A new approach for the identification of reciprocal screw systems and its application to the kinematics analysis of limited-DOF parallel manipulators. (December 2017)

• Record Type: Journal Article
• Authors: Chen, Genliang; Yu, Weidong; Chen, Chao; Wang, Hao; Lin, Zhongqin
• Is Part Of: Mechanism and machine theory. Volume 118(2017:Dec.)
• Page Start: 194
• Page End: 218
• Publication Date: 2017-12
• Subjects: Screw theory -- Reciprocal system -- Kinematics analysis -- Limited-DOF parallel manipulators; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2017.08.007
• Languages: English
• ISSNs: 0094-114X

Abstract

Highlights: A new approach for the identification of the corresponding reciprocal screw systems is proposed in this paper. The application of the proposed approach to the kinematics analysis of limited-DOF parallel manipulators is presented by taking the 3-RPS mechanism as an example. A geometric interpretation is provided to intuitively illustrate the exact distribution of the studied manipulator's screw systems. The proposed approach is extended to the application of several more typical limited-DOF parallel manipulators with the same procedure. Abstract: The theory of reciprocal screws plays an important role in the kinematics and statics analysis 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 comprise 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 effectiveness 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.