Jun Wang

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.

Calibration of Measured FRFs Based on Mass Identification Method

It is necessary to calibrate the equipment during each test in modal testing. This paper presented a practical method for the calibration of the measured FRFs based on mass identification method. One advantage of this proposed method is that the calibration is performed directly on the test structure. Thus, it is more reliable and convenient. It is shown that if the mass identification method is applied to the uncalibrated system, a different level between the identified mass and the given exact mass reveals that the set up is not calibrated. And the measured FRFs can be calibrated using the ratio factor of the identified mass and exact mass. The simulation testing demonstrates good performance. In practical testing, however, the accuracy of mass identification results may be vulnerable to the noise and further work is necessary in order to solve this difficulty.Copyright

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

Uncertainty of Coupler Point Position of Slider Crank Mechanisms

In this paper, a novel geometric model for a planar slider-crank mechanism is established to quantify the position uncertainty of a coupler point caused by joint clearances. The clearance of each revolute and prismatic joint is characterized by a short clearance link. The prismatic joint with clearance is modeled as a link with infinite link length and a variable short link. The linkage with joint clearance is thus modeled as one with redundant freedom. The uncertainty is the result of the redundancy and the extremity of the redundancy is determined through Ting’ N-bar rotatability laws.Copyright

Full Rotatability of Watt Six-Bar Linkages

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.Copyright

Singularity Analysis of Planar Multiple-DOF Linkages

Singularity analysis of multi-DOF (multiple-degree-of-freedom) multiloop planar linkages is much more complicated than the single-DOF planar linkages. This paper offers a degeneration method to analyze the singularity (dead center position) of multi-DOF multiloop planar linkages. The proposed method is based on the singularity analysis results of single-DOF planar linkages and the less-DOF linkages. For an N-DOF (N>1) planar linkage, it generally requires N inputs for a constrained motion. By fixing M (M<N) input joints or links, the N-DOF planar linkage degenerates an (N-M)-DOF linkage. If any one of the degenerated linkages is at the dead center position, the whole N-DOF linkage must be also at the position of singularity. With the proposed method, one may find out that it is easy to obtain the singular configurations of a multiple-DOF multiloop linkage. The proposed method is a general concept in sense that it can be systematically applied to analyze the singularity for any multiple-DOF planar linkage regardless of the number of kinematic loop or the types of joints. The velocity method for singularity analysis is also used to verify the results. The proposed method offers simple explanation and straightforward geometric insights for the singularity identification of multiple-DOF multiloop planar linkages. Examples are also employed to demonstrate the proposed method.Copyright

Equivalent Linkages and Dead Center Positions of Planar Single-DOF Complex Linkages

This paper proposes a simple and general approach for the identification of the dead center positions of single-DOF complex planar linkages. This approach is implemented through the first order equivalent four-bar linkages. The first order kinematic properties of a complex planar linkage can be represented by their instant centers. The basic idea behind this method is obvious and straightforward. The condition for the occurrence of a dead center position can be designed as when the three passive joints of the equivalent four-bar linkage become collinear. The proposed method is a general concept in the sense that it can be systematically applied to analyze the dead center positions for any type of single-DOF planar linkages regardless of the number of kinematic loops or the type of the kinematic pairs involved. The velocity method for the dead center analysis is also used to compare the results. The proposed method paves a novel and easy way to analyze the dead center positions for complex planar linkages. This concept is presented for the first time for the dead center analysis of planar complex linkages. Examples of complex linkages are employed to illustrate this concept in this paper.Copyright

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

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.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