scholarly journals Kinematics Analysis of a Novel Five-Degree-of-Freedom Spatial Parallel Micromanipulator

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Daniel Prusak ◽  
Konrad Kobus ◽  
Grzegorz Karpiel
Keyword(s):  
Mathematical Model ◽  
Piezoelectric Actuator ◽  
Analytical Solutions ◽  
Inverse Kinematics ◽  
Geometrical Model ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
Moving Platform ◽  
Position And Orientation ◽  
The Mathematical Model

A study of the inverse kinematics for a five-degree-of-freedom (DOF) spatial parallel micromanipulator is presented here below. The objective of this paper is the introduction of a structural and geometrical model of a novel five-degree-of-freedom spatial parallel micromanipulator, analysis of the effective and useful workspace of the micromechanism, presentation of the obtained analytical solutions of the microrobot’s inverse kinematics tasks, and verification of its correctness using selected computer programs and computation environments. The mathematical model presented in this paper describes the behaviour of individual elements for the applied 2-DOF novel piezoelectric actuator, resulting from the position and orientation of the microrobot’s moving platform.

scholarly journals Kinematics Simulation of Gough-Stewart Parallel Manipulator by Using Simulink Package in Matlab Software

2019 ◽  
Vol 27 (2) ◽  
pp. 10-20
Author(s):  
Hassan Mohammed Alwan ◽  
Riyadh Ahmed Sarhan
Keyword(s):  
Theoretical Model ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
Matlab Software ◽  
Kinematics Simulation ◽  
Moving Platform ◽  
Position And Orientation ◽  
Six Degree Of Freedom ◽  
Forward Equations

The Gough Stewart Robotic manipulator is a parallel manipulator with six-degree of freedom, which has six equations of Kinematics (Inverse and forward), with six variables (Lengths, Position, and Orientation). In this work derived the inverse equations, which used to compute the lengths of the linkages and its changes depended on the position and orientation of the platform's center, then derived the forward equations to calculate the position and orientation of the moving platform in terms of the lengths. This theoretical model of the kinematics analysis of the Gough Stewart has been built into the Simulink package in Matlab to obtain the lengths, position, and orientation for the manipulator at any time of motion. The input parameters (Position and Orientation) in inverse blocks compared with the output parameters (Position and Orientation) in the forward blocks, which show good results.

Kinematics Simulation of Parallel Mechanism Based on ADAMS

2012 ◽  
Vol 538-541 ◽  
pp. 479-482
Author(s):  
Xin Yu Du ◽  
Hong Wei Liu
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Virtual Prototype ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
Kinematics Simulation ◽  
Spatial Parallel Mechanism ◽  
Moving Platform ◽  
Simulation Results ◽  
Position And Orientation

In this paper,a kind of 3-UPU spatial parallel mechanism is introduced. Through deep analysis of the degree-of-freedom (DoF) for the platform using screw theory， the position and orientation of the moving platform is discussed. At last, the 3D virtual prototype modeling of this 3-UPU parallel mechanism based on software ADAMS is developed; the kinematics simulation and analysis are also carried out accordingly. From the simulation results, we can see that the proposed calculation of the DoFs and kinematics analysis is correct.

Parametric Design of a Spherical Eight-Bar Linkage Based on a Spherical Parallel Manipulator

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
Gim Song Soh ◽  
J. Michael McCarthy
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Parametric Design ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
End Effector ◽  
Arbitrary Base ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator

This paper presents a procedure that determines the dimensions of two constraining links to be added to a three degree-of-freedom spherical parallel manipulator so that it becomes a one degree-of-freedom spherical (8, 10) eight-bar linkage that guides its end-effector through five task poses. The dimensions of the spherical parallel manipulator are unconstrained, which provides the freedom to specify arbitrary base attachment points as well as the opportunity to shape the overall movement of the linkage. Inverse kinematics analysis of the spherical parallel manipulator provides a set of relative poses between all of the links, which are used to formulate the synthesis equations for spherical RR chains connecting any two of these links. The analysis of the resulting spherical eight-bar linkage verifies the movement of the system.

scholarly journals A Mathematical Model of Epidemics—A Tutorial for Students

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1174 ◽  
Author(s):  
Yutaka Okabe ◽  
Akira Shudo
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Sir Model ◽  
Exact Analytical Solutions ◽  
The Mathematical Model ◽  
Epidemic Diseases

This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.

Kinematics Analysis of a Hot-Line Live Working Manipulator

2014 ◽  
Vol 610 ◽  
pp. 28-34 ◽  
Author(s):  
Xiao Lin Ma ◽  
Hui Chai ◽  
Yun Jiang Li
Keyword(s):  
Analytical Solutions ◽  
Inverse Kinematics ◽  
Transformation Method ◽  
Forward Kinematics ◽  
Euler Angles ◽  
Kinematics Analysis ◽  
Hydraulic Actuator ◽  
End Effector

This paper introduces the development of hot-line live working manipulators and gives a new configuration manipulator driven by hydraulic actuator firstly. Then, its forward kinematics equations are derived with homogenous transformation method. Finally, the analytical solutions of its inverse kinematics are solved under the condition that the posture of the end-effector is known and given with z-y-z Euler angles.

scholarly journals Approximation of potential-driven flow dynamics in large-scale self-similar tree networks

2011 ◽  
Vol 467 (2134) ◽  
pp. 2810-2824 ◽  
Author(s):  
Jason Mayes ◽  
Mihir Sen
Keyword(s):  
Mathematical Model ◽  
Analytical Solutions ◽  
Large Scale ◽  
Differential Algebraic Equations ◽  
Flow Dynamics ◽  
Algebraic Equations ◽  
Tree Networks ◽  
Self Similar ◽  
Large Scale Flow ◽  
The Mathematical Model

Dynamic analysis of large-scale flow networks is made difficult by the large system of differential-algebraic equations resulting from its modelling. To simplify analysis, the mathematical model must be sufficiently reduced in complexity. For self-similar tree networks, this reduction can be made using the network’s structure in way that can allow simple, analytical solutions. For very large, but finite, networks, analytical solutions are more difficult to obtain. In the infinite limit, however, analysis is sometimes greatly simplified. It is shown that approximating large finite networks as infinite not only simplifies the analysis, but also provides an excellent approximate solution.

Grinding Process of Ball End Milling Cutter Flank

2018 ◽  
Vol 764 ◽  
pp. 383-390 ◽  
Author(s):  
Quan Qi Xin ◽  
Tai Yong Wang ◽  
Zhi Qiang Yu ◽  
Hong Yan Hu
Keyword(s):  
Mathematical Model ◽  
End Milling ◽  
Cutting Edge ◽  
Grinding Wheel ◽  
Grinding Process ◽  
Milling Cutter ◽  
Ball End Milling ◽  
Position And Orientation ◽  
The Mathematical Model

In this paper, the mathematical model of "S" - shaped cutting-edge curve is optimized, and the position and orientation of the grinding wheel of the first and second flank of the ball end milling cutter are calculated, The correctness of the algorithm is verified by VERICUT simulation.

Orientation Workspace Analysis of a Novel 3SPS+1PS Symmetrical Parallel Manipulator Based on Unit Quaternion

2011 ◽  
Vol 201-203 ◽  
pp. 1849-1853
Author(s):  
Jing Li Yu ◽  
Gang Cheng ◽  
Shuai Zhang ◽  
De Kun Zhang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Unit Quaternion ◽  
Structure Characteristics ◽  
Workspace Analysis ◽  
Moving Platform ◽  
Position And Orientation ◽  
4 Degrees Of Freedom ◽  
Orientation Workspace

For a novel 3SPS+1PS parallel manipulator with 4 degrees of freedom including three rotations and one translation, the formulae for solving the inverse kinematics equations are derived based on quaternion method. Unit quaternion is used to represent the position and orientation of moving platform, and the singularities caused by Euler angles are avoided. Combining the topological structure characteristics of the parallel manipulator, it only has three rotations when its moving platform is at a given translation position. Based on the inverse position/pose equations and the all the constraints of the parallel manipulator, the discrete algorithm for the orientation workspaces of 3SPS+1PS parallel manipulator where the moving platform is at some different given translation positions are designed. The research builds the theoretical basis for optimizing the orientation workspace with given position.

scholarly journals Simulation Analysis of One Degree of Freedom Motion of Electromagnetic Spherical Joint based on Maxwell

2021 ◽  
Vol 2085 (1) ◽  
pp. 012014
Author(s):  
Haoran Wang ◽  
Fucong Liu ◽  
Sai Lou
Keyword(s):  
Mathematical Model ◽  
Simulation Analysis ◽  
Lagrange Equation ◽  
Degree Of Freedom ◽  
Spherical Joint ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Structure And Motion ◽  
The Mathematical Model ◽  
The Relationship

Abstract In order to improve the stiffness of the spherical joint of the robot, reduce the difficulty of manufacturing and the complexity of the control system, this paper proposed a method of spherical joint and digital drive of the robot based on the electromagnetic principle. Firstly, introduces the structure and motion principle of the spherical joint of the robot, establishes the mathematical model of the spherical joint and establishes the dynamic model according to the second Lagrange equation. after that, the relationship between the number of ampire-turns of the electromagnet on the spherical joint, the attitude Angle of the rotor and the force of the rotor was obtained by simulating the single degree of freedom of the joint based on Ansys maxwell and Matlab, which provided a basis for the realization of the digital drive of the spherical joint.

Motion of a Sphere on a Plane

1994 ◽  
Author(s):  
Yong-Xian Xu ◽  
Dilip Kohli ◽  
Larry Vezina ◽  
Daniel R. Speranza
Keyword(s):  
Mathematical Model ◽  
Initial Conditions ◽  
Contact Point ◽  
Break Point ◽  
Degree Of Freedom ◽  
Geometric Center ◽  
Inertia Properties ◽  
Gyroscopic Motion ◽  
The Mathematical Model ◽  
First Time

Abstract The motion of a sphere on a plane is a five degree-of-freedom motion. It consists of two independent translations of the geometric center of the sphere and three rotations corresponding to gyroscopic motion of the sphere. The trajectory of an imbalanced sphere on the plane depends on: (1) the physical and inertia properties of the sphere, (2) the initial conditions of motion, and (3) the friction between the sphere and the plane. To predict the trajectory of the sphere, a general Eulerian mathematical model is developed which takes into account these conditions. The mathematical model is verified through experimentation. For the first time, general characteristics of the translatory and rotatory motions of the imbalanced sphere with general inertia distribution are presented. The existence of the “break point” in the trajectory is illustrated by examples. The trajectory (track) of the contact point on the surface of the sphere is also analyzed.

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