Type Synthesis of Parallel Mechanisms with the First Class G_F Sets and Two-Dimensional Rotations

Abstract

The novel design of parallel mechanisms plays a key role in the potential application of parallel mechanisms. In this paper, the type synthesis of parallel mechanisms with the first class GF sets and two-dimensional rotations is studied. The rule of two-dimensional rotations is given, which lays the theoretical foundation for the intersection operations of specific GF sets. Next, kinematic limbs with specific characteristics are designed according to the 2-D and 3-D axes movement theorems. Finally, several synthesized parallel mechanisms with the first class GF sets and two-dimensional rotations are illustrated to show the effectiveness of the proposed methodology.

Type Synthesis of Lower Mobility Parallel Mechanisms: A Review

“…Generalized function sets, called G F sets, were introduced by Gao et al [30][31][32][33][34][35] to denote the motion characteristics of the moving platforms of robots. A G F set is composed of six elements:…”

“…There is a total of 21 types of G F sets, which are classified into two classes according to the sequence of translational characteristics and rotational characteristics, that is, first-class G F sets and second-class G F sets, respectively. The type synthesis of PMs that have the motion of first [31,32] and second-class G F sets [33] is conducted successively.…”

“…The investigation on systematic type synthesis approaches of lower mobility PMs dates back to the last century and has experienced a gold period with great progress at the beginning of this century. Based on various mathematical tools, a variety of approaches have been presented in the literature, including the Lie group theory-based method [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], the method based on G F (generalized function) sets [30][31][32][33][34][35], linear transformation method [36][37][38][39][40][41][42][43][44][45][46], position and orientation characteristic (POC) set method [47][48][49][50][51][52], finite screw method [53][54][55][56][57][58][59], screw theory-based method …”

Type Synthesis Method for Parallel Robots With Special Topologies

“…Gogu [23][24][25] proposed a linear-transformation synthesis method based on the Jacobian matrix and comprehensively studied a class of fully isometric parallel robots. Gao and 2 VOLUME XX, 2023 colleagues [26][27][28][29] proposed a generalized function set (GF) synthesis method. Dai [30], Yang et al [31,32], and Sun et al [33][34][35] proposed a finite-screw-type synthesis method based on the screw triangle product.…”