Joint Rotation Space and Mobility of Linkages

2007 ◽  
Author(s):  
Kwun-Lon Ting
Keyword(s):  
Fundamental Principle ◽  
General Concept ◽  
Joint Rotation ◽  
Single Loop ◽  
Input Domain ◽  
Spatial Linkages ◽  
One To One

The paper presents a general concept regarding the joint rotation space (JRS) of single loop planar and spherical N-bar linkages as well as its significance and applicability in multiple loop and spatial linkages. A JRS refers to the input domain of a linkage. The paper first discusses and classifies the JRS types of single loop five-bar linkages based on the types of the JRS boundary. The concept of sheets and pages of JRS is then introduced as an aid to understand the mobility of linkages. A sheet refers to the JRS of a linkage branch (or circuit). A JRS sheet may have one or more pages and each page refers to an uncertainty singularity free JRS. The concept is then generalized to any single loop planar and spherical N-bar linkages (N ≥ 3). The paper offers geometric insights to the input domain of a linkage and establishes a one-to-one correspondence between the input domain and the linkage configurations. The applications to the mobility identification of complex linkages are discussed and demonstrated with geared five-bar linkages, Stephenson six-bar linkages, as well as spatial RCRCR mechanisms. The paper presents a useful model explaining the fundamental principle regarding the formation of branches and sub-branches in Stephenson six-bar linkages as well as some other multiloop and spatial linkages. The Mobility similarity between multiloop linkages and spatial linkages is also highlighted.

On the Input Joint Rotation Space and Mobility of Linkages

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
Kwun-Lon Ting
Keyword(s):  
Visualization Tool ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Single Loop ◽  
Spatial Linkages ◽  
One To One ◽  
Spherical Linkages ◽  
Virtual Loop

This paper presents the concept and application of input joint rotation space of linkages and offers updates on the N-bar rotatability laws. A thorough discussion on the joint rotation space of single-loop planar five-bar linkages is first presented. The concept is then extended to spherical linkages and the generalization to N-bar linkages is discussed. It offers a visualization tool for the input joint rotatability and fills up a void in the N-bar rotatability laws regarding the coordination among multiple inputs. It explains the formation of branches and how to establish a one-to-one correspondence between the inputs and the linkage configurations. The applications to multiloop linkages and spatial linkages are highlighted with Stephenson six-bar linkages, geared linkages, and spatial RCRCR mechanisms. These examples exhibit simplicity and benefits of the proposed concept to the mobility analysis of diversified mechanisms. The concept of virtual loop in spatial linkages is proposed and demonstrated with simple RCRCR and Stephenson six-bar mechanisms.

Velocity, Acceleration, and Static-Force Analyses of Spatial Linkages

1965 ◽  
Vol 32 (4) ◽  
pp. 903-910 ◽  
Author(s):  
J. Denavit ◽  
R. S. Hartenberg ◽  
R. Razi ◽  
J. J. Uicker
Keyword(s):  
Virtual Work ◽  
Algebraic Method ◽  
Degree Of Freedom ◽  
Static Force ◽  
Virtual Displacement ◽  
Single Loop ◽  
Loop Equation ◽  
The Matrix ◽  
Spatial Linkages

The algebraic method using 4 × 4 matrices is extended to the analysis of velocities, accelerations, and static forces in one-degree-of-freedom, single-loop, spatial linkages consisting of revolute and prismatic pairs, either singly or in combination. The methods are well suited for machine calculations and have been tested on a number of examples, one of which is presented. Velocities and accelerations are obtained by differentiation of the matrix-loop or position equation. Static forces are found by combining the method of virtual work with the matrix-loop equation to relate the virtual displacement of the load to given virtual deformations of the links.

Baron vom Stein, the Prussian Law on Municipal Government of 1808 and the Creation of the German Tradition of Participative Self-Government

10.4335/55 ◽  
2009 ◽  
Vol 6 (3) ◽  
pp. 271-285
Author(s):  
Martin Will
Keyword(s):  
Municipal Government ◽  
Fundamental Principle ◽  
General Concept ◽  
The Self ◽  
Federal Republic Of Germany ◽  
Self Administration ◽  
Structural Principles ◽  
Constitutional System ◽  
The Right ◽  
The Town

Most European States have their own particular form and tradition of local self-government. The German concept of local self-government goes back to the Prussian reformer Baron vom Stein who introduced local self-government 200 years ago in Prussia by means of the Prussian Law on Municipal Government. In essence, the then promoted concept of self-government meant that citizens with voting powers had the right to elect a representative assembly which in turn formed a central legislative as well as an administrative organ duly representing the whole citizenship of the town. The fundamental principle of self-government was later transferred to other areas such as the self-government of trade and industry, the self-government of liberal professions or the self-government of universities. As self-government was applied to ever more fields, various scholars contributed to a general concept of self-government or self administration which can now be seen as one of the basic structural principles of the constitutional system of the Federal Republic of Germany. Key words: • Prussian Law • municipial government • local self-government •constitutional system

Branch Identification of Spherical Six-Bar Linkages

2016 ◽  
Author(s):  
Liangyi Nie ◽  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Daxing Zhao ◽  
Quan Wang ◽  
...  
Keyword(s):  
Range Of Motion ◽  
Degree Of Freedom ◽  
Joint Rotation ◽  
Single Degree Of Freedom ◽  
Complex Issue ◽  
Single Degree ◽  
Identification Method ◽  
Spatial Linkages ◽  
Spherical Linkages

Branch (assembly mode or circuit) identification is a way to assure motion continuity among discrete linkage positions. Branch problem is the most fundamental, pivotal, and complex issue among the mobility problems that may also include sub-branch (singularity-free) identification, range of motion, and order of motion. Branch and mobility complexity increases greatly in spherical or spatial linkages. This paper presents the branch identification method suitable for automated motion continuity rectification of a single degree-of-freedom of spherical linkages. Using discriminant method and the concept of joint rotation space (JRS), the branch of a spherical linkage can be easily identified. The proposed method is general and conceptually straightforward. It can be applied for all linkage inversions. Examples are employed to illustrate the proposed method.

scholarly journals Spatial Straight-Line Linkages by Factorization of Motion Polynomials

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Zijia Li ◽  
Josef Schicho ◽  
Hans-Peter Schröcker
Keyword(s):  
End Effector ◽  
Single Loop ◽  
Revolute Joints ◽  
Straight Line ◽  
Prismatic Joints ◽  
Spatial Linkages ◽  
Line Trajectory ◽  
Straight Line Trajectory

We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight-line trajectory. Unlike previous examples of such linkages by other authors, they are single-loop linkages and the end-effector motion is not translational. In particular, we obtain a number of linkages with four revolute and two prismatic joints and a remarkable linkage with seven revolute joints one of whose joints performs a Darboux motion.

A Generalized Transmission Index for Spatial Linkages

2005 ◽  
Author(s):  
Chao Chen ◽  
Jorge Angeles
Keyword(s):  
Single Loop ◽  
Spatial Mechanisms ◽  
Transmission Index ◽  
Spatial Linkages

This paper proposes a generalized transmission index for spatial mechanisms, based on the transmission index introduced by Sutherland and Roth. This index is more general and welldefined in all the cases; it matches the virtual coefficient between the transmission wrench screw and the output twist screw exactly. A method is developed to compute the transmission wrench screw in spatial single-loop linkages. We illustrate the application of this index in a RSCR linkage.

Dwell Motion From Spatial Linkages

1973 ◽  
Vol 95 (2) ◽  
pp. 511-518 ◽  
Author(s):  
A. K. Shrivastava ◽  
K. H. Hunt
Keyword(s):  
Curve Matching ◽  
Single Loop ◽  
Spatial Linkages ◽  
Four Bar Linkage ◽  
Surface Curve

The potential of single-loop spatial linkages to produce an output dwell from a rotating input is broadly surveyed. Then three comparatively simple four-bar linkage arrangements are selected, and studied in detail. The dwell characteristics of all three are viewed via surface-surface or surface-curve “matching” at a spherical pair. Attention is mainly confined to symmetric output-input motions, and the accuracy of dwell is assessed.

A New Family of Deployable Mechanisms Derived From Two-Layer and Two-Loop Spatial Linkages With Five Revolute Pair Coupling Chains

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Wen-ao Cao ◽  
Donghao Yang ◽  
Huafeng Ding
Keyword(s):  
Structural Characteristics ◽  
Degree Of Freedom ◽  
Single Loop ◽  
New Family ◽  
Serial Chain ◽  
Spatial Linkages ◽  
Application Requirements ◽  
Pair Coupling

This paper aims to construct a novel family of deployable mechanisms from a class of two-layer and two-loop spatial linkages, each of which consists of an eight revolute pair (8R) single-loop linkage connected by a 5R serial chain. First, structural characteristics of the class of linkages as deployable units are analyzed and illustrated. Then, the two-layer and two-loop spatial linkages with 5R chains satisfying the structural characteristics are systematically synthesized. Mobile assembly modes between deployable units are established based on degree-of-freedom (DOF) analysis. Finally, a family of single DOF deployable mechanisms is constructed based on the synthesized deployable units and the established assembly modes. The derived deployable mechanisms have the characteristic of the umbrella-like structure, and they have various mesh shapes, which can meet different kinds of application requirements.

scholarly journals Mathematical Fundamentals of Modern Linear Optics

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Andrey V. Gitin
Keyword(s):  
Path Integral ◽  
Fundamental Principle ◽  
Short Wave ◽  
Quantum Mechanical ◽  
Linear Optics ◽  
Statistical Optics ◽  
Fermat’S Principle ◽  
One To One ◽  
Fermat's Principle

All known quantum-mechanical approaches to wave and statistical optics are united into a single theory, using Feynman's path integral as a fundamental principle. In short-wave approximations, this principle, the Fourier transformations, and concepts of the theory reproduce Fermat's principle, the Legendre transformations, and concepts of Hamilton's optics and radiometry in a one-to-one fashion.

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.

Sign in / Sign up

Export Citation Format

Share Document