Feasible workspace regions for general two-revolute manipulator

doi:10.1007/s11465-011-0228-9

Front Mech Eng

2011, Vol. 6

Issue (4) : 397-408 https://doi.org/10.1007/s11465-011-0228-9

RESEARCH ARTICLE

Feasible workspace regions for general two-revolute manipulator

Conghui LIANG(

), Marco CECCARELLI

Laboratory of Robotics and Mechatronics DIMSAT, University of Cassino, 03043 Cassino (FR), Italy

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Abstract

In this paper, a topology is presented for feasible workspace regions in general two-revolute manipulators. The design problem and concept of feasible workspace regions have been discussed as linked to each other. Design equations are formulated by arbitrarily prescribing four workspace boundary points. The so-called feasible workspace regions are the intersection of three different sub-regions, which are given by constraint curves as function of the relative positions of three workspace boundary points. By using a parametric study, all topologies for three sub-regions are figured out. Corresponding areas in cross section plane are determined for prescribing the position of a feasible workspace point as function of the topology for sub-regions. A classification has been proposed to determine and to characterize the combination of the topologies for those sub-regions. All topologies for feasible workspace regions are figured out and they are discussed as a design tool. Three general cases are analyzed in details to characterize workspace design capabilities for general two-revolute manipulators.

Keywords workspace two-revolute manipulators topology analysis design

Corresponding Author(s): LIANG Conghui,Email:Liang.conghui@unicas.it

Issue Date: 05 December 2011

Cite this article:

Conghui LIANG,Marco CECCARELLI. Feasible workspace regions for general two-revolute manipulator[J]. Front Mech Eng, 2011, 6(4): 397-408.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-011-0228-9
https://academic.hep.com.cn/fme/EN/Y2011/V6/I4/397

Fig.1 A scheme of a general 2R manipulator and its design parameters

Fig.2 An example of feasible workspace regions in grey areas for a general 2R manipulators with P = (4, 2), P = (2, 3.5), and P = (5, 5) in which P prescribed positions give different solutions for workspace boundary (coordinates unit are expressed in u unit)

Fig.3 A characterization for sub-regions in Fig. 2, when = (4, 2) and = (5, 5). (a) Parameter curves for = 0; (b) delimited areas for different topologies (coordinates unit are expressed in unit)

Fig.4 The three different topologies for sub-region as function of the position of workspace boundary point for the cases in Fig. 3. (a) with in area ; (b) with in area ; (c) with in area (coordinates unit are expressed in unit)

Fig.5 A characterization for sub-regions in Fig. 2, when = (4, 2) and = (5, 5). (a) Parameter curves for = 0; (b) delimited areas for different topologies (coordinates unit are expressed in unit)

Fig.6 The three different topologies for sub-region R as function of the position of workspace boundary point P for the case of Fig. 5. (a) R with P in area C; (b) R with P in area C ; (c) R with P in area C (coordinates unit are expressed in u unit)

Fig.7 A characterization for sub-regions in Fig. 2, when = (4, 2) and = (5, 5). (a) Parameter curves for = 0; (b) delimited areas for different topologies (coordinates unit are expressed in unit)

Fig.8 The two different topologies for sub-region as function of the position of workspace boundary point for the case of Fig. 7. (a) with in area ; (b) with in area (coordinates unit are expressed in unit)

Fig.9 Parameter curves of = 0, …, = 0 in - plane and corresponding delimited areas for prescribing the third workspace boundary point as referring to the example in Fig. 2 (coordinates unit are expressed in unit)

Tab.1 A classification for topologies of feasible workspace regions as function of sub-regions.

Fig.10 Examples for the three degenerated topology cases for feasible workspace regions that are computed with = (4, 2) and = (5, 5). (a) Topology with = (2.5, 5.1); (b) a zoomed view of ; (c) topology with = (3, 4.3); (d) a zoomed view of ; (e) topology with = (2, 3.5); (f) a zoomed view of FW (Coordinates unit are expressed in unit)

Fig.11 Examples for the three general topology cases for feasible workspace regions that are computed with = (4, 2) and = (5, 5). (a) Topology with = (2.5, 5.1); (b) a zoomed view of ; (c) topology with = (3, 4.3); (d) a zoomed view of ; (e) topology with = (2, 3.5); (f) a zoomed view of (Coordinates unit are expressed in unit)

Fig.12 A numerical example for the procedure prescribing workspace boundary as based on the result in Fig. 9 and Fig.11 with = (5, 1), = (4, 2), = (3, 4.3) and = (5, 5) (coordinates unit are expressed in unit)

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