonathan Wickert
Keyword(s):  
Natural Frequencies ◽  
Three Dimensional ◽  
System Level ◽  
Thin Plates ◽  
Mode Shapes ◽  
Design Parameters ◽  
Phase System ◽  
Acoustic Coupling ◽  
Annular Plates ◽  
Vibration Model

Abstract Vibration of an array of stacked annular plates, in which adjacent plates couple weakly through an acoustic layer, is investigated through experimental and theoretical methods. Such acoustic coupling manifests itself through split natural frequencies, beating in the time responses of adjacent or separated plates, and system-level modes in which plates in the array vibrate in- or out-of-phase at closely-spaced frequencies. Laboratory measurements, including a technique in which the frequency response function of all in-phase modes but no out-of-phase modes, or visa versa, is measured, demonstrate the contribution of coupling to the natural frequency spectrum, and identify the combinations of design parameters for which it is important. For the lower modes of primary interest here, the natural frequencies of the out-of-phase system modes decrease as the air layer becomes thinner, while those of the in-phase mode remain sensibly constant at the in vacuo values. A vibration model comprising N classical thin plates that couple through the three-dimensional acoustic fields established in the annular cavities between plates is developed, and its results are compared with measurements of the natural frequencies and mode shapes.

Vibrations of a Helicopter Rotor-Fuselage System Induced by the Main Rotor Blades in Flight

1955 ◽  
Vol 22 (3) ◽  
pp. 355-360
Author(s):  
M. Morduchow ◽  
S. W. Yuan ◽  
H. Reissner
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequencies ◽  
Rotor Blades ◽  
Helicopter Rotor ◽  
Simplified Model ◽  
Main Rotor ◽  
Numerical Examples ◽  
The Masses

Abstract Based on a simplified model of the hub-fuselage structure, a theoretical analysis is made of the response of the hub and fuselage of a helicopter in flight to harmonic forces transmitted by the rotor blades to the hub both in, and normal to, the plane of rotation. The assumed structure is in the form of a plane framework with masses concentrated at the joints. Simple expressions are derived for the vibration amplitudes of the mass points as functions of the masses and natural frequencies of the hub and the fuselage. The pertinent nondimensional parameters are determined, and simple explicit conditions of resonance are derived. Numerical examples are given to illustrate the results.

scholarly journals Nonlinear Forced Response of Electromechanical Integrated Toroidal Drive to Coupled Excitation

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Lizhong Xu ◽  
Fen Wang
Keyword(s):  
Natural Frequencies ◽  
Forced Response ◽  
Drive System ◽  
Mesh Stiffness ◽  
Electric Excitation ◽  
Time Period ◽  
Electromechanical Integrated ◽  
Exciting Frequency ◽  
Mesh Parameter ◽  
Forced Responses

The electric excitation and the parameter excitation from mesh stiffness fluctuation are analyzed. The forced response equations of the drive system to the coupled excitations are presented. For the exciting frequencies far from and near natural frequencies, the forced responses of the drive system to the coupled excitations are investigated. Results show that the nonlinear forced responses of the drive system to the coupled excitations change periodically and unsteadily; the time period of the nonlinear forced responses depends on the frequencies of the electric excitation, the mesh parameter excitation, and the nonlinear natural frequencies of the drive system; in order to improve the dynamics performance of the drive system, the frequencies of the electric excitations should not be taken as integral multiple of the mesh parameter exciting frequency.

Support Flexibility and Natural Frequencies of Pipe Mounted Thermowells

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
David S. Bartran
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Natural Frequencies ◽  
Pipe Wall ◽  
Simplified Model ◽  
Load Model ◽  
Distributed Load ◽  
Pipe Fittings ◽  
Insight Into ◽  
Design And Application

A simplified model of a pipe mounted thermowell provides a measure of insight into the design and application of intrusive pipe fittings. A combination of Fourier and Green’s function methods together with a distributed load model of the thermowell/pipe wall interface are used to calculate the support compliance and subsequently the natural frequencies of the thermowell. These are compared with limited though independent calculations. This comparison confirms a profound reduction in natural frequencies for commonly encountered thermowell installations, reductions that should not be ignored where the risk of flow-induced resonance is high.

Experimental Research on Parameters Identification of Dynamic Characteristic for Parallel Machine Tool

2013 ◽  
Vol 300-301 ◽  
pp. 181-184
Author(s):  
Chun Xia Zhu ◽  
Zhi Wen Chen ◽  
Bo Liu ◽  
Jing Wang
Keyword(s):  
Optimal Design ◽  
Theoretical Analysis ◽  
Machine Tool ◽  
Dynamic Characteristic ◽  
Parallel Machine ◽  
Vibration System ◽  
Flexible Coupling ◽  
Vibration Model ◽  
Experiment Method ◽  
Parallel Machine Tool

The dynamic characteristics of parallel 3-TPT machine tool are researched by experiment in this paper. Firstly, modal analysis principle of machine tool was analyzed in theory, and the parameters of dynamic characteristic were identified by theoretical analysis. Then vibration model of parallel machine tool was built and formed vibration system of rigid and flexible coupling for analysis. Then, the modal experiment method and steps were introduced, and the experiment parameters also were identified according to the experiment results. The result dates are showed that the result dates are validated. So the experiment method is feasible by experimental verification, which provides reference for dynamic optimal design.

Maximizing the lowest eigenvalue of a constrained affine sum with application to the optimal design of structures and vibrating systems

2008 ◽  
Vol 223 (3) ◽  
pp. 583-593 ◽  
Author(s):  
Y M Ram ◽  
S G Krishna
Keyword(s):  
Optimal Design ◽  
Discrete Model ◽  
Natural Frequencies ◽  
Symmetric Matrices ◽  
Vibratory System ◽  
Newton Iterative Method ◽  
Lagrange Problem ◽  
Repeated Use ◽  
Lowest Eigenvalue ◽  
Vibrating Systems

This article deals with the problem of maximizing the lowest eigenvalue of an affine sum of symmetric matrices subject to a constraint. It is shown that by the repeated use of eliminants, the problem may be reduced in a systematic manner to that of finding the roots of certain polynomials. However, the process of finding the analytical solution is tedious. Therefore, a Newton iterative method, which solves the problem numerically, is developed. To demonstrate the results, the Lagrange problem of determining the shape of the strongest column is formulated in the discrete model setting and solved by using the developed method. The design problem of finding the mass distribution in a vibratory system that optimizes its extreme natural frequencies is also given.

Comparison of Solid Oxide Fuel Cell Stack Performance Using Detailed and Simplified Models

2013 ◽  
Author(s):  
R. T. Nishida ◽  
S. B. Beale ◽  
J. G. Pharoah
Keyword(s):  
Fuel Cell ◽  
Solid Oxide Fuel Cell ◽  
Computational Cost ◽  
Transport Equations ◽  
Solid Oxide ◽  
Simplified Model ◽  
Oxide Fuel ◽  
Simplified Models ◽  
Detailed Model ◽  
Fuel Cell Stack

Two computational fluid dynamics models have been developed to predict the performance of a solid oxide fuel cell stack, a detailed and a simplified model. In the detailed model, the three dimensional momentum, heat, and species transport equations are coupled with electrochemistry. In the simplified model, the diffusion terms in the transport equations are selectively replaced by rate terms within the core region of the stack. This allows much coarser meshes to be employed at a fraction of the computational cost. Following the mathematical description of the problem, results for a single cell and multi-cell stack are presented. Comparisons of local current density, temperature, and cell voltage indicate that good agreement is obtained between the detailed and simplified models, confirming the validity of the latter as a practical option in stack design.

Sign in / Sign up

Export Citation Format

Share Document