Position and Orientation Characteristic Equation for Topological Design of Robot Mechanisms

Abstract

This paper presents the explicit mapping relations between topological structure and position and orientation characteristic (POC) of mechanism motion output. It deals with (1) the symbolic representation and the invariant property of the topological structure of the mechanism, (2) the matrix representation of POC of mechanism motion output, and (3) the POC equations of serial and parallel mechanisms and the corresponding symbolic operation rules. The symbolic operation involves simple mathematic tools and fewer operation rules and has clear geometrical meaning, so it is easy to use. The POC equations cannot only be used for structural analysis of the mechanism (such as determining POC of the relative motion between any two links of a mechanism and the rank of single-loop kinematic chain and calculating the full-cycle DOF of a mechanism, etc.) but can be used for structural synthesis of the mechanism as well (e.g., structural synthesis of the rank-degenerated serial mechanism, the over constrained single-loop mechanism, and the rank-degenerated parallel mechanism, etc.).

Number Synthesis of Parallel Robotic Mechanisms

“…Many researchers devoted themselves to automate and systemize this process. Several distinctive methodologies have been developed based on the screw theory Li, 2002a,b, 2003;Kong and Gosselin, 2007), the theory of differential geometry (Herve, 1978(Herve, , 1999Herve and Sparacino, 1991;Meng et al, 2007), the theory of linear transformation (Gogu, 2007(Gogu, , 2009(Gogu, , 2010, the theory of position and orientation characteristic sets (Yang, 2004;Yang et al, 2009), and the theory of G F sets (Gao et al, 2005Yang 212 MENG ET AL. et al, 2011).…”

The kinematic design of spatial, hybrid closed chains including planar parallelograms

“…Since the introduction of parallel manipulators, a planar four-bar linkage -coupled by four revolute joints -with its opposite links of the same length (usually known as parallelogram or P joint) has attracted the attention of several researchers 1 [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Thus, a suitable combination of a P joint with other kinematic pairs leads to the design of HCCs.…”

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.…”