Determination of the Singularity-Free Compatible Reachable Workspace for Different Types of Three Degrees-of-Freedom Parallel Manipulators

This paper deals with the wrench workspace (WW) determination of parallel manipulators. The WW is the set of end-effector poses (positions and orientations) for which the active joints are able to balance a set of external wrenches acting at the end-effector. The determination of the WW is important when selecting an appropriate manipulator design since the size and shape of the WW are dependent on the manipulator’s geometry (design) and selected actuators. Algorithms for the determination of the reachable workspace and the WW are presented. The algorithms are applicable to manipulator architectures utilizing actuators with positive and negative limits on the force/torque they can generate, as well as cable-driven parallel manipulator architectures which require nonnegative actuator limits to maintain positive cable tensions. The developed algorithms are demonstrated in case studies applied to a cable-driven parallel manipulator with 2-degrees-of-freedom and three cables and to a 3-RRR parallel manipulator. The approaches used in this paper provide guaranteed results and are based on methods utilizing interval analysis techniques for the representation of end-effector poses and design parameters.

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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

Journal of Mechanisms and Robotics ◽

10.1115/1.4031656 ◽

2015 ◽

Vol 8 (2) ◽

Cited By ~ 7

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.

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Maximum load determination of nonholonomic mobile manipulator using hierarchical optimal control

Robotica ◽

10.1017/s0263574711000336 ◽

2011 ◽

Vol 30 (1) ◽

pp. 53-65 ◽

Cited By ~ 24

Author(s):

M. H. Korayem ◽

V. Azimirad ◽

H. Vatanjou ◽

A. H. Korayem

Keyword(s):

Optimal Control ◽

Degrees Of Freedom ◽

Large Scale ◽

Maximum Load ◽

Mobile Manipulator ◽

Interaction Terms ◽

Different Types ◽

Interaction Variables ◽

Maximum Allowable Dynamic Load

SUMMARYThis paper presents a new method using hierarchical optimal control for path planning and calculating maximum allowable dynamic load (MADL) of wheeled mobile manipulator (WMM). This method is useful for high degrees of freedom WMMs. First, the overall system is decoupled to a set of subsystems, and then, hierarchical optimal control is applied on them. The presented algorithm is a two-level hierarchical algorithm. In the first level, interaction terms between subsystems are fixed, and in the second level, the optimization problem for subsystems is solved. The results of second level are used for calculating new estimations of interaction variables in the first level. For calculating MADL, the load on the end effector is increased until actuators get into saturation. Given a large-scale robot, we show how the presenting in distributed hierarchy in optimal control helps to find MADL fast. Also, it enables us to treat with complicated cost functions that are generated by obstacle avoidance terms. The effectiveness of this approach on simulation case studies for different types of WMMs as well as an experiment for a mobile manipulator called Scout is shown.

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

Journal of Mechanisms and Robotics ◽

10.1115/1.4031500 ◽

2015 ◽

Vol 8 (2) ◽

Cited By ~ 17

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.

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Contributions to the Determination of the Equations of Motion for Multidegree of Freedom Systems

Journal of Engineering for Industry ◽

10.1115/1.3427874 ◽

1971 ◽

Vol 93 (1) ◽

pp. 191-195 ◽

Cited By ~ 3

Author(s):

Desideriu Maros ◽

Nicolae Orlandea

Keyword(s):

Differential Equations ◽

Degrees Of Freedom ◽

Equations Of Motion ◽

System Of Differential Equations ◽

Original Contribution ◽

Deductive Method ◽

Method Of Solution ◽

Further Development ◽

Three Degrees Of Freedom

This paper is a further development of the kinematic problem presented in our 1967 paper [1] in which we have obtained the transmission functions for different orders of plane systems with many degrees of freedom. This paper establishes the corresponding system of differential equations of motion beginning with these functions. The purpose of this paper is to facilitate computer programming. Our study is based on the work of R. Beyer [2, 3] and is the first original addition to his papers. A second original contribution to Beyer’s theories is the deductive method of solution, from general to particular, which we have, incorporated in our work. Beyer concluded that the cases having two or three degrees of freedom can be considered as particular solutions to the results obtained.

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Introducing the Theory of Bonds for Stewart Gough Platforms With Self-Motions1

Journal of Mechanisms and Robotics ◽

10.1115/1.4025623 ◽

2013 ◽

Vol 6 (1) ◽

Cited By ~ 12

Author(s):

Georg Nawratil

Keyword(s):

Degrees Of Freedom ◽

Parallel Manipulators ◽

Geometric Characterization ◽

Basic Facts ◽

Self Motion ◽

Three Degrees Of Freedom

We transfer the basic idea of bonds, introduced by Hegedüs, Schicho, and Schröcker for overconstrained closed chains with rotational joints, to the theory of self-motions of parallel manipulators of Stewart Gough (SG) type. Moreover, we present some basic facts and results on bonds and demonstrate the potential of this theory on the basis of several examples. As a by-product we give a geometric characterization of all SG platforms with a pure translational self-motion and of all spherical three-degrees of freedom (DOF) RPR manipulators with self-motions.

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Performance Optimization for a 3-DOF Micro-Motion Device

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.291-294.3108 ◽

2011 ◽

Vol 291-294 ◽

pp. 3108-3111 ◽

Cited By ~ 1

Author(s):

Dan Zhang ◽

Irene Fassi ◽

Pei Gang Jiang

Keyword(s):

Fiber Optics ◽

Performance Optimization ◽

Degrees Of Freedom ◽

Compliant Mechanism ◽

Parallel Manipulators ◽

Mechanical Joints ◽

Micro Motion ◽

Optics Industry ◽

And Behavior ◽

Three Degrees Of Freedom

Traditional parallel manipulators suffer from errors due to backlash, hysteresis, and vibration in the mechanical joints. In this paper, a new 3SPS+RPR spatial compliant mechanism which has three degrees of freedom (DOF) and can generate motions in a microscopic scale is proposed. It can be utilized for biomedical engineering and fiber optics industry. The detailed design of the structure is introduced, followed by the performance evaluation. Then, the genetic algorithms and radial basis function networks are implemented to search for the optimal architecture and behavior parameters in terms of global stiffness/compliance, dexterity and manipulability.

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Evaluation and Optimum Design of Parallel Manipulators Having Defined Workspace

Volume 7A: 26th Biennial Mechanisms and Robotics Conference ◽

10.1115/detc2000/mech-14092 ◽

2000 ◽

Author(s):

Jürgen Schönherr

Keyword(s):

Optimum Design ◽

Degrees Of Freedom ◽

Parallel Manipulators ◽

Parallel Structure ◽

Transmission Quality ◽

6 Degrees Of Freedom ◽

Kinematic Optimization ◽

Method Of Design

Abstract The condition of the Jacobian characterizes the transmission quality of manipulators and is used in this paper for the determination of the dimensions of manipulators having best mobility for a defined workspace. Typical planar and spatial manipulators of parallel structure and having 3 or 6 degrees of freedom are used to demonstrate the method of design used. Manipulators having identical degrees of freedom and workspaces and different structures, including those having fixed or variable leg lengths, are compared with respect to their mobility. The computing program developed for the purpose of optimum design performs the kinematic optimization of machines and manipulators of any structure.

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Kinematic Analysis of a New 3-DOF Translational Parallel Manipulator

Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

10.1115/detc2005-84299 ◽

2005 ◽

Cited By ~ 2

Author(s):

Yangmin Li ◽

Qingsong Xu

Keyword(s):

Inverse Kinematics ◽

Parallel Manipulator ◽

Degrees Of Freedom ◽

Screw Theory ◽

Industrial Applications ◽

Forward Kinematics ◽

Physical Constraints ◽

Mechanical Joints ◽

Reachable Workspace ◽

Three Degrees Of Freedom

A novel three-degrees-of-freedom (3-DOF) translational parallel manipulator (TPM) with orthogonally arranged fixed actuators is proposed in this paper. The mobility of the manipulator is analyzed via screw theory. The inverse kinematics, forward kinematics, and velocity analyses are performed and the singularities and isotropic configurations are investigated in details afterwards. Under different cases of physical constraints imposed by mechanical joints, the reachable workspace of the manipulator is geometrically generated and compared. Especially, it is illustrated that the manipulator in principle possesses a fairly regular like workspace with a maximum cuboid defined as the usable workspace inscribed and one isotropic configuration involved. Furthermore, the singularity within the usable workspace is verified, and simulation results show that there exist no any singular configurations within the specified workspace. Therefore, the presented new manipulator has a great potential for high precision industrial applications such as assembly, machining, etc.

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Fully-Isotropic T1R2-Type Parallel Robots With Three Degrees of Freedom

Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2005-84313 ◽

2005 ◽

Cited By ~ 8

Author(s):

Grigore Gogu

Keyword(s):

Degrees Of Freedom ◽

Jacobian Matrix ◽

Parallel Manipulators ◽

Parallel Robots ◽

Velocity Space ◽

Linear Transformations ◽

Matrix Mapping ◽

Joint Velocity ◽

First Time ◽

Three Degrees Of Freedom

The paper presents singularity-free fully-isotropic T1R2-type parallel manipulators (PMs) with three degrees of freedom. The mobile platform has one independent translation (T1) and two rotations (R2). A method is proposed for structural synthesis of fully-isotropic T1R2-type PMs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic T1R2-type PMs presented in this paper is the 3x3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware, this paper presents for the first time in the literature solutions of singularity-free T1R2-type PMs with decoupled an uncoupled motions, along with the fully-isotropic solutions.

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