Mechanism and Machine Theory 137 (2019) 459–475 Contents lists available at ScienceDirect Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmachtheory Research paper A novel criterion for singularity analysis of parallel mechanisms Michael Slavutin ∗ , Offer Shai † , Avshalom Sheffer , Yoram Reich School of Mechanical Engineering, Tel Aviv University, Ramat Aviv 69978, Israel a r t i c l e i n f o Article history: Received 19 December 2018 Revised 2 March 2019 Accepted 2 March 2019 Keywords: Instantaneous screw axis (ISA) Minimal parallel robots Screw theory Singular characterization 3D Kennedy theorem 3/6 and 6/6 Stewart Platform a b s t r a c t A novel criterion for singularity analysis of parallel robots is presented. It relies on screw theory, the 3-dimensional Kennedy theorem, and the singular properties of minimal par- allel robots. A parallel robot is minimal if in any generic configuration, activating any leg/limb causes a motion in all its joints and links. For any link of the robot, a pair of legs is removed. In the resulting 2 degrees-of-freedom mechanism, all possible instanta- neous screw axes belong to a cylindroid. A center axis of this cylindroid is determined. This algorithm is performed for three different pairs of legs. The position is singular, if the instantaneous screw axis of the chosen link crosses and is perpendicular to three center axes of the cylindroids. This criterion is applied to a 6/6 Stewart Platform and validated on a 3/6 Stewart Plat- form using results known in the literature. It is also applied to two-platform minimal par- allel robots and verified through the Jacobian; hence demonstrating its general applicabil- ity to minimal robots. Since any parallel robot is decomposable into minimal robots, the criterion applies to all constrained parallel mechanisms. © 2019 Elsevier Ltd. All rights reserved. 1. Introduction This paper introduces a novel criterion for singularity analysis of general parallel mechanism. We distinguish between characterization and criterion of a singular configuration. The former provides a geometric description of a parallel robot in a singular position, while the latter checks whether the geometry of a given robot indicates that it is in a singular configuration. Singularity analysis is one of the fundamental issues of parallel mechanisms. Singular configuration is the position where the mechanism gains or loses degrees of freedom. It is known to be one of the main concerns in the analysis and design of mechanisms [1]. Although singularity of parallel mechanisms was studied early in the 1980s, this problem is still very difficult. Besides studying singularity positions, it is also critical to avoid them [2], to escape them as fast as possible [3], and in general, to characterize the geometry of the singularity spaces [4]. Among the methods used in determining singularity positions are the analysis of the Jacobian matrix, obtained from analytical expressions [5,6], or from geometric analysis that uses Grassmann-Cayley algebra [7–10], or using quaternion algebra [11]; motion/force transmissibility analysis [12]; and rigidity matrix analysis [13]. The latter is extensively used in the mathematics community [14] in rigidity theory. Some papers dealt with criteria for singularity of different types of ∗ Corresponding author. E-mail addresses: slavutin@post.tau.ac.il (M. Slavutin), sheffer@mail.tau.ac.il (A. Sheffer), yoram@eng.tau.ac.il (Y. Reich). † Deceased https://doi.org/10.1016/j.mechmachtheory.2019.03.001 0094-114X/© 2019 Elsevier Ltd. All rights reserved.