A screw theory approach to compute instantaneous rotation axes of indeterminate spherical linkages

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

“…The ratio of the inputs of an instantaneous configuration is specified, the momentary input is known and invariable. In literatures above [9,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], instant centers are classified into two types: primary instant center and secondary instant center. For a given linkage, primary instant center is constantly the coincident point for a pair of rigid bodies of a planar linkage.…”

“…The inputs and the motions of the links (not including the virtual links) in the virtual Stephenson linkage are the same compared to the original single-loop five-bar linkage. The instant centers which are formed by the virtual links 1', 3', and 6', such as I 1'2 , I 1'3' , I 1'4 , I 1'5 , I 1'6' , I 23 The loop equation of the virtual Stephenson linkage (Figure 7b) can be expressed as Loop ABFG: a 2 e iθ 2 + a 31 e i(2π+θ 3 −β) − a 11 e iα − a 6 e iθ 6 = 0 (7)…”

“…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 main issue is how to use the techniques, and it is not universal for different linkages. Valderrama-Rodríguez [23,24] presented a screw theory approach for the computation of instant rotation axes of the spherical linkages requiring the solution and comparison of two quadratic equations. Although this method is simpler than the previous literature, the calculation is relatively complex.…”

“…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.…”