Mobility Analysis of Parallel Manipulators and Pattern of Transform Matrix

2010 ◽  
Vol 2 (4) ◽  
Author(s):  
Chao Chen
Keyword(s):  
Degrees Of Freedom ◽  
Pattern Analysis ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Fundamental Issue ◽  
Mobility Analysis ◽  
Geometric Conditions ◽  
Special Cases ◽  
Transform Matrix ◽  
And Robotics

The mobility or degrees of freedom is a fundamental issue in mechanisms and robotics. In this work, we investigate the mobility of parallel manipulators from a new point of view, and introduce a new concept, the pattern of transform matrix. It is shown that both general and modified Chebychev–Gruble–Kutzbach formulas are the special cases of the pattern analysis. We further propose a framework upon the pattern analysis of transform matrix to calculate the mobility, to evaluate the property of the motion, and to determine the exact-actuation arrangement. The proposed approach should be general enough to evaluate any existing parallel manipulator. Five parallel manipulators with special geometric conditions and lower mobilities are discussed.

On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

2005 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Alessandro Cammarata ◽  
Rosario Sinatra
Keyword(s):  
Finite Number ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Closed Curves ◽  
Special Cases ◽  
Dynamic Performances ◽  
Definition Of ◽  
Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

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.

Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator

1999 ◽  
Vol 122 (4) ◽  
pp. 439-446 ◽  
Author(s):  
Lung-Wen Tsai ◽  
Sameer Joshi
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Structural Characteristics ◽  
Translational Motion ◽  
Parallel Manipulators ◽  
Condition Index ◽  
Mirror Image ◽  
Geometric Conditions ◽  
Design Variables ◽  
Opposite Limb

The structural characteristics associated with parallel manipulators are investigated. Using these characteristics a class of 3 degree-of-freedom parallel manipulators are enumerated. Several parallel manipulators with only translational degrees of freedom are identified and the 3-UPU parallel manipulator is chosen for design analysis and optimization. The kinematics of this 3-UPU parallel manipulator is studied. Two geometric conditions that lead to pure translational motion of the moving platform are described. Due to the simple kinematic structure, the inverse kinematics yields two equal and opposite limb lengths whereas the direct kinematics produces two possible manipulator postures with one being the mirror image of the other. The Jacobian matrix is derived and several singular conditions are discussed. Furthermore the conditions for existence of an isotropic point within the workspace are discussed and equations to compute the isotropic configurations of a 3-UPU manipulator are derived. Finally, we undertake architecture optimization and show that certain values of design variables maximize the global condition index of the 3-UPU manipulator. [S1050-0472(00)01404-5]

Enumeration and instantaneous mobility analysis of a class of 3-UPU parallel manipulators with equilateral triangular platforms

Robotica ◽  
2021 ◽  
pp. 1-32
Author(s):  
Sercan Boztaş ◽  
Gökhan Kiper
Keyword(s):  
Software Package ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Mobility Analysis ◽  
Specific Design ◽  
Design Task ◽  
Moving Platforms ◽  
Joint Axis ◽  
Motion Characteristics

Abstract In this study, several joint axis orientations on equilateral platforms and the limbs of 3-UPU parallel manipulators (PMs) are examined. The generated joint layouts for the platforms were matched with each other to generate and enumerate manipulator architectures based on certain assumptions. The structures of thus obtained manipulators are examined and limb types were determined. These limb types were analyzed using screw theory. The instantaneous mobility of the manipulators and the motion characteristics of the moving platforms are tabulated. The finite mobility analysis of one of the manipulators is performed using a software package as an example. Among several different 3-UPU PM architectures, 118 novel 3-UPU PMs with non-parasitic 3-degrees-of-freedom are significantly important. The classified 3-UPU PMs with determined motion characteristics can be used by researchers as a design alternative for their specific design task.

Branch Identification of Planar Two-DOF Seven-Bar Linkages

2009 ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Changyu Xue
Keyword(s):  
Degrees Of Freedom ◽  
Robot Navigation ◽  
Parallel Manipulators ◽  
Companion Paper ◽  
Physical Experiment ◽  
Analysis Method ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Multiple Degrees Of Freedom ◽  
Linkage Synthesis

Mobility identification mainly refers to the problems with the motion continuity and smoothness of a potential design or plan. In any linkage synthesis or robot navigation, it is highly desirable that the ability of any of the numerous design candidates to reach the desired positions in a favorable manner can be determined in a single decisive step automatically rather than through a blind trial or even a physical experiment. Mobility of complex linkages has been one of the most troublesome problems in linkage synthesis and programming and the problem is further complicated with multiple degrees-of-freedom. For multiloop parallel manipulators this paper may represent the first mobility analysis method that can not only decisively and unambiguously rectify motion continuity between discrete positions but also provide clear geometric insight or interpretation regarding the formation of discontinuity. The treatment is based on the principle that the mobility of a multiloop linkage is affected by the mobility of each individual loop as well as the interaction between loops. Since the N-bar rotatability laws govern the mobility of an individual loop, the main mobility issue for multiloop linkages is how the mobility of these loops affects each other. One may find that the concept of joint rotation space (JRS) offers simple and intuitive explanation on how the mobility is affected by the combination of loops. The treatment is very suitable for an automated computer-aided mobility analysis. Examples are employed to demonstrate the proposed method. Continuity is a pivotal issue in linkage mobility analysis. Once the continuity can be rectified, problems with smoothness or singularity, which are discussed in the companion paper [28], can be resolved.

scholarly journals Screw-System-Based Mobility Analysis of a Family of Fully Translational Parallel Manipulators

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ernesto Rodriguez-Leal ◽  
Jian S. Dai ◽  
Gordon R. Pennock
Keyword(s):  
System Approach ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
System Analysis ◽  
Parallel Manipulators ◽  
Mobility Analysis ◽  
Redundant Constraints ◽  
The Common

This paper investigates the mobility of a family of fully translational parallel manipulators based on screw system analysis by identifying the common constraint and redundant constraints, providing a case study of this approach. The paper presents the branch motion-screws for the 3-RP̲C-Y parallel manipulator, the 3-RCC-Y (or 3-RP̲RC-Y) parallel manipulator, and a newly proposed 3-RP̲C-T parallel manipulator. Then the paper determines the sets of platform constraint-screws for each of these three manipulators. The constraints exerted on the platforms of the 3-RP̲Carchitectures and the 3-RCC-Y manipulators are analyzed using the screw system approach and have been identified as couples. A similarity has been identified with the axes of couples: they are perpendicular to theRjoint axes, but in the former the axes are coplanar with the base and in the latter the axes are perpendicular to the limb. The remaining couples act about the axis that is normal to the base. The motion-screw system and constraint-screw system analysis leads to the insightful understanding of the mobility of the platform that is then obtained by determining the reciprocal screws to the platform constraint screw sets, resulting in three independent instantaneous translational degrees-of-freedom. To validate the mobility analysis of the three parallel manipulators, the paper includes motion simulations which use a commercially available kinematics software.

A Family of Rotational Parallel Manipulators With Equal-Diameter Spherical Pure Rotation

2013 ◽  
Vol 6 (1) ◽  
Author(s):  
Kang Wu ◽  
Jingjun Yu ◽  
Guanghua Zong ◽  
Xianwen Kong
Keyword(s):  
Degrees Of Freedom ◽  
Theoretical Models ◽  
Parallel Manipulators ◽  
Graphical Approach ◽  
Curves And Surfaces ◽  
Pure Rotation ◽  
Geometric Conditions ◽  
Moving Platform ◽  
Constraint Model ◽  
Spatial Curves

In this work, a family of two degrees of freedom (2-DOF) rotational parallel manipulators (RPMs) with an equal-diameter spherical pure rotation (ESPR) is presented and discussed systematically. The theoretical models of both kinematics and constraints inherited in the manipulators are analyzed through a graphical approach. Based on the established constraint model, these 2-DOF ESPR RPMs are classified into three types according to their compositions of constraint spaces and several novel parallel manipulators are illustrated correspondingly. Finally, two common necessary geometric conditions satisfied for these manipulators are discussed in details with examples. The two conditions will be helpful for engineers with designing ESPR RPMs. Moreover, as one characteristic existing in the ESPR RPMs, two cases of self-rotations accompanying revolutions around fixed axes are revealed. As a result, the corresponding loci of points in the moving platform are proved to be compositions of two subrotations, which are spatial curves and surfaces rather than spherical curves and surfaces.

Geometric Factor in Skeletal Reactions of 2-Methylpentane on Stepped Surfaces of Platinum Catalyst

1992 ◽  
Vol 57 (10) ◽  
pp. 2012-2020
Author(s):  
Vladimír Hejtmánek
Keyword(s):  
Active Sites ◽  
Platinum Catalyst ◽  
Point Of View ◽  
Geometric Factor ◽  
Published Data ◽  
Stepped Surfaces ◽  
Geometric Conditions ◽  
Surface Intermediates ◽  
Isomerization Mechanism

The role of geometric factor in the course of skeletal reactions (isomerization, hydrogenolysis) of 2-methylpentane on stepped (119), (557) and reconstructed R(557) surfaces of single crystals of platinum was evaluated with computer designed models. These calculations were compared with reported experimental data. It was found by analysis of geometric conditions that there are accessible active ensembles on double step of the reconstructed R(557) surface. In addition, these active sites are unsaturated in their coordination sphere and thus catalytically effective. This finding is consistent with published data, confirming higher catalytic activity of this surface. The various pathways of Bond Shift isomerization mechanism of 2-methylpentane from the point of view of steric demands of surface intermediates on differently located ensembles are discussed, too.

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.

scholarly journals From Loschmidt daemons to time-reversed waves

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150156 ◽  
Author(s):  
Mathias Fink
Keyword(s):  
Wave Propagation ◽  
Time Reversal ◽  
Degrees Of Freedom ◽  
Point Of View ◽  
Propagation Time ◽  
Reversal Invariance ◽  
Spatial Boundary ◽  
Dual Approaches ◽  
Spatio Temporal

Time-reversal invariance can be exploited in wave physics to control wave propagation in complex media. Because time and space play a similar role in wave propagation, time-reversed waves can be obtained by manipulating spatial boundaries or by manipulating time boundaries. The two dual approaches will be discussed in this paper. The first approach uses ‘time-reversal mirrors’ with a wave manipulation along a spatial boundary sampled by a finite number of antennas. Related to this method, the role of the spatio-temporal degrees of freedom of the wavefield will be emphasized. In a second approach, waves are manipulated from a time boundary and we show that ‘instantaneous time mirrors’, mimicking the Loschmidt point of view, simultaneously acting in the entire space at once can also radiate time-reversed waves.

Sign in / Sign up

Export Citation Format

Share Document