Composition Principle Based on Single-Open-Chain Unit for General Spatial Mechanisms and Its Application—In Conjunction With a Review of Development of Mechanism Composition Principles

Abstract

Based on the general degree-of-freedom (DOF) formula for spatial mechanisms proposed by the author in 2012, the early single open chain (SOC)-based composition principle for planar mechanisms is extended to general spatial mechanisms in this paper. First, three types of existing mechanism composition principle and their characteristics are briefly discussed. Then, the SOC-based composition principle for general spatial mechanisms is introduced. According to this composition principle, a spatial mechanism is first decomposed into Assur kinematic chains (AKCs) and an AKC is then further decomposed into a group of ordered SOCs. Kinematic (dynamic) analysis of a spatial mechanism can then be reduced to kinematic (dynamic) analysis of AKCs and finally to kinematic (dynamic) analysis of ordered SOCs. The general procedure for decomposing the mechanism into ordered SOCs and the general method for determining AKC(s) contained in the mechanism are also given. Mechanism's kinematic (dynamic) analysis can be reduced to the lowest dimension (number of unknowns) directly at the topological structure level using the SOC-based composition principle. The SOC-based composition principle provides a theoretical basis for the establishment of a unified SOC-based method for structure synthesis and kinematic (dynamic) analysis of general spatial mechanisms.

Kinematics of Articulated Planar Linkages

“…Actually, such procedures can be accomplished through vector-loop processing for planar linkages (Brát and Lederer, 1973;Kong et al, 2018). The forward kinematics are either established in the functions of structure parameters and input variables numerically (Yang et al, 2018) or presented in algebraic coordinates (Wu et al, 2013;Kong et al, 2019). The inverse kinematic problem consists of finding the joint variables to achieve a desired configuration of a mechanism (Chapelle and Bidaud, 2004;Wu et al, 2013).…”

“…To understand the kinematic performance of a linkage, many scholars have been proposing different theories (McCarthy, 1990;Duffy, 1996;Davidson and Hunt, 2004;Dai, 2014;Zhao et al, 2016;Amiri and Mazaheri, 2020;Faghidian and Mohammad-Sedighi, 2020), methods (Angeles, 1982;Kong et al, 2018;Yang et al, 2018;Kong et al, 2019;Shen et al, 2020), algorithms (García de Jalón and Bayo, 1994;Kong et al, 2016;Saura et al, 2019) and software (Brát and Lederer, 1973;García de Jalón and Bayo, 1994;Wu et al, 2009;Wu et al, 2017). This paper focuses on an algorithm in the screw coordinates to solve the velocity of articulated planar linkage and investigates the displacement and acceleration.…”

A Translational Three-Degrees-of-Freedom Parallel Mechanism With Partial Motion Decoupling and Analytic Direct Kinematics

“…Lu et al [14] proposed a 3-RRRP (4R) three-translation PM and analyzed the kinematics and workspace. Yang et al [15,16] studied 3T0R PMs based on the single opened chains (SOC) units, and a variety of new TPMs were synthesized and then classified [17,18]. Considering the anisotropy of kinematics, Zhao et al [19] analyzed the dimensional synthesis and kinematics of the 3-DOF translational Delta PM.…”

A Survey of Mathematical Tools in Topology and Performance Integrated Modeling and Design of Robotic Mechanism

“…Hence, type synthesis is to obtain all the possible topologies according to the expected motion pattern. The description of expected motion patterns can be classified into two formats [45,46]. One takes the finite motion form, which expresses the displacement of the robot from the initial pose to another.…”