Full Rotatability of Stephenson Six-Bar and Geared Five-Bar Linkages

2008 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Jun Wang ◽  
Changyu Xue ◽  
Kenneth R. Currie
Keyword(s):  
Linkage Analysis ◽  
Degree Of Freedom ◽  
Comprehensive Treatment ◽  
Joint Rotation ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Input And Output ◽  
Difficult Condition ◽  
Center Position ◽  
Analysis And Synthesis

Full rotatability identification is a problem frequently encountered in linkage analysis and synthesis. The full rotatability of a linkage is referred to a linkage in which the input may complete a full revolution without the possibility of encountering a dead center position. In a complex linkage, the input rotatability of each branch may be different. This paper presented a unified and comprehensive treatment for the full rotatability identification of six-bar and geared five-bar linkages disregard the choice of input and output joints or fixed link. A simple way to identify all dead center positions and the associated branches is discussed. Special attention and detail discussion is given to the more difficult condition with the input given through a link or joint not in the four-bar loop or on a gear-link. A branch without a dead center position has full rotatability. Using the concept of joint rotation space, the branch of each dead center position, and hence the branch without a dead center position can be identified easily. The proposed method is simple and conceptually straightforward and the process can be automated easily. It can be extended to any other single-degree-of-freedom complex linkages.

Full Rotatability and Singularity of Six-Bar and Geared Five-Bar Linkages

2010 ◽  
Vol 2 (1) ◽  
Author(s):  
Kwun-Lon Ting ◽  
Jun Wang ◽  
Changyu Xue ◽  
Kenneth R. Currie
Keyword(s):  
Linkage Analysis ◽  
Comprehensive Treatment ◽  
Not Given ◽  
Joint Rotation ◽  
Difficult Condition ◽  
Continuous Rotation ◽  
Center Position ◽  
Analysis And Synthesis

Full rotatability identification is a problem frequently encountered in linkage analysis and synthesis. The full rotatability of a linkage refers to a linkage, in which the input may complete a continuous rotation without the possibility of encountering a dead center position. In a complex linkage, the input rotatability of each branch may be different. This paper presents a unified and comprehensive treatment for the full rotatability identification of six-bar and geared five-bar linkages, regardless of the choice of input joints or reference link. A general way to identify all dead center positions and the associated branches is discussed. Special attention and detail discussion is given to the more difficult condition, in which the input is not given through a joint in the four-bar loop or to a gear link. A branch without a dead center position has full rotatability. Using the concept of joint rotation space, the branch of each dead center position, and hence, the branch without a dead center position can be identified. One may find the proposed method to be generally and conceptually straightforward. The treatment covers all linkage inversions.

Mobility Identification of a Group of Single Degree-of-Freedom Eight-Bar Linkages

2010 ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting
Keyword(s):  
Linkage Analysis ◽  
Range Of Motion ◽  
Configuration Space ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Computer Aided ◽  
Analysis And Synthesis ◽  
First Time

This paper presents the first complete and automated mobility identification method for a group of single-DOF planar eight-bar linkages and thus represents a breakthrough on the recognition and understanding of complex linkage mobility. The mobility identification in this paper refers to the configuration space, the range of motion, and configuration recognition. It is a troublesome problem encountered in any linkage analysis and synthesis. The problem becomes extremely confusing with complex multiloop linkages. The proposed approach is simple and straightforward. It recognizes that the loop equations are the mathematical fundamentals for the formation of branches, sub-branches, and other mobility issues of the entire linkage. The mobility information is then extracted through the discriminant method. The paper presents complete answers to all typical mobility issues, offers the mathematical insight as well as explanation on the effects of multiple loops via joint rotation space, and casts light for treating the mobility problems of other complex linkages. The merits of the discriminant method for mobility identification are clarified and examples are employed to showcase the proposed method. The computer-aided automated mobility analysis of eight-bar linkages is made possible for the first time.

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.

Full Rotatability of Watt Six-Bar Linkages

2014 ◽  
Author(s):  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Daxing Zhao ◽  
Quan Wang ◽  
Jinfeng Sun ◽  
...  
Keyword(s):  
Linkage Analysis ◽  
Range Of Motion ◽  
Analytical Method ◽  
Joint Rotation ◽  
Center Position ◽  
Analysis And Synthesis ◽  
Prismatic Joints

The full rotatability of a linkage refers to a linkage in which the input may complete a continuous and smooth rotation without the possibility of encountering a dead center position. Full rotatability identification is a problem generally encountered among the mobility problems that may include branch (assembly mode or circuit), sub-branch (singularity-free) identification, range of motion, and order of motion in linkage analysis and synthesis. In a complex linkage, the input rotatability of each branch may be different while the Watt six-bar linkages may be special. This paper presents a unified and analytical method for the full rotatability identification of Watt six-bar linkages regardless of the choice of input joints or reference link or joint type. The branch of a Watt without dead center positions has full rotatability. Using discriminant method and the concept of joint rotation space (JRS), the full rotatability of a Watt linkage can be easily identified. The proposed method is general and conceptually straightforward. It can be applied for all linkage inversions. Examples of Watt linkage and a six-bar linkage with prismatic joints are employed to illustrate the proposed method.

Joint Rotation Space of Five-Bar Linkages

1992 ◽  
Author(s):  
Kwun-Lon Ting ◽  
J. H. Shyu
Keyword(s):  
Extensive Study ◽  
Degree Of Freedom ◽  
Joint Rotation ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
The Relationship

Abstract Unlike single degree of freedom linkages, the rotatability at a joint of a five-bar linkage is affected by the rotatability at another joint. Unless the linkage has full rotatability, the allowable inputs of a five-bar linkage are related. This article, by taking the interrelationship between the rotatability of two input angles into consideration, presents the most extensive study on the rotatability of five-bar linkages. The joint rotation space of a five-bar linkage is the region between the singular curves which represent the relationship between the input angular positions of the linkage at singular positions. By distinguishing five-bar linkages into C-C (crank-crank), C-R (crank-rocker), and R-R (rocker-rocker) types, there are totally nine C-C types, four C-R types and four R-R types of joint rotation space in classes I and II five-bar linkages. The results in this paper are essential for understanding the basic mobility and limitation of five-bar linkages. One may also find them useful in manipulators or multi-loop linkages which have a five-bar chain as the major or minor structure. The results are also applicable to spherical five-bar linkages.

Kinematic comparison of single degree-of-freedom robotic gait trainers

2021 ◽  
Vol 159 ◽  
pp. 104258
Author(s):  
Jeonghwan Lee ◽  
Lailu Li ◽  
Sung Yul Shin ◽  
Ashish D. Deshpande ◽  
James Sulzer
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Robotic Gait
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