Theory for Topology Synthesis of Parallel Manipulators and Its Application to Three-Dimension-Translation Parallel Manipulators

Abstract

A systematic theory for topology synthesis of parallel manipulators considering basic requirements such as kinematics, dynamics, control, and actuation is built. The kernel part of the theory is its proper application of a new mobility formula, output character equation of parallel manipulators, and units for single-opened-chains that have topological features. A feasible methodology for synthesizing parallel manipulators is also given, by which a detailed application is focused on the synthesis of three-dimension-translation parallel manipulators. The result synthesized encompasses not only most known mechanisms, but also some novel mechanisms with fine performances, such as simple forward/inverse kinematics and decoupling of input-output parameters that especially benefit control of theses structures.

Using characteristic strings to derive valid contracted graphs with hexagonal links plus other links for type synthesis of closed mechanisms

“…Suppose there are two different CG x and CG y. Since any TG derived from CG x must be non-isomorphism of TGs derived from CG y [9], it is significant to derive valid CGs and to identify their isomorphism for type synthesis of mechanisms. However, when an AL includes more links, the number of different CGs must increase greatly.…”

“…Vucina and Freudenstein [8] applied graph theory into type synthesis of mechanisms. Yang and Jin [4,9] studied topology structure design of robot mechanisms. Johnson [5] derived the associated linkages (ALs) for planar mechanisms by determining tree.…”

“…However, to directly derive and identify the isomorphic kinematic chain from TGs before identifying isomorphic/invalid CGs may lead to great unnecessary mental work, and may even have different solutions when identifying the same kinematic chain. In fact, many different CGs can be derived from the same AL, many different TGs can be derived from the same CG, and many different mechanisms can be derived from the same TG [1][2][3][4][5][6][7][8][9]26]. Suppose there are two different CG x and CG y.…”

A finite screw approach to type synthesis of three-DOF translational parallel mechanisms

“…This is followed by seeking all the potential equivalences of the sub-manifolds or subsets attributed to a limb, a process that was conventionally done with the aid of the intuition-based rules or the properties of subgroup products, resulting in numerous possible limb structures that may generate the specified sub-manifolds or subsets. The proposed approaches along this track include the displacement sub-manifold method [6][7][8], the position and orientation characteristic method [9], and the differential geometry method [10]. However, developing a more vigorous approach that enables the rationality of the produced limb structures to be ensured remains an open issue to be tackled, relying upon analytical formulations of finite motions of limbs and joints.…”

“…The approaches available to hand can roughly be divided into two categories, i.e. the finite motion based methods [6][7][8][9][10] and the instantaneous constraint based methods [11][12][13]. The basic idea of the first category is to find all the possible limb sub-manifolds or characteristic subsets so that their intersection leads to three-DOF finite translational motions of the moving platform.…”