Studies on Isotropy of Planar 5-Bar Linkages

2004 ◽  
Author(s):  
C. Amarnath ◽  
K. N. Umesh
Keyword(s):  
Geometric Approach ◽  
Geometrical Approach ◽  
End Effector ◽  
Isotropic Point ◽  
Important Requirement ◽  
Point To Point

The ability to move at reasonable ease in all directions is an important requirement in the design of manipulators. The degree of ease of mobility varies from point to point in the workspace of the manipulator’s end effector. Maximum ease of mobility is obtained at an isotropic point, and the minimum occurs at singularities. An attempt has been made here to use a geometric approach for determining the isotropic points in the workspace of planar 5-bar linkages. The geometrical approach leads to interesting observations on the location of isotropic points in the workspace. The procedure also yields a technique for the synthesis of 5-bar linkages and associated coupler points exhibiting isotropic behaviour. Additionally it has been shown that coupler points exhibiting isotropic mobility occur in pairs.

scholarly journals Frequency-Domain Robust Performance Condition for Controller Uncertainty in SISO LTI Systems: A Geometric Approach

2009 ◽  
Vol 2009 ◽  
pp. 1-9
Author(s):  
Vahid Raissi Dehkordi ◽  
Benoit Boulet
Keyword(s):  
Frequency Domain ◽  
Linear Time ◽  
Order Reduction ◽  
Geometric Approach ◽  
Geometrical Approach ◽  
Robust Performance ◽  
Linear Time Invariant ◽  
Additive Perturbation ◽  
Plant Uncertainty ◽  
Invariant Control

This paper deals with the robust performance problem of a linear time-invariant control system in the presence of robust controller uncertainty. Assuming that plant uncertainty is modeled as an additive perturbation, a geometrical approach is followed in order to find a necessary and sufficient condition for robust performance in the form of a bound on the magnitude of controller uncertainty. This frequency domain bound is derived by converting the problem into an optimization problem, whose solution is shown to be more time-efficient than a conventional structured singular value calculation. The bound on controller uncertainty can be used in controller order reduction and implementation problems.

Variable-Velocity Exponential Input Shaping for Position Controlled Robotic Systems

2010 ◽  
Author(s):  
P. Iravani ◽  
M. N. Sahinkaya
Keyword(s):  
Inverse Dynamics ◽  
Vibration Reduction ◽  
Robotic Systems ◽  
Input Shaping ◽  
Control Input ◽  
End Effector ◽  
Flexible System ◽  
Flexible Loads ◽  
New Form ◽  
Point To Point

This paper demonstrates a new form of Input Shaping for vibration reduction applied to robotic systems that manipulate flexible loads. The method is based on using an exponential function to define asymptotic and vibration-free trajectories for the flexible system. The required control input is calculated analytically by using inverse dynamics which ensures the desired end-effector trajectory. The method is demonstrated experimentally on the control of point-to-point movements of a robotic manipulator.

Modeling and control of new model in a spatial coordinates -3D- for cable-based robots

2015 ◽  
Vol 12 (2) ◽  
pp. 189-200 ◽  
Author(s):  
Fouad Inel ◽  
Billel Bouchmal ◽  
Lakhdar Khochmane
Keyword(s):  
Closed Loop ◽  
Geometric Model ◽  
Kinematic Model ◽  
End Effector ◽  
Modeling And Control ◽  
New Model ◽  
Spiral Trajectory ◽  
Spatial Coordinates ◽  
Point To Point ◽  
And Control

This paper presents a modeling and control of new model in a spatial coordinates (x, y, z), from this structures we choose: regular pyramid of a square basis manipulated by five cables and eight cables for a cubic shape. The main objective of this work is to integrate the axe (z) on the horizontal plane (x, y) i-e the plan 3D. This last their intervention especially when we obliged to transfer the end effector from point to point, for that we used the direct and inverse geometric model to study and simulate the end effector position of the robot with five and eight cables. A graphical user interface has been implemented in order to visualizing the position of the robot. Secondly, we present the desired path and determination the tensions and cables lengths of kinematic model required to follow spiral trajectory. At the end, we study the response of our systems in closed loop with a Proportional-Integrated-Derivative (PID) using MATLAB/Simulink which used to verify the performance of the controller.

Motion planning for multiple non-holonomic robots: a geometric approach

Robotica ◽  
2008 ◽  
Vol 26 (4) ◽  
pp. 525-536 ◽  
Author(s):  
Elias K. Xidias ◽  
Nikos A. Aspragathos
Keyword(s):  
Genetic Algorithm ◽  
Euclidean Space ◽  
Motion Planning ◽  
Optimization Problem ◽  
Geometric Approach ◽  
Dynamic Environments ◽  
Planning Problem ◽  
Geometrical Approach ◽  
Moving Obstacles ◽  
Geometric Entity

SUMMARYIn this paper, a geometrical approach is developed to generate simultaneously optimal (or near-optimal) smooth paths for a set of non-holonomic robots, moving only forward in a 2D environment cluttered with static and moving obstacles. The robots environment is represented by a 3D geometric entity called Bump-Surface, which is embedded in a 4D Euclidean space. The multi-motion planning problem (MMPP) is resolved by simultaneously finding the paths for the set of robots represented by monoparametric smooth C2 curves onto the Bump-Surface, such that their inverse images onto the initial 2D workspace satisfy the optimization motion-planning criteria and constraints. The MMPP is expressed as an optimization problem, which is solved on the Bump-Surface using a genetic algorithm. The performance of the proposed approach is tested through a considerable number of simulated 2D dynamic environments with car-like robots.

A Geometric Approach for Error Space Estimation of Planar Linkage

2021 ◽  
Author(s):  
Jianzhong Ding ◽  
Chunjie Wang
Keyword(s):  
Closed Form ◽  
Error Propagation ◽  
Evaluation Method ◽  
Geometric Approach ◽  
Simple Expression ◽  
Propagation Path ◽  
End Effector ◽  
3 Dimensional ◽  
Error Space ◽  
Four Bar Linkage

Abstract This article develops a geometric method to estimate the clearances-induced error space of any planar linkage. The error space discussed here represents the unconstrained mobility of the end-effector when actuators of the mechanism are locked, and is expressed by a connected geometry in 3-dimensional Euclidean frame {x, y, θ}. First, error space of the planar mechanism is modeled and closed-form expressions are derived. Then, levels of joints in error propagation analysis are defined and illustrated with an example of a eight-bar linkage, following which error propagation path among closed-loop structures is given. The modeling of error propagation and accumulation is introduced in detail. Moreover, a simplification technique is discussed for simple expression of the error space propagated from previous joints. This study provides a way to have a deep insight into the accuracy performance of any planar linkage and the proposed error space evaluation method is validated by case study of error space estimation of a four-bar linkage and a six-bar linkage. For the four-bar linkage, the structure with optimal accuracy is obtained. And for the six-bar linkage, the error space of the end-effector is expressed in closed form and visualized in the 3-dimensional frame. Finally, this work is concluded and advances of the proposed method are emphasized.

A Geometric Constructive Approach for the Workspace Analysis of Symmetrical 5-PRUR Parallel Mechanisms (3T2R)

2010 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Mohammad Hossein Saadatzi ◽  
Cle´ment Gosselin ◽  
Hamid D. Taghirad
Keyword(s):  
Geometric Approach ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
End Effector ◽  
Workspace Analysis ◽  
Architecture Optimization ◽  
Insight Into ◽  
Orientation Workspace

This paper investigates an important kinematic property, the constant-orientation workspace, of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical limbs of the PRUR type. The general mechanism originates from the type synthesis performed for symmetrical 5-DOF parallel mechanism. In this study, the emphasis is placed on the determination of constant-orientation workspace using geometrical interpretation of the so-called vertex space, i.e., motion generated by a limb for a given orientation, rather than relying on classical recipes, such as discretization methods. For the sake of better understanding a CAD model is also provided for the vertex space. The constructive geometric approach presented in this paper provides some insight into the architecture optimization. Moreover, this approach facilitates the computation of the evolution of the volume of the constant-orientation workspace for different orientations of the end-effector.

GEOMETRIC APPROACH TO SOLVING THE INVERSE DISPLACEMENT PROBLEM OF CALIBRATED DECOUPLED 6R SERIAL ROBOTS

2014 ◽  
Vol 38 (1) ◽  
pp. 31-44 ◽  
Author(s):  
Albert Nubiola ◽  
Ilian A. Bonev
Keyword(s):  
Inverse Kinematics ◽  
Computation Time ◽  
Geometric Approach ◽  
End Effector ◽  
Forward Displacement ◽  
Displacement Problem ◽  
Robot Controller ◽  
Serial Robots ◽  
Level 3 ◽  
Direct Kinematics

This paper presents a simple but efficient way to numerically calculate the inverse displacement problem of calibrated decoupled 6R serial robots. The method is iterative and works with any type of calibrated robot model, such as level-3 models, since it requires no algebraic computation and no resolution of high-order polynomials, only the computation of the forward displacement problem of the calibrated robot model and the inverse kinematics of the nominal robot model. The method proposed can find up to eight possible solutions for a given end-effector pose. A numerical example is presented, with one million arbitrary end-effector poses of a level-3 calibrated ABB IRB 120 robot. The computation time for solving the inverse problem is analyzed, and in most cases is found to be only four times the time needed to calculate the nominal inverse kinematics and the calibrated direct kinematics. Furthermore, the method is fast enough to be implemented directly into the robot controller using the RAPID programming language.

RELATIVISTIC EINSTEIN–PODOLSKY–ROSEN CORRELATIONS IN COSMIC STRING SPACE–TIME VIA FERMI–WALKER TRANSPORT

2010 ◽  
Vol 08 (08) ◽  
pp. 1277-1288 ◽  
Author(s):  
KNUT BAKKE ◽  
ALEXANDRE M. DE M. CARVALHO ◽  
CLAUDIO FURTADO
Keyword(s):  
General Relativity ◽  
Bell Inequality ◽  
Geometric Approach ◽  
Space Time ◽  
Geometrical Approach ◽  
Wigner Rotation ◽  
Curved Space ◽  
Einstein Podolsky Rosen ◽  
Epr Correlations ◽  
Lorentz Boosts

We present a geometric approach to study the relativistic EPR correlations in curved space–time background given by the application of the Fermi–Walker transport in the relativistic EPR states and show that its result has the same effect as the applications of successive infinitesimal Lorentz boosts in the relativistic EPR states. We also show that the expression for the Bell inequality due to the Fermi–Walker transport is equivalent to the expression demonstrated by Terashima and Ueda,20 where the degree of violation of the Bell inequality depends on the angle of the Wigner rotation. This geometrical approach for study of the relativistic EPR correlations is a promising formulation to investigate the EPR correlations in the general relativity background.

A Geometrical Approach to the Inverse Kinematics of 6R Serial Robots With Offset Wrists

2015 ◽  
Author(s):  
Cuong Trinh ◽  
Dimiter Zlatanov ◽  
Matteo Zoppi ◽  
Rezia Molfino
Keyword(s):  
Inverse Kinematics ◽  
Joint Angle ◽  
Geometric Analysis ◽  
Geometrical Approach ◽  
Analysis Method ◽  
End Effector ◽  
Serial Robots ◽  
Spherical Wrist ◽  
Numerical Solver ◽  
Trigonometric Equations

The computation of the joint-angle values of a 6R serial manipulator for a given end-effector pose is more difficult for architectures lacking the conventional spherical wrist. Despite this added complexity, such arms have increasingly gained acceptance as they provide better dexterity for a number of tasks. The paper presents a geometric-analysis method for the inverse kinematics of a robot with an offset wrist. The sought postures are shown to correspond to the roots of four separate univariate trigonometric equations for the sixth joint angle. A standard numerical solver is applied to derive all sets of possible real solutions. By back-substitution, all the remaining angular variables are found in succession. Two particular arm designs are considered and full sets of solutions are obtained by the discussed approach. The method is easy to implement and can be applied to various 6R serial robots.

Overall Motion Planning for Kinematically Redundant Parallel Manipulators

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Juan A. Carretero ◽  
Iman Ebrahimi ◽  
Roger Boudreau
Keyword(s):  
Motion Planning ◽  
Parallel Manipulators ◽  
Redundant Manipulator ◽  
End Effector ◽  
New Approach ◽  
Singular Configurations ◽  
Point Motion ◽  
Point To Point ◽  
Better Than

In this work, a new approach for motion planning of kinematically redundant parallel manipulators is proposed and compared with a method previously proposed by the authors called point-to-point motion planning (PPMP). Overall motion planning (OMP) consists of determining actuation schemes that optimize the manipulator’s performance while considering the entire given trajectory of the end-effector at once. The results of OMP are compared with those of PPMP of a kinematically redundant manipulator. It is shown that the proposed OMP strategy can generate actuation schemes for given trajectories such that the manipulator avoids singular configurations better than the PPMP strategy.

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