Abstract
Unifying the models for topology design and kinematic analysis has long been a desire for the research of parallel kinematic machines (PKMs). This requires that analytical description, formulation and operation for both finite and instantaneous motions are performed by the same mathematical tool. Based upon finite and instantaneous screw theory, a unified and systematic approach for topology design and kinematic analysis of PKMs is proposed in this paper. Using the derivative mapping between finite and instantaneous screws built in the authors’ previous work, the finite and instantaneous motions of PKMs are analytically described by the simple and non-redundant screws in quasi-vector and vector forms. And topological and parametric models of PKMs are algebraically formulated and related. These related topological and parametric models are ready to do type synthesis and kinematic analysis of PKMs under the unified framework of screw theory. In order to show the validity of the proposed approach, a kind of two-translational and three-rotational (2T3R) 5-axis PKMs is taken as example. Numerous new structures of the 2T3R PKMs are synthesized as the results of topology design, and their Jacobian matrix is obtained easily for parameter optimization and performance evaluation. Some of the synthesized PKMs have outstanding capabilities in terms of large workspaces and flexible orientations, and have great potential for industrial applications of machining and manufacture. Among them, METROM PKM is a typical example which has attracted a lot of attention from global companies and already been developed as commercial products. The approach is a general and unified approach that can be used in the innovative design of different kinds of PKMs.
Highlights
CNC and robot based equipment are important parts to push “Made in China 2025” plan [1, 2]
The algebraic structures of these two kinds of screws were revealed and the derivative mapping between them was built by the authors [33]. All these achievements show that finite and instantaneous screw theory has the potential to unify topology design and kinematic analysis into a general and consistent process by doing type synthesis and kinematic analysis under this concise mathematical tool, which can overcome the shortcomings of the above matrix group and dual quaternion based approaches
2 Screw Theory: Finite and Instantaneous Screws we firstly introduce the basic concepts and properties of finite and instantaneous screws, which lays the theoretical foundations of type synthesis and kinematic analysis for innovative design of parallel kinematic machines (PKMs)
Summary
CNC and robot based equipment are important parts to push “Made in China 2025” plan [1, 2]. (2018) 31:44 topological models and carried out type synthesis of PKMs through describing finite motions of PKMs by subgroups of the matrix representation of the special Euclidean group SE(3) and their composite manifolds Using this approach, many PKMs having different motions were synthesized by Li and Hervé [18, 19]. The algebraic structures of these two kinds of screws were revealed and the derivative mapping between them was built by the authors [33] All these achievements show that finite and instantaneous screw theory has the potential to unify topology design and kinematic analysis into a general and consistent process by doing type synthesis and kinematic analysis under this concise mathematical tool, which can overcome the shortcomings of the above matrix group and dual quaternion based approaches.
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