A General Degree of Freedom Formula for Parallel Mechanisms and Multiloop Spatial Mechanisms

Abstract

Based on the position and orientation characteristic (POC) set and the POC equations for serial mechanisms and parallel mechanisms proposed by authors, this paper presents a novel general degree of freedom (DOF) formula which is totally different from approaches based on the screw theory and the displacement group. It can be used to determine the full-cycle DOF of parallel mechanisms (PMs) and multiloop spatial mechanisms using symbolic “union” and “intersection” operations for POC sets. These operations involve only several rules and only simple mathematical tools (vector algebra, theory of sets, etc.) are used. Furthermore, criteria for determination of the inactive joints and selection of the actuating joints are proposed. The presented approach is illustrated with several examples.

On the Correctness and Strictness of the Position and Orientation Characteristic Equation for Topological Structure Design of Robot Mechanisms

“…(iii) Based on the POC equations (Eqs. (13) and (15)) of the serial mechanisms and parallel mechanisms, a novel general DOF formula has been proposed by Yang and Sun for parallel mechanisms and multiloop mechanisms [30]:…”

“…Since DOF ¼ 1 of this mechanism [30], according to Eq. (B1m), its POC set has only one independent elements The other elements must be a nonindependent elements and be put inside a pair of braces.…”

“…For a parallel mechanism containing an inactive pair, the inactive pair must be determined [30] and eliminated first, then the POC of the moving platform is calculated using Eq. (15).…”

“…[27]) based method [27][28][29][30][31]. Anonymous reviewers of our previous papers have two doubts about this POC set based method:…”

“…12 [30], according to Eqs. (B1c) and (B1l) of the intersection operation rules for POC sets in Appendix B or paper [27], the above equation can be rewritten as…”