Changyu Xue

Mobility Criteria of Planar Single-Loop N-Bar Chains With Prismatic Joints

This paper presents the extension of the N-bar rotatability laws to N-bar chains containing prismatic joints. The extension is based on the principle that a prismatic joint may be regarded as a revolute joint located at infinity in the direction normal to the sliding path. The effects of long and short links, full rotatability, linkage classification, and formation of branches and sub-branches are discussed. The extension provides a consistent method to understand all aspects of linkage rotatability disregarding the existence of prismatic joints. The results are demonstrated by several examples.

Unified Mobility Identification and Rectification of Six-Bar Linkages

This paper offers a unified method for a complete and unified treatment on the mobility identification and rectification of any planar and spherical six-bar linkages regardless the linkage type and the choice of the input, output, or fixed links. The method is based on how the joint rotation spaces of the four-bar loop and a five-bar loop in a Stephenson six-bar linkage interact each other. A Watt six-bar linkage is regarded as a special form of Stephenson six-bar linkage via the stretch and rotation of a four-bar loop. The paper offers simple explanation and geometric insights for the formation of branch (circuit), sub-branch, and order of motion of six-bar linkages. All typical mobility issues, including branch, sub-branch, and type of motion under any input condition can be identified and rectified with the proposed method. The method is suitable for automated computer-aided mobility identification. The applicability of the results to the mobility analysis of serially connected multiloop linkages is also discussed.Copyright

General Mobility Identification and Rectification of Watt Six-Bar Linkages

Mobility identification is a common problem encountered in linkage analysis and synthesis. Mobility of linkages refers to the problems concerning branch defect, full rotatability, singularities, and order of motion. By introducing the concept of stretch rotation, the paper shows the existence of a hidden five-bar loop in a Watt six-bar linkage and how it affects the formation of branches, sub-branches, as well as the whole mobility of the entire linkage. The paper presents the first methodology for a fully automated computer-aided complete mobility analysis of Watt six-bar linkages.Copyright

On the Mobility of Spatial Group 2 Mechanisms

Spatial linkages are classified into four groups according to the number of fundamental equations or virtual loops that govern linkage displacement. The number of virtual loops represents the complexity of a spatial linkage as that of planar or spherical multiloop linkages. The concept of generalized branch points offers the explanation of how branches are formed in spatial group 2 linkages. In this paper, the mobility analysis is carried out based on the similarity of the mobility features rather than the specific or individual linkage structure. A branch rectification scheme is presented and demonstrated with examples.Copyright

Singularity and Sub-Branch Identification of Two-DOF Seven-Bar Parallel Manipulators

Mobility analysis of multi-DOF multiloop planar linkages is much more complicated than the single-DOF planar linkages and has been little explored. This paper offers a unified method to treat the singularity (dead center position) and sub-branch identification of the planar two-DOF seven-bar linkages regardless of the choice of the inputs or fixed links. This method can be extended for the singularity analysis of other multi-DOF multiloop linkages. Based on the concept of joint rotation space and N-bar rotatability laws, this paper presents a general method for the sub-branch identification of the seven-bar linkages. It offers simple explanation and geometric insights for the formation of branch, singularity and sub-branch of the two-DOF seven-bar linkages. The presented algorithm for sub-branch identification is suitable for automated computer-aided mobility identification. Examples are employed to demonstrate the proposed method.Copyright

On the Branch Formation of Linkages

A spatial linkage with the displacement governed by two fundamental equations can be regarded as a virtual double loop system. The mobility of the linkage is affected by the mobility of each individual “loop” as well as the interaction between the loops. The current use of branch points for branch identification is limited to linkages with simple topology, such as Stephenson-type linkages, which are simplified versions of group 2 mechanisms. However, in a general spatial group 2 linkage, both the fundamental equations are equivalent to virtual five-bar loops. Branch points in Stephenson-type linkages should be generalized to explain and define the interaction between two virtual five-bar loops. The concept of generalized branch points offers the explanation of how branches are formed in spatial group 2 linkages. This paper presents the theoretical background for the mobility analysis of complex spatial linkages.Copyright

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

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.Copyright