A Comprehensive Theory of Type Synthesis of Fully Parallel Platforms

Abstract

This contribution presents a comprehensive theory for the type synthesis of fully parallel platforms. The theory deals with both types of platforms, 6 D.O.F. parallel platforms and lower mobility platforms. The theory is based on an analysis of the subsets and subgroups of the Euclidean group, SE(3). It is likely that the theory can be also developed based on an analysis of the subspaces and subalgebras of the Lie algebra, se(3), of the Euclidean group, SE(3).

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

“…Much of the literature dealt with topological structure synthesis of mechanisms with displacement subgroup structure [14][15][16][17][18][19][20][22][23][24][25][26]. A few public papers discussed topological structure synthesis of mechanisms with submanifold structure [21], but a general method for topological structure synthesis of mechanisms with submanifold structure has not been established.…”

“…Over the years, there were two well-established methods for topological structure synthesis of parallel mechanisms, i.e., the screw theory based method [1][2][3][4][5][6][7][8][9][10][11][12][13] and the displacement subgroup based method [14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Parallel Manipulators with Lower Mobility

“…According to this (Rico et al 2006), the set of the LM-Ms can be separated into two subsets: (i) the subset of the pure-motion LM-Ms and (ii) the subset of the mixed-motion LM-Ms. The first subset collects all the LM-Ms whose end effector exhibits motions that belong to only one out of the ten motion subgroups of {D}, whereas the second one collects all the other LM-Ms.…”

“…In the literature, the analyses that bring to identify such topologies have been mainly addressed through three different approaches: (i) group theory (Hervé 1978(Hervé , 1995(Hervé , 1999(Hervé , 2004Hervé & Sparacino 1991;Karouia & Hervé 2000Huynh & Hervé 2005;Lee & Hervé 2006;Rico et al 2006), (ii) screw theory (Tsai 1999;Fang & Tsai 2002;Frisoli et al 2000;Kong & Gosselin 2002, 2005Huang & Li 2002Carricato 2005) and (iii) velocity-loop equations (Di Gregorio & Parenti-Castelli 1998;Di Gregorio 2001a, 2001bCarricato & Parenti-Castelli 2002. The first approach (group theory) determines the generic {L j } by composing the set of motions generated by each joint of the kinematic chain that is candidate to be a limb, and, then, searches for the geometric conditions the potential limb must satisfy in order to make a subset of an assigned motion subgroup of {D} be a subset of {L j }.…”

New Family of 3-DOF UP-Equivalent Parallel Mechanisms with High Rotational Capability

“…Theoretically, type synthesis of PMs with two rotational DOFs is more difficult and complicated than that of PMs with either one or no rotation. Hence, although considerable progress has been made in terms of the general method for type synthesis of lower-mobility PMs [14][15][16][17][18][19][20][21][22][23][24][25][26][27], and some 3T or 3T1R PMs with specified kinematic properties have been proposed [28][29][30][31][32], few architectures of UP-equivalent PMs without spherical joints and strict assembly requirement have been disclosed.…”