Joint Rotation Space, Workspace, and Singularity-Free Workspace of Parallel Five-Bar Manipulators

2000 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Yi Zhang
Keyword(s):  
Trajectory Planning ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Parallel Manipulators ◽  
Extensive Study ◽  
Open Loop ◽  
Joint Rotation ◽  
One To One ◽  
The One

Abstract Closed-loop manipulators, while offering some advantages over the open-loop manipulators, also introduce new topics of study such as their joint rotation space (JRS) and workspace. In the previous studies, the concept of JRS was very effective in the study of the allowable inputs of five-bar linkages[11], and the concepts of sheet and side[7] were later introduced for the purpose of clearly describing all of the joint rotation spaces associated to a parallel manipulator with two degrees of freedom. However, of the two types of singularity of parallel manipulators, only the uncertainty singularity was considered in the aforementioned studies. The stationarity singularity was not indicated in the JRS of the manipulators, which would not be sufficient in the design and trajectory planning of parallel manipulators where the one-to-one correspondence between the JRS and the wrist point workspace would be required. This paper reports an extensive study on the JRS and singularity-free workspace of the parallel five-bar manipulators. The objective of the study is to establish a one-to-one corresponding relationship between the JRS and singularity-free workspace. A concise and sufficient way is proposed to thoroughly recognize the JRS and workspace of the parallel five-bar manipulators. The result can be applied in the design and trajectory planning of parallel five-bar manipulators, and the concepts can be extended to other parallel manipulators.

Integrated Kinematic Calibration for All the Parameters of a Planar 2DOF Redundantly Actuated Parallel Manipulator

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Chunshi Feng ◽  
Shuang Cong ◽  
Weiwei Shang
Keyword(s):  
Parallel Manipulator ◽  
Closed Loop ◽  
Open Loop ◽  
Kinematic Calibration ◽  
Constraint Equations ◽  
Integrated Method ◽  
Uniqueness Of The Solution ◽  
Redundantly Actuated ◽  
Loop Constraint ◽  
Two Degree Of Freedom

In this paper, the kinematic calibration of a planar two-degree-of-freedom redundantly actuated parallel manipulator is studied without any assumption on parameters. A cost function based on closed-loop constraint equations is first formulated. Using plane geometry theory, we analyze the pose transformations that bring infinite solutions and present a kinematic calibration integrated of closed-loop and open-loop methods. In the integrated method, the closed-loop calibration solves all the solutions that fit the constraint equations, and the open-loop calibration guarantees the uniqueness of the solution. In the experiments, differential evolution is applied to compute the solution set, for its advantages in computing multi-optima. Experimental results show that all the parameters involved are calibrated with high accuracy.

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong ◽  
James Ritchie
Keyword(s):  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Workspace Analysis ◽  
Computer Aided ◽  
Aided Design

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

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.

scholarly journals Evasion-Pursuit Strategy against Defended Aircraft Based on Differential Game Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qilong Sun ◽  
Minghui Shen ◽  
Xiaolong Gu ◽  
Kang Hou ◽  
Naiming Qi
Keyword(s):  
Game Theory ◽  
Differential Game ◽  
Optimal Strategies ◽  
Open Loop ◽  
Active Defense ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Differential Game Theory ◽  
One To One ◽  
The One

The active defense scenario in which the attacker evades from the defender and pursues the target is investigated. In this scenario, the target evades from the attacker, and the defender intercepts the attacker by using the optimal strategies. The evasion and the pursuit boundaries are investigated for the attacker when the three players use the one-to-one optimal guidance laws, which are derived based on differential game theory. It is difficult for the attacker to accomplish the task by using the one-to-one optimal guidance law; thus, a new guidance law is derived. Unlike other papers, in this paper, the accelerations of the target and the defender are unknown to the attacker. The new strategy is derived by linearizing the model along the initial line of sight, and it is obtained based on the open-loop solution form as the closed-loop problem is hard to solve. The results of the guidance performance for the derived guidance law are presented by numerical simulations, and it shows that the attacker can evade the defender and intercept the target successfully by using the proposed strategy.

Direct Position Analysis in Analytical Form of Parallel Manipulators Generating Structures With Topology SR-2PS

2004 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Analytical Form ◽  
Solution Procedure ◽  
Generic Structure ◽  
Kinematic Chains ◽  
Position Analysis ◽  
In Series ◽  
The One ◽  
Wide Family

A wide family of parallel manipulators (PMs) is the one that groups all the PMs with three legs where the legs become kinematic chains constituted of a passive spherical pair (S) in series with either a passive prismatic pair (P) or a passive revolute pair (R) when the actuators are locked. The topologies of the structures generated by these manipulators, when the actuators are locked, are ten. One out of these topologies is the SR-2PS topology (one SR leg and two PS legs). This paper presents an algorithm that determines all the assembly modes of the structures with topology SR-2PS in analytical form. The presented algorithm can be applied without changes to solve, in analytical form, the direct position analysis of any parallel manipulator which generates a SR-2PS structure when the actuators are locked. In particular, the closure equations of a generic structure with topology SR-2PS are written. The eliminant of this system of equations is determined and the solution procedure is presented. Finally, the proposed procedure is applied to a real case. This work demonstrates that the solutions of the direct position analysis of any parallel manipulator which generates a SR-2PS structure when the actuators are locked are at most eight.

A Novel Parallel Mechanism With 3-RRUR Legs

2007 ◽  
Author(s):  
Yanwen Li ◽  
Yueyue Zhang ◽  
Lumin Wang ◽  
Zhen Huang
Keyword(s):  
Machine Tools ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Symmetrical Structure ◽  
Forward Kinematic ◽  
Accumulated Error

This paper investigates a novel 4-DOF 3-RRUR parallel manipulator, the number and the characteristics of its degrees of freedom are determined firstly, the rational input plan and the invert and forward kinematic solutions are carried out then. The corresponding numeral example of the forward kinematics is given. This type of parallel manipulators has a symmetrical structure, less accumulated error, and can be used to construct virtual-axis machine tools. The analysis in this paper will play an important role in promoting the application of such manipulators.

A Measure for Evaluation of Maximum Acceleration of Redundant and Nonredundant Parallel Manipulators

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Jun Wu ◽  
Binbin Zhang ◽  
Liping Wang
Keyword(s):  
Dynamic Model ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Virtual Work ◽  
Parallel Manipulators ◽  
Maximum Acceleration ◽  
Virtual Work Principle ◽  
Joint Force ◽  
Joint Forces ◽  
Three Degrees Of Freedom

The paper deals with the evaluation of acceleration of redundant and nonredundant parallel manipulators. The dynamic model of three degrees-of-freedom (3DOF) parallel manipulator is derived by using the virtual work principle. Based on the dynamic model, a measure is proposed for the acceleration evaluation of the redundant parallel manipulator and its nonredundant counterpart. The measure is designed on the basis of the maximum acceleration of the mobile platform when one actuated joint force is unit and other actuated joint forces are less than or equal to a unit force. The measure for evaluation of acceleration can be used to evaluate the acceleration of both redundant parallel manipulators and nonredundant parallel manipulators. Furthermore, the acceleration of the 4-PSS-PU parallel manipulator and its nonredundant counterpart are compared.

Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator

2003 ◽  
Vol 125 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Han Sung Kim ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Solution Methods ◽  
Moving Platform ◽  
At Will

This paper presents the design of spatial 3-RPS parallel manipulators from dimensional synthesis point of view. Since a spatial 3-RPS manipulator has only 3 degrees of freedom, its end effector cannot be positioned arbitrarily in space. It is shown that at most six positions and orientations of the moving platform can be prescribed at will and, given six prescribed positions, there are at most ten RPS chains that can be used to construct up to 120 manipulators. Further, solution methods for fewer than six prescribed positions are also described.

A 2(3-RRPS) parallel manipulator inspired by Gough–Stewart platform

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. García-Murillo ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Triangular Prism ◽  
Input Output ◽  
Six Degrees Of Freedom ◽  
Moving Platform

SUMMARYThis study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.

Optimal attitude trajectory planning method for CMG actuated spacecraft

2017 ◽  
Vol 232 (1) ◽  
pp. 131-142 ◽  
Author(s):  
Lijun Zhang ◽  
Chunmei Yu ◽  
Shifeng Zhang ◽  
Hong Cai
Keyword(s):  
Trajectory Planning ◽  
Closed Loop ◽  
Pseudospectral Method ◽  
Linear Quadratic Regulator ◽  
Fixed Time ◽  
Open Loop ◽  
Planning Method ◽  
Global Perspective ◽  
Linear Quadratic ◽  
Loop Control

This paper presents an optimal attitude trajectory planning method for the spacecraft equipped with control moment gyros as the actuators. Both the fixed-time energy-optimal and synthesis performance optimal cases are taken into account. The corresponding nonsingular attitude maneuvering trajectories (i.e. open-loop control trajectories) with the consideration of a series of constraints are generated via Radau pseudospectral method. Compared with the traditional steering laws, the optimal steering law designed by this method can explicitly avoid the singularity from the global perspective. A linear quadratic regulator closed-loop controller is designed to guarantee the trajectory tracking performance in the presence of initial errors, inertia uncertainties and external disturbances. Simulation results verify the validity and feasibility of the proposed open-loop and closed-loop control methods.

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