Singularity Analysis of Planar Multiple-DOF Linkages

Abstract

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.

Dead Center Identification of Single-DOF Multi-Loop Planar Manipulator and Linkage Based on Graph Theory and Transmission Angle

“…Automatic. The decomposition method [22] is a geometrical method that can be applied widely but requires artificially decomposing planar linkages, because of which its efficiency is low. The proposed method can be programmed according to the topological graph and the adjacency matrix, and thus the process of identification of the dead center position of the planar linkage can be automated.…”

“…Wang et al [21] used equivalent linkages to find the dead center positions of planar single-degree-of-freedom complex linkages, but the equivalent linkages are difficult to form. Wang et al [22] proposed a decomposition method to analyze the singularity problem of multi-DOF multi-loop linkages. The method is universal but requires prior manual analysis.…”

“…In the above-mentioned studies, the relevant methods can be mainly classified into three cases as follows: (a) the loop equation method [5]- [19]; (b) the equivalent method [21]; and (c) the decomposition method [22]. Although they can determine some dead center positions of linkages, they also have clear disadvantages.…”

“…The equivalent method [21] first needs to find the instant centers, which is a challenging problem. The drawback of the decomposition method [22] is efficiency, given that the method cannot be programmed.…”

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

“…The concept of instant center is proposed by Bernoulli [1], which refers to the zero velocity point for two rigid bodies in a planar motion. It is not only used to analyze kinematics of linkages such as absolute velocity and angular velocity, but also to research singular configurations [2][3][4][5], configuration synthesis [6] and dynamics modeling [7]. Generally, instant centers are obtained by Aronhold-Kennedy theorem [8], but if the linkages contain more links or link loops, the traditional method fails.…”