The Effects of Actuation Schemes on the Kinematic Performance of Manipulators

1997 ◽  
Vol 119 (2) ◽  
pp. 212-217 ◽  
Author(s):  
R. Matone ◽  
B. Roth
Keyword(s):  
Performance Measures ◽  
Condition Number ◽  
Jacobian Matrix ◽  
Kinematic Model ◽  
Joint Space ◽  
Singular Value ◽  
End Effector ◽  
Kinematic Performance ◽  
Actuation Scheme ◽  
Space Description

This paper is concerned with the effects of actuation schemes on three measures of kinematic performance which depend upon a manipulator’s Jacobian matrix (namely, the minimum singular value, the manipulability, and the condition number). We begin by presenting a simple framework on how to incorporate actuator location and drive mechanisms in the kinematic model. Then, we redefine the performance measures using the new model. For each measure we derive properties relating its joint space to its actuator space description. Next we demonstrate that the choice of actuation scheme influences the size, shape, and direction of the velocity ellipsoid of the end-effector. Finally, we employ the above concepts in the design of a 2R planar mechanical arm. Its transmission ratios and drive mechanisms are selected in order to obtain good kinematic characteristics. We show that the choice of actuation scheme can be used to improve kinematic performance.

The Effects of Actuation Schemes on the Kinematic Performance of Manipulators

1996 ◽  
Author(s):  
Ricardo Matone ◽  
Bernard Roth
Keyword(s):  
Performance Measures ◽  
Condition Number ◽  
Jacobian Matrix ◽  
Kinematic Model ◽  
Joint Space ◽  
Singular Value ◽  
End Effector ◽  
Kinematic Performance ◽  
Actuation Scheme ◽  
Space Description

Abstract This paper is concerned with the effects of actuation schemes on three measures of kinematic performance which depend upon a manipulator’s Jacobian matrix (namely, the minimum singular value, the manipulability, and the condition number.) We begin by presenting a simple framework on how to incorporate actuator location and drive mechanisms in the kinematic model. Then, we redefine the performance measures using the new model. For each measure we derive properties relating its joint space to its actuator space description. Next we demonstrate that the choice of actuation scheme influences the size, shape, and direction of the velocity ellipsoid of the end-effector. Finally, we employ the above concepts in the design of a 2R planar mechanical arm. Its transmission ratios and drive mechanisms are selected in order to obtain good kinematic characteristics. We show that the choice of actuation scheme can be used to improve kinematic performance.

scholarly journals Simulación del Modelo Matemático de la Cinemática Diferencial de Robots Seriales Planos Configuración RRR y RPR

2019 ◽  
pp. 1-8
Author(s):  
Patricio Martinez-Zamudio ◽  
Victor Gonzalez-Villela ◽  
Hector Leon-Nuñez
Keyword(s):  
Jacobian Matrix ◽  
Kinematic Model ◽  
Joint Space ◽  
Differential Model ◽  
End Effector ◽  
Model And Simulation ◽  
Serial Robot ◽  
Serial Chains ◽  
Robot Configurations ◽  
The Relationship

This article presents the model and simulation of the serial robot configurations of the types RRR and RPR, applying the theories of differential kinematics, to obtain the representation of its mathematical model (Jacobian matrix) and its simulation. The differential kinematics in robotics is the relationship between vector spaces, so it is possible to make the velocity map in the joint space in the end effector workspace. We present the differential kinematic model that is obtained from the position kinematics by differentiation techniques and with the help of the asymmetric matrix we obtain the information that is part of the Jacobian matrix, which allows us to know the velocities of the joint variables as a function of linear and angular velocity in the end effector and vice versa. The simulation of the manipulators is carried out validating the mathematical differential model; through the validation of the differential kinematics of serial chains it is possible to apply the procedure to complicated manipulator robots. The method presented here is the basis of a useful tool for solving complex robots, as in the case of redundant, parallel and hybrid serial manipulator robots.

The Characteristic Point and the Characteristic Length of Robotic Manipulators

1992 ◽  
Author(s):  
Murat Tandirci ◽  
Jorge Angeles ◽  
Farzam Ranjbaran
Keyword(s):  
Condition Number ◽  
Jacobian Matrix ◽  
Characteristic Length ◽  
Characteristic Point ◽  
Robotic Manipulators ◽  
End Effector ◽  
Industrial Manipulators

Abstract The characteristic point of a serial manipulator is defined here as a point on the end-effector, at which the condition number of the Jacobian matrix is minimized. However, when evaluating the condition number of the Jacobian matrix, dimensional inhomogeneities arise, that render the condition number physically meaningless. As a means to cope with this problem, the entries of the Jacobian that have units of length are divided by a characteristic length L that is chosen so as to minimize the condition number of the dimensionless Jacobian matrix thus resulting. Finally, the values of the joint variables minimizing the condition number of the dimensionless Jacobian lead to a naturally defined home configuration of the manipulator. The concepts introduced here are illustrated with a few examples involving industrial manipulators.

Force/Motion Transmissibility Analysis of Six Degree of Freedom Parallel Mechanisms

2014 ◽  
Vol 6 (3) ◽  
Author(s):  
Tian Huang ◽  
Manxin Wang ◽  
Shuofei Yang ◽  
Tao Sun ◽  
Derek G. Chetwynd ◽  
...  
Keyword(s):  
Linear Functional ◽  
Systematic Approach ◽  
Screw Theory ◽  
Joint Space ◽  
Singular Value ◽  
Parallel Mechanisms ◽  
Dual Basis ◽  
Singular Configurations ◽  
Kinematic Performance ◽  
Six Degree Of Freedom

Drawing mainly on the concepts of dual space and dual basis in linear algebra and on existing screw theory, this paper presents a novel and systematic approach for the force/motion transmissibility analysis of 6DOF parallel mechanisms. By taking the reciprocal product of a wrench on a twist as a linear functional, the property exhibited by the dual basis allows the formulation of the force/motion transmissibility between the joint space and operation space in an accurate and concise manner. The consistency between the force/motion transmissibility and the minimum singular value of the Jacobian for singularity identification is rigorously proved. This leads to the development of a set of homogeneously dimensionless local and global transmission indices for measuring the closeness to singular configurations as well as for kinematic performance evaluation over a given workspace. A Stewart platform is employed an exemplar to illustrate the effectiveness of the approach.

scholarly journals Configuring a virtual prototype of a BiSCARA robot

Tehnika ◽  
2021 ◽  
Vol 76 (3) ◽  
pp. 311-317
Author(s):  
Nikola Slavković ◽  
Saša Živanović ◽  
Nikola Vorkapić
Keyword(s):  
Jacobian Matrix ◽  
Kinematic Model ◽  
Virtual Prototype ◽  
Open Architecture ◽  
Cad Model ◽  
End Effector ◽  
Graphical Environment ◽  
Workspace Analysis ◽  
Cad Cam ◽  
The Given

The paper presents the configuring of a virtual prototype BiSCARA robot generated on the basis of a fully developed kinematic model of the robot. The virtual CAD model developed in this way will enable its implementation in the Python graphical environment as an integral part of the open architecture control system developed on the basis of the presented kinematic model. The developed kinematic model included solving the inverse and direct kinematic problem, determining the Jacobian matrix and workspace analysis. Verification of the kinematic model, i.e. the configured virtual prototype of the robot, was performed by simulations of the end-effector tip movement according to the given program in a CAD / CAM environment.

Workspace Decomposition Based Dimensional Synthesis of a Novel Hybrid Reconfigurable Robot

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Tao Sun ◽  
Yimin Song ◽  
Yonggang Li ◽  
Jun Zhang
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Dimensional Synthesis ◽  
End Effector ◽  
Global View ◽  
Hybrid Module ◽  
Reconfigurable Robot ◽  
Parallel Kinematic ◽  
Kinematic Performance ◽  
Position Problem

A novel 5-axis hybrid reconfigurable robot named Tricept-IV, including one 4-degree-of-freedom (4DOF) hybrid module and one 2DOF end effector, is investigated. Compared with extensive research that has been pursued for the parallel kinematic machines such as Tricept, Sprint Z3 Head, and so on, the hybrid kinematic machines have not adequately been studied. This paper demonstrates a method of workspace decomposition applied in the dimensional synthesis of a 4DOF hybrid module, which is the underlying architecture of the newly invented robot. This paper starts with an introduction of the Tricept-IV robot. After dividing the 4DOF hybrid module into one position-orientation coupling (POC) subsystem and one position-feed (PF) subsystem, its workspace is decomposed into POC and PF subspaces accordingly, and then the inverse position problem may be solved by means of one prejudgment method. Furthermore, the Jacobian matrix of the POC subsystem is obtained by the screw theory so as to formulate its kinematic performance index. Finally, the dimensional synthesis based on workspace decomposition of the hybrid module is carried out by taking a global view of the dimensional synthesis of these two subsystems.

Cooperation and Null-Space Control of Networked Omni-Directional Mobile Manipulators

2020 ◽  
Author(s):  
Michael John Chua ◽  
Yen-Chen Liu
Keyword(s):  
Degrees Of Freedom ◽  
Null Space ◽  
Kinematic Model ◽  
Mobile Manipulator ◽  
Main Task ◽  
Mobile Manipulators ◽  
Robot Arm ◽  
Task Space ◽  
End Effector ◽  
Mobile Base

Abstract This paper presents cooperation and null-space control for networked mobile manipulators with high degrees of freedom (DOFs). First, kinematic model and Euler-Lagrange dynamic model of the mobile manipulator, which has an articulated robot arm mounted on a mobile base with omni-directional wheels, have been presented. Then, the dynamic decoupling has been considered so that the task-space and the null-space can be controlled separately to accomplish different missions. The motion of the end-effector is controlled in the task-space, and the force control is implemented to make sure the cooperation of the mobile manipulators, as well as the transportation tasks. Also, the null-space control for the manipulator has been combined into the decoupling control. For the mobile base, it is controlled in the null-space to track the velocity of the end-effector, avoid other agents, avoid the obstacles, and move in a defined range based on the length of the manipulator without affecting the main task. Numerical simulations have been addressed to demonstrate the proposed methods.

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