The Virtual Cam – Hexagon Method Authentication on Locating Key Instant Centers of All Planar Single Degree of Freedom Kinematically Indeterminate Linkages up to Ten-Bar

Abstract

At this moment all the methods which had been proposed have extremely limited application to only several specific constructions of kinematically indeterminate linkages, i.e. their complete sets of instant centers cannot be obtained simply from Kennedy Theorem due to lack of enough four-bar loop information in their constructions. Planar single degree of freedom linkages up to ten-bar include two different types of mechanisms, i.e. pure bar linkages, such as four-, six-, eight-, and ten-bar; and geared-bar linkages, i.e. geared-five, seven, and nine-bar. The huge varieties of different types and constructions can serve as great testbeds for these methods. This research systematically investigates and modifies the graphical approach, i.e. virtual cam method, whose employment will show it to be an almost-universal method which can be compliantly applied on very wide range of kinematically indeterminate linkages. The procedures and criteria of the methodology are proposed and examined thoroughly to help locate key instant centers of all planar single degree of freedom kinematically indeterminate linkages up to ten-bar so that their complete sets of instant centers can be located successfully. We call this modified and improved technique as Virtual Cam – Hexagon Method. The results are verified carefully against traditional Kennedy Theorem approach and CAD modeling.

Instant Center Identification of Single-Loop Multi-DOF Planar Linkage Using Virtual Link

“…The first contribution of this paper is to provide a virtual link method to identify instant centers of the single-loop multi-DOF planar linkage, which is a graphical method and sticks to the definition of instant center. Compared to the previous literature [10][11][12][13][14][15][16][17][18][19][20][21][22], the proposed method has three advantages: simplification, concision, and validity. Firstly, to build virtual link operation, a few steps are carried out and normally, only one virtual link added operation is required.…”

“…The instant center which cannot be directly located by Aronhold-Kennedy theorem, is called "indeterminate instant center" [9] or indeterminate secondary instant center in Refs. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Moreover, it exists in almost all linkages besides single-loop four-bar linkage and Stephenson linkage.…”

“…The essence of this method is first to determine one indeterminate secondary instant center by combing two arbitrary possible positions, then to reverse all the indeterminate instant centers, but its implementation method is roundabout. Based on instant centers of the cam pair residing on the extension line of a primary adjacent link, Chang [17][18][19] introduced a virtual cam method to help locate key instant centers of the linkages up to ten-bar. This method is a graphical one and is accurate in AutoCAD, but the applicable rate is not high.…”

“…Although instant center, which is a basic kinematic property, is a useful tool to analyze kinematics of the linkages [2][3][4][5]31], rigid-body synthesis [6], dynamics modeling [7], and dynamic balancing analysis [29] of planar linkages, and it can be used in spatial mechanisms [26,27], redundant mechanisms [28], imperfect systems of real devices [30], and is even available in commercial packages, the identification of instant center is difficult since the lack of relationship of the interval links in a N-bar loop (N ≥ 5). As discussed above, the existing methods can be classified three types: (1) graphical method [10,12,[17][18][19]22], (2) analytical method [11,20,23,24], and (3) both analytical method and graphical method [9,[14][15][16]. The graphical method has the advantage of visualization, but the defects are complex process and low applicable rate.…”

“…Thirdly, the proposed method is only based on instantaneous configuration of the linkage and the definition of instant center, and to ensure universality, the parameters of the virtual links are arbitrary. As a result, the application of this method is universal no matter what the degrees of freedom and the components of the joints of the linkage are [17][18][19]. The second contribution is to redefine three types of instant centers.…”