scholarly journals Forward Dynamic Solution and Optimization of a 1-DOF Parallel Mechanism for Vibrating Screen

2021 ◽  
Author(s):  
Si-Jin Xiao ◽  
Guang-Lei Wu ◽  
Ju Li ◽  
Hui-Ping Shen ◽  
Ting-Li Yang
Keyword(s):  
Parallel Mechanism ◽  
Virtual Work ◽  
Differential Evolution Algorithm ◽  
Coefficient Matrix ◽  
Euler Method ◽  
Open Chain ◽  
Vibrating Screen ◽  
Dynamic Performances ◽  
Response Equation ◽  
Velocity Equation

Abstract In this paper, the ordered single-open-chain (SOC) method in combination with the principle of virtual work is adopted to model and solve the forward dynamics of a single degree-of-freedom (DOF) parallel mechanism (PM), featuring one translation and two rotations (1T2R), which is applied in spatial vibrating screen (i.e., parallel vibrating screen mechanism, PVSM). Afterwards, the dynamic performances of the PVSM is optimized using differential evolution algorithm. Based on the kinematics of the PM, the forward dynamic model is derived and the dynamic response equation is built, of which the coefficient matrix is determined by means of the generalized velocity equation. Moreover, the Euler method was adopted to solve the numerical solution of the differential equation of motion to characterize the motion law and dynamics of the screen surface of the PVSM, which is verified with ADAMS simulation. With the parametric model, the dynamic optimization of PVSM is carried out to maximize the energy transfer efficiency, subject to the constraints on the link mass. The comparison of the dynamic performances of the PVSM with and without optimization reveals the improvement of the PM.

Inverse Kinematic Solution and Dynamic Model to 3PTT Parallel Mechanism

2014 ◽  
Vol 945-949 ◽  
pp. 1421-1425
Author(s):  
Xiu Qing Hao
Keyword(s):  
Dynamic Model ◽  
Dynamic Simulation ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Euler Method ◽  
Research Subject ◽  
Adams Software ◽  
Inverse Kinematic Analysis ◽  
Simulation Results ◽  
Kinematic Solution

Take typical parallel mechanism 3PTT as research subject, its inverse kinematic analysis solution was gotten. Dynamic model of the mechanism was established by Newton-Euler method, and the force and torque equations were derived. Dynamic simulation of 3PTT parallel mechanism was done by using ADAMS software, and simulation results have verified the correctness of the theoretical conclusions.

scholarly journals Sparsity-Constrained NMF Algorithm Based on Evolution Strategy for Hyperspectral Unmixing

2018 ◽  
Vol 232 ◽  
pp. 04019
Author(s):  
ShangBin Ning ◽  
FengChao Zuo
Keyword(s):  
Optimization Technique ◽  
Differential Evolution Algorithm ◽  
Real Data ◽  
Coefficient Matrix ◽  
Selection Strategy ◽  
Blind Separation ◽  
Basis Matrix ◽  
Hyperspectral Unmixing ◽  
Update Rules ◽  
Multiplicative Update

As a powerful and explainable blind separation tool, non-negative matrix factorization (NMF) is attracting increasing attention in Hyperspectral Unmixing(HU). By effectively utilizing the sparsity priori of data, sparsity-constrained NMF has become a representative method to improve the precision of unmixing. However, the optimization technique based on simple multiplicative update rules makes its unmixing results easy to fall into local minimum and lack of robustness. To solve these problems, this paper proposes a new hybrid algorithm for sparsity constrained NMF by intergrating evolutionary computing and multiplicative update rules (MURs). To find the superior solution in each iteration,the proposed algorithm effectively combines the MURs based on alternate optimization technique, the coefficient matrix selection strategy with sparsity measure, as well as the global optimization technique for basis matrix via the differential evolution algorithm .The effectiveness of the proposed method is demonstrated via the experimental results on real data and comparison with representative algorithms.

Development of Equations of Motion for a Stewart Platform Under Prescribed Mount Motion

2018 ◽  
Author(s):  
Takeyuki Ono ◽  
Ryosuke Eto ◽  
Junya Yamakawa ◽  
Hidenori Murakami
Keyword(s):  
Rigid Body ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Base Plate ◽  
Stewart Platform ◽  
Euler Method ◽  
Moving Frame ◽  
Real Time Control ◽  
Precise Positioning ◽  
Time Control

Analytical equations of motion are critical for real-time control of translating manipulators, which require precise positioning of various tools for their mission. Specifically, when manipulators mounted on moving robots or vehicles perform precise positioning of their tools, it becomes economical to develop a Stewart platform, whose sole task is stabilizing the orientation and crude position of its top table, onto which various precision tools are attached. In this paper, analytical equations of motion are developed for a Stewart platform whose motion of the base plate is prescribed. To describe the kinematics of the platform, the moving frame method, presented by one of authors [1,2], is employed. In the method the coordinates of the origin of a body attached coordinate system and vector basis are expressed by using 4 × 4 frame connection matrices, which form the special Euclidean group, SE(3). The use of SE(3) allows accurate description of kinematics of each rigid body using (relative) joint coordinates. In kinetics, the principle of virtual work is employed, in which system virtual displacements are expressed through B-matrix by essential virtual displacements, reflecting the connection of the rigid body system [2]. The resulting equations for fixed base plate reduce to those for the top plate, obtained by the Newton-Euler method. A main result of the paper is the analytical equations of motion in matrix form for dynamics analyses of a Stewart platform whose base plate moves. The control applications of those equations will be deferred to subsequent publications.

A Systematical Approach for Structure Synthesis of Parallel Mechanisms Based on Single-Open-Chain Modules and Its Application

2009 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Lu-Bin Hang ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Systematic Approach ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Open Chain ◽  
Structure Synthesis ◽  
Vector Algebra ◽  
Algebra Theory ◽  
Position And Orientation

Based on previous research results presented by authors, this paper proposes a novel systematic approach for structure synthesis of all parallel mechanisms (excluding Bennett mechanism etc), which is totally different from the approaches based on screw theory and based on displacement subgroup. Main characteristics of this approach are: (a) the synthesized mechanisms are non-instantaneous ones, and (b) only simple mathematical tools (vector algebra, theory of sets, etc.) are used. Main steps of this approach include: (1) Determining functional and structural requirements of the parallel mechanism to be synthesized, such as position and orientation characteristic (POC) matrix, degree of freedom (DOF), etc. (2) Type synthesis of branches. (3) Assembling of branches (determining the geometry constraint conditions among the branches attached between the moving platform and the frame, and checking the DOF). (4) Identifying the inactive joints. (5) Selecting the actuating joints. In order to illustrate the whole procedure, the type synthesis of spherical parallel mechanisms is studied using this approach.

Acceleration and Dexterity Performance Indices for 6-DOF and Lower-Mobility Parallel Mechanism

2004 ◽  
Author(s):  
X. J. Guo ◽  
F. Q. Chang ◽  
S. J. Zhu
Keyword(s):  
Parallel Mechanism ◽  
Robot Manipulator ◽  
Coefficient Matrix ◽  
Second Order ◽  
Influence Coefficient ◽  
Global Index ◽  
Performance Indices ◽  
First Order ◽  
Lower Mobility

On the basis of first-order and second-order kinematic influence coefficient matrices, dynamics characteristics indices for robot manipulator are presented in the paper. Different from indices before, these indices include not only the first-order kinematics influence coefficient matrix G, but also the second-order kinematic influence coefficient matrix H. Then with the global index, these indices can be used to guide the dynamics design.

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.

Dynamic performances analysis of hybrid press based on dependent generalized coordinates

2014 ◽  
Vol 229 (12) ◽  
pp. 2187-2194
Author(s):  
Jinliang Gong ◽  
Xiaoming Wang ◽  
Fengan Huang ◽  
Yanfei Zhang
Keyword(s):  
Dynamic Model ◽  
Virtual Work ◽  
Single Degree Of Freedom ◽  
Virtual Work Principle ◽  
Generalized Coordinates ◽  
Hybrid Mechanism ◽  
Adams Simulation ◽  
Angular Velocities ◽  
Dynamic Performances ◽  
Angular Displacements

A kind of multi-link hybrid press mechanism is brought forth. It adopts three motors as actuations to fulfill the single degree of freedom output of end effector. For hybrid press mechanism, the forward kinematics is usually complicated and its numerical solution is computation-intensive and time-consuming. Therefore, the dynamic model is difficult to build up when it needs to analyze the input function’s effect on system dynamic performances. Concept of dependent generalized coordinates is adpoted here and a kind of dynamic modeling method of multi-link hybrid mechanism is presented based on the virtual work principle. The linear and angular displacements of every component can be expressed concisely in the form of dependent generalized coordinates. They are much simpler than that of independent generalized coordinates. Accordingly, linear and angular velocities will be derived by differentiating with respect to displacements. Velocity Jacobian matrix will be simplified under dependent generalized coordinates system and the virtual work principle-based dynamic model will also be simplified accordingly. Then it needs to introduce constraint conditions and multiplier in order to acquire actuation forces. Introduction of the constraints guarantees the real kinetic characteristics of mechanism. In the end, the curves of actuation forces and spherical joints’ inner forces variations are presented using Matlab. By comparing with Adams simulation results, validity of the method has been proved.

Design and Analysis of 3-DOF Micromanipulator Driven by Piezoelectric Actuators

2008 ◽  
Author(s):  
Shihua Li ◽  
Yue Zhang ◽  
Zhen Huang ◽  
Changcheng Yu ◽  
Wenhua Ding
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Parallel Mechanism ◽  
Piezoelectric Actuators ◽  
Coefficient Matrix ◽  
Influence Coefficient ◽  
Velocity Analysis ◽  
First Order ◽  
Flexure Hinges ◽  
Moving Platform

A novel 3-DOF parallel micromanipulator which is driven by piezoelectric actuators has been developed that based on 3–5R parallel mechanism. The micromanipulator consists of a moving platform, a fixed platform, three 5R fixed-length chains and three piezoelectric actuators. In this paper, the first-order influence coefficient matrix of the micromanipulator is given, and then the velocity analysis is given. The dimension of the platform and flexure hinges and the position of flexure are designed, and the safety check of the flexible hinges and the designed mechanism is done with the aid of finite element modeling to provide good stiffness with little bending deformation of the platform. The merits of parallel mechanism and piezoelectric actuators are reflected in this mechanism.

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