Transmission index of a class of parallel manipulators with 3-RS(SR) primary structures based on pressure angle and equivalent mechanism with 2-SS chains replacing RS chain

In this paper, we present a new transmission index (TI) for kinematic performance evaluation of a class of parallel manipulators with a 3-RS (or 3-SR) structure; termed the primary structure obtained by locking all actuated joints in the manipulators. TI is based on the pressure angle that is defined in a kinematically equivalent structure, a 6-SS structure by replacing an RS chain of the primary structure with a pair of SS chains, which can reflect the practical force transmission and constraint characteristics of R joint composed of two bearings in the original manipulator. The effectiveness of TI is verified by considering 3-PRS and 3-RPS parallel manipulators. The singularity analysis, relationships between the maximum joint forces and index values, distribution of TI inside the workspace, and an application of TI to a kinematic design are demonstrated. The proposed approach can indicate both output and constraint singularity conditions with a single index, can be achieved by simple calculation process without complicated normalization, and can include the width of the revolute joint in the kinematic performance evaluation of this class of parallel manipulators. (C) 2019 Elsevier Ltd. All rights reserved.