Mechanism and Machine Theory 118 (2017) 194–218 Contents lists available at ScienceDirect Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmachtheory Research paper A new approach for the identification of reciprocal screw systems and its application to the kinematics analysis of limited-DOF parallel manipulators Genliang Chen a , Weidong Yu a , Chao Chen b , Hao Wang a,∗ , Zhongqin Lin a a State Key Laboratory of Mechanical Systems and Vibration, Shanghai Key Laboratory of Digital Manufacturing for Thin-Walled Structures, Shanghai Jiao Tong University, Shanghai 200240, PR China b Department of Mechanical and Aerospace Engineering, Monash University, Clayton, Victoria 3802, Australia a r t i c l e i n f o Article history: Received 8 May 2017 Revised 13 August 2017 Accepted 14 August 2017 Keywords: Screw theory Reciprocal system Kinematics analysis Limited-DOF parallel manipulators a b s t r a c t The theory of reciprocal screws plays an important role in the kinematics and statics anal- ysis of robot manipulators. Thus, efficient algorithms are usually required to identify the reciprocal screw system in closed-form. Inspired by the spatial stiffness/compliance, this paper presents a new approach for the identification of reciprocal screw system for any given one. The concept of symmetric screw matrix is introduced to uniformly represent the screw systems with 6 × 6 symmetric positive semidefinite matrices. By means of the change of coordinates and the recombination of base elements, any screw system can be decomposed into the direct sum of a general subsystem and a special one, which com- prise only finite- and infinite-pitch elements belonging to the original system, respectively. Hence, for an arbitrary screw system, the corresponding reciprocal system can be achieved as the direct sum of those reciprocal to its subsystems. In the proposed framework, the decomposed subsystems can be uniquely identified by a diagonal and a symmetric 3 × 3 matrices, respectively, with respect to a particular choice of coordinate frame. Based on the theory of orthogonal complement spaces, the reciprocal subsystems can then be obtained in a straightforward manner with intuitive geometric interpretation. To verify the effec- tiveness of the proposed method in the kinematics analysis of limited degree-of-freedom (DOF) parallel manipulators, several typical candidates are investigated as examples. In all these examples, the screw systems can be identified in closed-form and the instantaneous kinematics can be characterized according to the properties of the obtained subsystems. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction Due to its intuitive geometric insights and elegant formalism in representation, the theory of screws [1–3] has been suc- cessfully utilized in a wide range of applications in the fields of mechanisms and robotics during the past decades, including Jacobian analysis [4,5] of limited-DOF parallel mechanisms, mobility [6,7] and singularity [8,9] analysis of spatial linkages, type synthesis of lower-mobility parallel manipulators [10–12], and analysis/synthesis of robot compliance [13–15]. In these types of applications, identification of the corresponding reciprocal screw system from a given one plays an important role ∗ Corresponding author. E-mail addresses: leungchan@sjtu.edu.cn (G. Chen), wanghao@sjtu.edu.cn (H. Wang). http://dx.doi.org/10.1016/j.mechmachtheory.2017.08.007 0094-114X/© 2017 Elsevier Ltd. All rights reserved.