Global Performance Index System for Kinematic Optimization of Robotic Mechanism

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Pu Zhang ◽  
Zhenqiang Yao ◽  
Zhengchun Du
Keyword(s):  
Performance Index ◽  
Index System ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Linear Mapping ◽  
Distribution Characteristics ◽  
Global Performance ◽  
Kinematic Performance ◽  
Performance Distribution ◽  
Kinematic Optimization

Correct evaluation of robot performance has been a problem in the field of robotics. Many scholars have proposed a variety of performance indices, such as manipulability, condition number, and minimum singular value, to describe quantitatively the kinematic performance of a robotic mechanism. However, two questions remain: (1) how to describe the kinematic performance completely for the design of a robotic mechanism, and (2) how to comprehensively describe the global performance distribution characteristics in the workspace. This paper presents a global performance index system for kinematic optimization of a robotic mechanism based on Jacobian matrix, manipulability ellipsoid, and descriptive statistics theory that can comprehensively describe the kinematic performance and the performance distribution characteristics in a robot's workspace. First, the Jacobian matrix, a linear mapping from the joint space to the task space of a robotic mechanism, is analyzed, and the kinematic transmission ability indices and the kinematic transmission accuracy index are determined. Second, four indices, including global average value, global volatility, global skewness, and global kurtosis, are presented to describe the global performance index's distribution in the workspace. Third, the global performance index system is established to evaluate a robot's global kinematic performance based on the above analysis. Finally, a two-degrees of freedom (DOF) robotic mechanism is designed based on the global performance index system as a case, analysis of which shows that the final mechanism has good kinematic performance in the workspace. This demonstrates that the global performance index system proposed in this paper can be useful for the evaluation of the kinematic performance and kinematic optimization of a robotic mechanism.

A Global Performance Index for the Kinematic Optimization of Robotic Manipulators

1991 ◽  
Vol 113 (3) ◽  
pp. 220-226 ◽  
Author(s):  
C. Gosselin ◽  
J. Angeles
Keyword(s):  
Condition Number ◽  
Performance Index ◽  
Jacobian Matrix ◽  
Robotic Manipulators ◽  
Degree Of Freedom ◽  
Global Index ◽  
Global Performance ◽  
Three Degree Of Freedom ◽  
Kinematic Optimization

In this paper, a novel performance index for the kinematic optimization of robotic manipulators is presented. The index is based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the kinematic and static transformations between the joint and Cartesian spaces. Moreover, the index proposed here, termed global conditioning index (CGI), is meant to assess the distribution of the aforementioned condition number over the whole workspace. Furthermore, the concept of a global index is applicable to other local kinematic or dynamic indices. The index introduced here is applied to a simple serial two-link manipulator, to a spherical three-degree-of-freedom serial wrist, and to three-degree-of-freedom parallel planar and spherical manipulators. Results of the optimization of these manipulators, based on the GCI, are included.

OPTIMAL MOTION PLANNING OF A PLANAR PARALLEL MANIPULATOR WITH KINEMATICALLY REDUNDANT DEGREES OF FREEDOM

2016 ◽  
Vol 40 (3) ◽  
pp. 383-397 ◽  
Author(s):  
Bahman Nouri Rahmat Abadi ◽  
Sajjad Taghvaei ◽  
Ramin Vatankhah
Keyword(s):  
Motion Planning ◽  
Feedback Linearization ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Redundant Manipulator ◽  
Optimal Motion ◽  
Planar Parallel Manipulator ◽  
Optimal Motion Planning ◽  
Planning Algorithm ◽  
Actuation Method

In this paper, an optimal motion planning algorithm and dynamic modeling of a planar kinematically redundant manipulator are considered. Kinematics of the manipulator is studied, Jacobian matrix is obtained and the dynamic equations are derived using D’Alembert’s principle. Also, a novel actuation method is introduced and applied to the 3-PRPR planar redundant manipulator. In this approach, the velocity of actuators is determined in such a way to minimize the 2-norm of the velocity vector, subjected to the derived kinematic relations as constraints. Having the optimal motion planning, the motion is controlled via a feedback linearization controller. The motion of the manipulator is simulated and the effectiveness of the proposed actuation strategy and the designed controller is investigated.

Design of a Four Legged Parallel Mechanism to Improve the Dexterity of Walking Robot

2009 ◽  
Author(s):  
ChiHyo Kim ◽  
KunWoo Park ◽  
TaeSung Kim ◽  
MinKi Lee
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Topology Design ◽  
Condition Numbers ◽  
Walking Robots ◽  
Rough Terrain ◽  
Parallel Mechanisms ◽  
Walking Robot ◽  
Intermediate Mechanism

This paper designs a four legged parallel mechanism to improve the dexterity of three layered parallel walking robot. Topology design is conducted for a leg mechanism composed of four legs, base and ground, which constitute a redundant parallel mechanism. This mechanism is subdivided into four sub-mechanism composed of three legs. A motor vector is adopted to determine the 6×8 Jacobian of the redundant parallel mechanism and the 6×6 Jacobian of the sub-mechanisms, respectively. The condition number of the Jacobian matrix is used as an index to measure a dexterity. We analyze the condition numbers of the Jacobian over the positional and orientational walking space. The analytical results show that a sub-mechanism has lots of singularities within workspace but they are removed by a redundant parallel mechanism improving the dexterity. This paper presents a parallel typed walking robot to enlarge walking space and stability region. Seven types of three layered walking robots are designed by inserting an intermediate mechanism between the upper and the lower legged parallel mechanisms. They provide various types of gaits to walk rough terrain and climb over a wall with small degrees of freedom.

Architecture Optmization of a 3-DOF Parallel Mechanism

1998 ◽  
Author(s):  
J. A. Carretero ◽  
R. P. Podhorodeski ◽  
M. Nahon
Keyword(s):  
Parallel Mechanism ◽  
Architectural Design ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Design Parameters ◽  
Objective Functions ◽  
Constraint Equations ◽  
Three Degree Of Freedom ◽  
Architecture Optimization ◽  
Three Degrees Of Freedom

Abstract This paper presents a study of the architecture optimization of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described. Since the mechanism has only three degrees of freedom, constraint equations describing the inter-relationship between the six Cartesian coordinates are given. These constraints allow us to define the parasitic motions and, if incorporated into the kinematics model, a constrained Jacobian matrix can be obtained. This Jacobian matrix is then used to define a dexterity measure. The parasitic motions and dexterity are then used as objective functions for the optimizations routines and from which the optimal architectural design parameters are obtained.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Kinematic and Dynamic Analysis of a Two-Degree-of-Freedom Spherical Wrist

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
M. Ruggiu
Keyword(s):  
Condition Number ◽  
Performance Index ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Scanning System ◽  
Spherical Wrist ◽  
Moving Platform ◽  
Two Degree Of Freedom ◽  
Spherical Motion ◽  
Motion Generator

The present paper proposes the analysis of a spherical wrist with two degrees of freedom for scanning system applications. The wrist consists of two chains of revolute-revolute pairs. A slotted arc connecting the two chains behaves as a further revolute pair. Thus, the mechanism is an overconstrained (meaning of this definition is discussed in this work) single-loop kinematic chain composed of five revolute pairs equivalent to a spherical motion generator since all its axes intersect at a point. Throughout the paper, the kinematic analysis is developed including some details about the workspace, which depends on the design of the slotted arc. The performance index given as the inverse of the condition number is used to measure the performances of the motion of the moving platform of the wrist. The singularity poses found were examined in detail. A simplified dynamic model is proposed that provides the torques suitable for satisfying a given kinematics. Finally, the paper presents a motorized hardware model of the mechanism assembled in the laboratory.

Jacobian Derivation of 5-DOF 3R2T Parallel Mechanisms

2004 ◽  
Author(s):  
Qinchuan Li ◽  
Xudong Hu ◽  
Zhen Huang
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Mobility Analysis

This paper presents a method for the Jacobian derivation of 5-DOF 3R2T PMs (parallel mechanisms), where 3R denotes three rotational DOFs (degrees of freedom) and 2T denotes two translational DOFs. First the mobility analysis of such kind of parallel mechanisms is reviewed briefly. The Jacobian matrix of the single limb kinematic chain is obtained via screw theory, which is a 6 × 5 matrix. Then it is shown that the mobility analysis of such kind of PM is important when simplifying the 6 × 5 matrix into a 5 × 5 Jacobian matrix. After obtaining the 5 × 5 Jacobian matrix for each limb, a 5 × 5 Jacobian matrix for the whole mechanism can be established.

Evaluation of the Kinematic Performance of a 3-RRS Parallel Mechanism

Robotica ◽  
2020 ◽  
pp. 1-12
Author(s):  
Manxin Wang ◽  
Qiusheng Chen ◽  
Haitao Liu ◽  
Tian Huang ◽  
Hutian Feng ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Mean Value ◽  
Spherical Joint ◽  
Performance Indices ◽  
Active Joint ◽  
Strongly Coupled ◽  
The Mean ◽  
Kinematic Performance

SUMMARY This paper proposes a set of novel indices for evaluating the kinematic performance of a 3-RRS (R and S denote revolute and spherical joint respectively, R denotes active joint.), parallel mechanism whose translational and rotational movements are strongly coupled. First, the indices are formulated using the decoupled overall Jacobian matrix, which is developed using coordinate transformation. Then, the influences of the homogeneous dimensionless parameters on these indices are investigated. In addition, the dimension synthesis of the 3-RRS parallel mechanism is carried out by minimizing the mean value of the kinematic performance indices and their standard deviation. The results demonstrate that the established approach facilitates good global kinematic performance of the parallel mechanism.

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