Feasible workspace regions for general two-revolute manipulator

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

References

[1] Freudenstein F, Primrose E J. On the analysis and synthesis of the workspace of a three-link, turning-pair connected robot arm. ASME Journal of Mechanisms, Transmission and Automation in Design, 1984, 106(3): 365-370

[2] Fichter E F, Hunt K H. The fecund torus, its bitangent-circles and derived linkages. Mechanism and Machine Theory, 1975, 10(2-3): 167-176

[3] Hansen J A, Gupta K C, Kazerounian S M K. Generation and evaluation of the workspace of a manipulator. International Journal of Robotics Research, 1983, 2(3): 22-31

[4] Roth B. Performance evaluation of manipulators f rom a kinematic viewpoint. NBS Special Publication on Performance Evaluation of Programmable Robots and Manipulators, 1975, 495: 39-61

[5] Roth B. Analytical design of two-revolute open chains. In: Preprints of the Sixth CISM-IFTOMM Symposium on Theory and Practice of Robots and Manipulators. Cambridge: The MIT Press, 1986, 207-214

[6] Ceccarelli M. On the workspace of 3R robot arms. In: Proceedings of the Fifth International IFToMM Symposium on Theory and Practice of Mechanisms, Bucharest, 1989, 37-46

[7] Ceccarelli M. A synthesis algorithm for three-revolute manipulators by using an algebraic formulation of workspace boundary. ASME Journal of Mechanical Design, 1995, 117(2A): 298-302

[8] Ottaviano E, Husty M, Ceccarelli M. Identification of the workspace boundary of a general 3-R manipulator. ASME Journal of Mechanical Design, 2006, 128(1): 236-242

[9] Ceccarelli M, Vinciguerra A. On the workspace of general 4R manipulators. International Journal of Robotics Research, 1995, 14(2): 152-160

[10] Ceccarelli M. A formulation for the workspace boundary of general N-revolute manipulators. Mechanism and Machine Theory, 1996, 31(5): 637-646

[11] Tsai Y C, Soni A H. An algorithm for the workspace of a general n-R Robot. ASME Journal of Mechanisms, Transmissions and Automation in Design, 1983, 105(1): 52-57

[12] Lee T W, Yang D C H. On the evaluation of manipulator workspace. ASME Journal of Mechanisms, Transmissions and Automation in Design, 1987, 105(1): 70-77

[13] Alciatore D G. Ng C D. Determining manipulator workspace boundaries using the Monte-Carlo method and least square segmentation. In: Proceedings of the ASME Design Technical Conference, Minneapolis, Minnesota, 1994, 141-146

[14] Hsu M S, Kohli D. Boundary surfaces and accessibility regions for regional structures of manipulators. Mechanism and Machine Theory, 1987, 22(3): 277-289

[15] Jo D Y, Haug E J. Workspace analysis of multibody mechanical systems using continuation methods. ASME Journal of Mechanisms, Transmissions and Automation in Design, 1989, 111(4): 581-589

[16] Ceccarelli M, Lanni C. A multi-objective optimum design of general 3R manipulators for prescribed workspace limits. Mechanism and Machine Theory, 2004, 39(2): 119-132

[17] Bergamaschi P R, Nogueira A C, Saramago S F P. Design and optimization of 3R manipulators using the workspace features. Applied Mathematics and Computation, 2003, 172(1): 439-463

[18] Mavroidis C, Alam M, Lee E. Analytic geometric design of spatial R-R robot manipulators. In: Proceedings of the 2000 ASME Mechanisms and Robotics Conference, Baltimore, 2000

[19] Carbone G, Ottaviano E, Ceccarelli M. An optimization problem approach for designing both serial and parallel manipulators. In: Proceedings of the Institution of Mechanical Engineers. Part C, Journal of Mechanical Engineering Science, 2007, 7: 829-843

[20] Wenger P. Some guidelines for the kinematic design of new manipulators. Mechanism and Machine Theory, 1999, 35(3): 437-449

[21] Gupta K C, Roth B. Design considerations for manipulator workspace. ASME Journal of Mechanical Design, 1982, 104(4): 704-711

[22] Ceccarelli M. Design two-revolute manipulators for prescribed feasible workspace regions. ASME Journal of Mechanical Design, 2002, 124(3): 427-434

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