Type Synthesis of Parallel Mechanisms Having the Second Class GF Sets and Two Dimensional Rotations

Abstract

With the introduction of generalized function sets (GF set) to represent the characteristics of the end-effectors of parallel mechanisms, two classes of GF sets are proposed. The type synthesis of parallel mechanisms having the second class GF sets and two dimensional rotations, including 2-, 3-, and 4DOF parallel mechanisms, is investigated. First, the intersection algorithms for the GF sets are established via the axiom of two dimensional rotations. Second, the kinematic limbs with specific characteristics are designed according to the axis movement theorem. Finally, several parallel mechanisms having the second class GF sets and two dimensional rotations have been illustrated to show the effectiveness of the proposed methodology.

Structural synthesis of two-layer and two-loop spatial mechanisms with coupling chains

“…Gogu [9] synthesized spatial parallel mechanisms based on linear transformation. Gao et al [10,11] proposed the concept of G f set to synthesize parallel mechanisms. Dai and Rees Jones [12] proposed the concept of metamorphic mechanisms and then structural synthesis associated with this kind of mechanisms has been investigated by many researchers [13][14][15].…”

Type synthesis of 2T2R, 1T2R and 2R parallel mechanisms

“…Accordingly, several systematic approaches on type synthesis have been proposed. They are the enumeration approach based on the general Chebyshev-Grubler-Kutzbach (CGK) mobility formula [1], configuration evolution approach [2] based on the classical mechanism makeup, the constraint synthesis approach based on the reciprocal screw theory [3][4][5], the synthesis approach based on Lie group theory [6][7][8], the synthesis approach based on single-open-chain theory [9,10], the linear transformations theory [11], and the synthesis approach based on G F set [12][13][14]. The screw theory describes instantaneous motion of mechanisms, so the mechanisms synthesized need instantaneous kinematic analysis.…”

Type Synthesis and Typical Application of 1T2R-Type Parallel Robotic Mechanisms

“…A lot of work has been contributed to this area and has promoted the development of lower mobility PKMs. Many effective theories or methods dealing with type synthesis have been proposed, such as the methods based on screw theory [18][19][20][21], displacement group theory [22][23][24][25] using Lie Group Algebra, single-opened-chains units [26,27], set [28], and theory of linear transformation and geometrical analysis [29]. All of the theories are very effective, and lots of novel mechanisms have been generated and proposed based on these theories.…”