Stiffness Optimization of redundant mechanism based on elastic coupling and inertial coupling characteristics

2021 ◽  
pp. 1-29
Author(s):  
Xiao-Jin Wan ◽  
Dengfeng Jia
Keyword(s):  
Natural Frequency ◽  
Parallel Mechanism ◽  
Virtual Work ◽  
Structural Parameters ◽  
Dynamic Performance ◽  
Algebraic Solution ◽  
Elastic Coupling ◽  
Inertial Coupling ◽  
Two Indices ◽  
Redundant Mechanism

Abstract Aiming to redundant parallel mechanism, on the basis of the kinetic energy method, virtual work principle and perturbation method, the generalized mass matrix and generalized stiffness matrix are obtained, respectively. Two indices on inertial coupling and elastic coupling are defined to measure the decoupling level of the redundant parallel mechanism in terms of two generalized matrices. Furthermore, an algebraic solution method for natural frequency equation of the mechanism is utilized to obtain the natural frequency by means of the Cholesky decomposition method. And then, in order to minimize inertial coupling and elastic coupling, and maximize the natural frequency of the mechanism, two indices and natural frequency are taken as objective functions to optimize the structural parameters of the redundant mechanism, so that optimal dynamic performance of the mechanism is acquired. In the optimization of natural frequency, two optimal solutions are selected. One is to consider inertial coupling and elastic coupling and the other is to ignore inertial coupling and elastic coupling. Finally, the dynamic performance of the two indexes is better by comparing the dexterity of the two solutions

Dynamic Performance Study of Stewart Parallel Mechanism Based on Natural Frequency

2014 ◽  
Vol 635-637 ◽  
pp. 1246-1250 ◽  
Author(s):  
Bang Jun Lv ◽  
Li Kun Peng ◽  
Jia Chen
Keyword(s):  
Natural Frequency ◽  
Parallel Mechanism ◽  
Dynamic Performance ◽  
Transmission Mechanism ◽  
Local Dynamic ◽  
Performance Study ◽  
Performance Indices ◽  
Inertia Parameters ◽  
Moving Platform ◽  
Variation Trends

The stiffness of transmission mechanism, assembled joints and moving platform, the compressibility of oil, and the load inertia of hydraulic Stewart mechanism will cause synthetically mechanical and hydraulic resonance problems, which will directly influence the system dynamic performance. The natural frequency and local dynamic isotropy index are adopted to evaluate dynamic performance. The variation trends of performance indices with configuration and inertia parameters are analyzed, and general optimal design rules and conclusions are obtained.

Transfer of Energy From High- to Low-Frequency Modes in the Bending-Torsion Oscillation of Cantilever Beams

1999 ◽  
Author(s):  
Haider N. Arafat ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequency ◽  
Virtual Work ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Nonlinear Bending ◽  
Torsional Mode ◽  
Bending Mode ◽  
Plane Bending

Abstract We investigate the nonlinear bending-torsion response of a cantilever beam to a transverse harmonic excitation, where the forcing frequency is near the natural frequency of the first torsional mode. We analyze the case where the first in-plane bending mode is activated by a nonresonant mechanism. We use the method of time-averaged Lagrangian and virtual work to determine the equations governing the modulations of the phases and amplitudes of the interacting modes. These equations are then used to investigate the nonlinear behavior of limit-cycle oscillations of the beam as the excitation amplitude is slowly varied. As an example, we consider the response of an aluminum beam for which the natural frequency of the first in-plane bending mode is fv1 ≈ 5.7 Hz and the natural frequency of the first torsional mode is fϕ1 ≈ 138.9 Hz.

The Optimization of Thermocouple Galvanometer System Dynamics When Measuring Temperature Transients

1973 ◽  
Vol 6 (9) ◽  
pp. 384-388
Author(s):  
W. H. McKenzie ◽  
A. H. Richards
Keyword(s):  
System Dynamics ◽  
Natural Frequency ◽  
Time Constant ◽  
Exponential Type ◽  
Natural Frequencies ◽  
Low Voltage ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Ultra Violet ◽  
Dimensional Parameter

When using thermocouples directly connected to ultra-violet galvanometers for recording temperature transients, the low-voltage outputs necessitate the use of galvanometers with low natural frequencies. This puts a limitation on the overall dynamic performance. In a particular application, the user has to select the damping resistor for the galvanometer and the work describes how this is done so that the system is optimised for minimum integrated errors during a transient. The transient considered was of an exponential type which occurs frequently in practice and it is shown that the correct damping ratio and hence damping resistor for the galvanometer depends upon the non-dimensional parameter defined by the product of the natural frequency of the galvanometer and the time constant of the exponential. The results show that the usual value of damping ratio of 0·64 based on minimum sinusoidal distortion has to be modified for best dynamic performance. However, if the non-dimensional parameter is sufficiently large, higher values of damping can be used, which produce a large trace with acceptably small errors.

scholarly journals A Novel Control Strategy for Grid-Connected Inverter Based on Iterative Calculation of Structural Parameters

Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3306 ◽  
Author(s):  
Zhenao Sun ◽  
Dazhi Wang ◽  
Tianqing Yuan ◽  
Zairan Liu ◽  
Jiahui Yu
Keyword(s):  
Control Strategy ◽  
Structural Parameters ◽  
Dynamic Performance ◽  
Open Loop ◽  
Output Current ◽  
Open Loop System ◽  
Iterative Calculation ◽  
Static Performance ◽  
Grid Connected Inverter ◽  
Pv Grid

A novel control strategy that is based on iterative calculation of structural parameters is proposed for grid-connected inverter in this paper. The proposed strategy has a good dynamic performance, which makes it particularly suitable for the application of PV grid-connected generation. First, a second-order discretization mathematical model of grid-connected inverter control is established in the dq frame. The corresponding relation between the control signal and the output current is deduced in formulas. Then, the values of structural parameters in the formulas can be obtained through iterative calculation, which can further reduce the amount of calculation. After several iteration cycles, the structural parameters are approximately equal to their actual values and the inverter can be controlled as an open-loop system with its dynamic performance optimized. At last, simulation and experiments are performed. The results show that the static performance of the proposed strategy is as good as that of the classical ones, but its dynamic performance is improved significantly.

Dimensional Synthesis of a Novel 2T2R Parallel Manipulator for Medical Applications

2014 ◽  
Author(s):  
Nitish Kumar ◽  
Olivier Piccin ◽  
Bernard Bayle
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Structural Parameters ◽  
Geometric Analysis ◽  
Medical Applications ◽  
Dimensional Synthesis ◽  
Synthesis Algorithm ◽  
Percutaneous Procedures ◽  
Actuated Joints

This paper deals with the dimensional synthesis of a novel parallel manipulator for medical applications. This parallel mechanism has a novel 2T2R mobility derived from the targeted application of needle manipulation. The kinematic design of this 2T2R manipulator and its novelty are illustrated in relation to the percutaneous procedures. Due to the demanding constraints on its size and compactness, achieving a large workspace especially in orientation, is a rather difficult task. The workspace size and kinematic constraint analysis are considered for the dimensional synthesis of this 2T2R parallel mechanism. A dimensional synthesis algorithm based on the screw theory and the geometric analysis of the singularities is described. This algorithm also helps to eliminate the existence of voids inside the workspace. The selection of the actuated joints is validated. Finally, the dimensions of the structural parameters of the mechanism are calculated for achieving the required workspace within the design constraints of size, compactness and a preliminary prototype without actuators is presented.

Natural Frequency Analysis of Hydraulic Quadruped Robot and Structural Optimization of the Leg

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Qingjun Yang ◽  
Rui Zhu ◽  
Zhenguo Niu ◽  
Chen Chen ◽  
Qi Mao ◽  
...  
Keyword(s):  
Natural Frequency ◽  
Load Capacity ◽  
Structural Parameters ◽  
Multiple Input Multiple Output ◽  
State Equation ◽  
Point Of View ◽  
System Response ◽  
Response Characteristics ◽  
Research Fields ◽  
Natural Frequency Analysis

Abstract Hydraulic quadruped robots can adapt to very complex ground conditions, as they have good maneuverability and high load capacity and, therefore, have received great attention in military research fields all over the world. However, there is no mature theory on how to ensure stable, efficient, and fast walking of robots. In this paper, from the point of view of the natural frequency of the hydraulic system, we first calculate the natural frequency of the robot's legs during the whole motion period of the robot and verify the accuracy of calculation through system identification. Then, through the analysis of the state equation and transfer function matrix of the multiple-input multiple-output system, it is found that the zero and pole of the system are very close, this is why the natural frequency is low but the system response is acceptable and then we prove that no parameter for the simultaneous zero-pole cancelation of two hydraulic cylinders exists. With the goal of increasing the natural frequency, we optimized the leg structure of the robot to find the best structural parameters. Finally, a single-leg test bench was built. The experimental results show that the optimization of the structure can actually increase the natural frequency of the system and significantly improve the response characteristics of the robot.

A Study on Calculation Method of Natural Frequency for Rubber Damped Torsional Vibration Absorbers

2014 ◽  
Author(s):  
Wen-Bin Shangguan ◽  
Yumin Wei ◽  
Subhash Rakheja ◽  
Xu Zhao ◽  
Jun-wei Rong ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Natural Frequency ◽  
Dynamic Performance ◽  
Model Parameters ◽  
Dynamic Shear ◽  
Shear Properties ◽  
Rubber Ring ◽  
Constructive Models ◽  
Dynamic Performances ◽  
The Moment

The natural frequency is the key performance parameters of a rubber materials damper, and it is determined by the static and dynamic shear properties of the rubber materials (rubber ring) and the moment of inertia of the inertia ring. The rubber ring is usually in compression state, and its static and dynamic shear properties are dependent on its sizes, compression ratio and chemical ingredients. A special fixture is designed and used for measuring static and dynamic shear performance of a rubber ring under different compression ratios in the study. To characterize the shear static and dynamic performances of rubbers, three constructive models (Kelvin-Voigt, the Maxwell and the fractional derivative constitutive model) are presented and the method for obtaining the model parameters in the fractional derivative constructive models are developed using the measured dynamic performance of a rubber shear specimen. The natural frequency of a rubber materials damper is calculated using the fractional derivative to characterize the rubber ring of the damper, and the calculated frequencies are compared with the measurements.

The Mechanics of Parallel Mechanisms and Walking Machines

1994 ◽  
Vol 208 (6) ◽  
pp. 367-377 ◽  
Author(s):  
S J Zhang ◽  
D J Sanger ◽  
D Howard
Keyword(s):  
Parallel Mechanism ◽  
Virtual Work ◽  
The Body ◽  
Position Vector ◽  
Parallel Mechanisms ◽  
Active Joint ◽  
End Effector ◽  
Walking Machine ◽  
Walking Machines ◽  
Fixed Base

A parallel mechanism is one whose links and joints form two or more serially connected chains which join the fixed base and the end effector The mechanism of a multi-legged walking machine can be considered as a parallel mechanism whose base is not fixed and whose configuration changes during different phases of its gait. This paper presents methods for analysing the mechanics of parallel mechanisms and walking machines using vector and screw algebra Firstly, displacement analysis is covered; this includes general methods for deriving the position vector of any joint in any leg and for calculating the active joint displacements in any leg. Secondly, velocity analysis is covered which tackles the problem of calculating active joint velocities given the velocity, position and the orientation of the body and the positions of the feet. Thirdly, the static analysis of these classes of mechanisms using the principle of virtual work and screw algebra is given. Expressions are derived for the actuator forces and torques required to balance a given end effector (or body) wrench and, in the case of a walking machine, the ground reactions at the feet. Numerical examples are given to demonstrate the application of these methods.

Study on Modal Change Dual Planetary Composite Transmission System

2014 ◽  
Vol 620 ◽  
pp. 388-394
Author(s):  
Xue Zeng Zhao ◽  
Xi Gui Wang ◽  
Yong Mei Wang
Keyword(s):  
Natural Frequency ◽  
Dynamic Performance ◽  
Transmission System ◽  
Frequency Curve ◽  
Modal System ◽  
Mode Change ◽  
Mode Localization ◽  
Modal Change ◽  
System Mode ◽  
Influence Degree

In the study of the dynamic characteristics of the system, should pay attention to the influence on the dynamic performance of the system mode change. Mode change is closely related with mutation phenomena of mode localization process, in the natural frequency with the change of parameters, with a large curvature are quickly turned to separate the two natural frequency curve in the close position. Mode change will lead to the drastic changes in the natural frequency and modal energy, the variation of system parameters is also the location of the influence degree mutation position. Based on the modal characteristics of unique two stage power branch double wide helical planetary composite transmission system, studied the mode change phenomena, reveal the modal system changes.

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